Economics is not science
news.ilhawaii.net
neoclassical economic theory to scientific status. Given contemporary views
on the nature of scientific theory, I examined neoclassical economic theory
in terms of both its historical and contemporary phases. I demonstrated that
the cardinal theory of utility that formed the foundation for early
neoclassical theory foundered on account of its inability to measure utility
in any acceptable scientific way. Its substitute, the ordinal theory of
utility, was shown to be equally unacceptable. The scientific pretensions of
ordinal utility theory and its correlate, revealed preference theory, were
shown compromised by the normative structure of the foundational postulate
of rationality. The unscientific nature of ordinal utility theory was
further shown to be reinforced by the insulating role played by the ceteris
paribus proviso.
"This general critique was extended not only to the neoclassical theory of
individual agent choice but also to general equilibrium theory and positive
neoclassical welfare economic theory. Given the general dissatisfaction with
neoclassical theory, a number of alternative theories have been proposed,
but the problem with the latter is that, with few exceptions, they are
founded on the premise that an objective science of economics is still
possible despite its present failings. I pointed out the shortcomings of
those theories and argued that on account of the nature of human decision
making, no analysis of it could be scientific in the way in which the
natural sciences are scientific. Mental states that must be invoked to
explain behavior are just not subject to empirical analysis. The attempts by
theorists to establish explanatory theories by appeal to heuristic concepts
such as rationality were shown to be unsuccessful. The point is that
'rationality' plays a normative role similar to that of 'goodness' in
ethical theory.
"The sociologist can indeed record the behavior of individuals in terms of
cultural norms of 'goodness,' 'badness,' 'deviancy,' and so on, but he or
she must recognize that theories of behavior founded on such concepts are
necessarily normative. Similarly, the neoclassical theorist who embraces a
particular notion of rationality and grounds his or her theories on such a
notion is certainly formulating a normative theory. My analysis showed that
the neoclassical theorist of economic behavior is confronted with the
dilemma of restricting his or her analysis to a case-by-case taxonomy of
individual agent choice, given the inaccessibility to mental states, or
grounding his or her explanatory theories on the normative heuristic of
rational choice. Neither alternative yields scientific results." [ pp.
150-151, SCIENCE, RATIONALITY, AND NEOCLASSICAL ECONOMICS, L.D. Keita;
Delaware, 1992. http://www.amazon.com/exec/obidos/ASIN/0874134102 ]
j_t...@my-deja.com
"news.ilhawaii.net" <j...@ilhawaii.net> wrote:
> "The bulk of this text was taken up with examining the claims of
> neoclassical economic theory to scientific status.
> Delaware, 1992. http://www.amazon.com/exec/obidos/ASIN/0874134102 ]
>
>
there are other areas of economics that can hardly be accepted as
science.
In an otherwise excellent book on the stock market, Lorrie and Fisher
make that the statement that the rate of interest equals the marginal
product of capital. This is hardly an exceptional statement; it can be
found in hundreds of articles and books. However, it is not true, and
can be accepted only as ideology.
For one thing, there is a problem with units. The rate of interest is a
pure number and the MP of capital is measured in units of output. To
make the two equal, we must multiply the MP of capital for the price of
output and divide by the price of capital. Some models of the firm
measure capital in terms of dollars, but this simply amounts to hiding
the problem in the production function. The interesting thing about
this formulation is that after a little algebra, the MP of capital
cancels out, and the rate of interest depends on the life of the capital
good and the rate of interest assumed in calculating the price of the
capital good.
This brings us to another problem. Since the rate of interest depends
on the price of capital goods, which assumes a rate of interest, the
whole problem becomes circular. Both Boehm-Bawerk and Schumpeter were
aware of the circularity involved in the standard productivity theory of
interest and made this the starting point for their own theories of
interest.
Another problem is that the Lorrie and Fisher statemnt ignores
depreciation. Better theorists, like Milton Friedman and Paul
Sasmuelson, have recognized that interest must be equal to MNP, the MP
minus depreciation. However, this is as far as they go. Recognizing
depreciation changes a lot of things, like the definition of
the elasticity of substitution. Taking depreciation into account the
elasticity of substitution for the Cobb-Douglas production function is
not constant and it is not 1.
That the Lorrie and Fisher statement is received doctrine can only be
understood on the assumption that economics is an ideology, not a
science.
John Tyler
Sent via Deja.com http://www.deja.com/
Before you buy.
con...@inow.com
> In article <e_l14.196$Bd5....@news.aloha.net>,
> "news.ilhawaii.net" <j...@ilhawaii.net> wrote:
> > "The bulk of this text was taken up with examining the claims of
> > neoclassical economic theory to scientific status.
> > 150-151, SCIENCE, RATIONALITY, AND NEOCLASSICAL ECONOMICS, L.D. Keita;
> > Delaware, 1992. http://www.amazon.com/exec/obidos/ASIN/0874134102 ]
> >
> >
> The text quoted concerns itself primarily with utility theory. However,
> there are other areas of economics that can hardly be accepted as
> science.
>
> In an otherwise excellent book on the stock market, Lorrie and Fisher
> make that the statement that the rate of interest equals the marginal
> product of capital. This is hardly an exceptional statement; it can be
> found in hundreds of articles and books. However, it is not true, and
> can be accepted only as ideology.
>
This is a recent recurring theme in this group; the religion, dogma,
ideology, of economics.
Aren't the hypothesis of economics testable?
John
--
John Conover, 631 Lamont Ct., Campbell, CA., 95008, USA.
VOX 408.370.2688, FAX 408.379.9602, whois '!JC154'
con...@inow.com, http://www2.inow.com/~conover/john.html
Chasna1
>For one thing, there is a problem with units. The rate of interest is a
>pure number and the MP of capital is measured in units of output.
Right off, you've made two incorrect assumptions:
1) the rate of interest is not a pure number, that is magnitude without
dimension, and
2) you've accepted Boehm-Bawerk's definition of capital as the agreed
definition by economics in general. You made a strawman argument, in other
words.
Don Libby
>
> j. tyler writes:
> > In article <e_l14.196$Bd5....@news.aloha.net>,
> > "news.ilhawaii.net" <j...@ilhawaii.net> wrote:
> > > "The bulk of this text was taken up with examining the claims of
> > > neoclassical economic theory to scientific status.
> > > 150-151, SCIENCE, RATIONALITY, AND NEOCLASSICAL ECONOMICS, L.D. Keita;
> > > Delaware, 1992. http://www.amazon.com/exec/obidos/ASIN/0874134102 ]
> > >
> > >
> > The text quoted concerns itself primarily with utility theory. However,
> > there are other areas of economics that can hardly be accepted as
> > science.
> >
> > In an otherwise excellent book on the stock market, Lorrie and Fisher
> > make that the statement that the rate of interest equals the marginal
> > product of capital. This is hardly an exceptional statement; it can be
> > found in hundreds of articles and books. However, it is not true, and
> > can be accepted only as ideology.
> >
>
> This is a recent recurring theme in this group; the religion, dogma,
> ideology, of economics.
>
> Aren't the hypothesis of economics testable?
Consider this:
"The final factor that affects the fitness of a theory is
*overdetermination*. Every theory has a certain number of adjustable
parameters, some of which define initial conditions; others, properties
of the system under consideration. ... The values of these adjustable
parameters are *determined* by an equal number of independent data...
when the number of independent data exceeds the number of adjustable
parameters, the theory is said to be overdetermined by the data. (p 19)
"An Archemedian theory has: (1) a set of mathematical axioms or laws
that implicitly or explicitly define the theory's basic notions, such as
mass and equilibrium in the theory of the Archimedian balance; (2) a set
of well-defined procedures for testing the theory's predictions; and (3)
the ability to become strongly overdetermined in some well-defined
domain.
"A theory that could become strongly overdetermined in a well-defined
domain evidently could be *falsified* in that domain. Falsifiability is
Karl Popper's well-known criterion for distinguishing scientific from
nonscientific theories. A falsifiable theory, however, need not be
capable of becoming strongly overdetermined, for it may not be able to
generate enough testable predictions. Economic theories--at least those
that are testable--belong to this category. By Popper's criterion, they
are scientific; but they are not Archemedian. (p. 57)
From David Layzer, 1984, _Constructing the Universe_, Scientific
American Library, New York, NY
-dl
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con...@inow.com
Thanks for posting that, Don.
Let me ask a question. Doesn't Layzer's interpretation imply that
economic theories are qualitative, as opposed to being quantitative?
Doesn't that interpretation of economics place bounds on its use as a
predictive science?
Thanks,
Don Libby
>
> Don Libby writes:
> > "A theory that could become strongly overdetermined in a well-defined
> > domain evidently could be *falsified* in that domain. Falsifiability is
> > Karl Popper's well-known criterion for distinguishing scientific from
> > nonscientific theories. A falsifiable theory, however, need not be
> > capable of becoming strongly overdetermined, for it may not be able to
> > generate enough testable predictions. Economic theories--at least those
> > that are testable--belong to this category. By Popper's criterion, they
> > are scientific; but they are not Archemedian. (p. 57)
> >
> > From David Layzer, 1984, _Constructing the Universe_, Scientific
> > American Library, New York, NY
> >
>
> Thanks for posting that, Don.
>
> Let me ask a question. Doesn't Layzer's interpretation imply that
> economic theories are qualitative, as opposed to being quantitative?
Economic theories are both qualitative and quantitative: guns and
butter are qualitatively distinct but both can be measured
quantitatively.
I think Layzer's interpretation implies that economic theories are
difficult to test empirically. For example, we can predict that "a
decrease in the quantity of a good (e.g. oil) supplied will cause an
increase in price, all other things being equal". The problem is how to
satisfy the "ceteris paribus" - "all other things being equal" clause
without being able to resort to the experimental method to control "all
other things".
We can test the hypothesis by observation with well-defined methods, but
we can't always be sure that "all other things" are equal, which is why
the theory may not be "strongly overdetermined". For example, we may
observe that quantity of oil supplied decreases, but price of oil goes
down instead of up -- we look for some of the "other things" that are
not equal to explain the paradoxical result and find, perhaps, that
technology has changed or less costly substitutes for oil have become
available, etc.
We then modify the hypothesis to account for these "other things that
are not equal" by adding more parameters to the model, which then
requires more observations to become "strongly overdetermined". So this
kind of non-Archemedian science becomes a contest between having just
enough parameters to describe a phenomenon accurately and having too
many parameters to enable empircal falsification if the number of
observations necessary to determine the values of system parameters is
impossibly large.
Suppose you have a theory of "the wealth of nations" with 2,000
parameters. Since there are only a few hundred nations, the theory is
under-determined: there are more "unknowns" than "knowns" in the system
of equations that comprise the theoretical model. A theory with 20
parameters, on the other hand, is at least determined and therefore
falsifiable, and is even over-determined, but is still not "strongly
overdetermined" because the state of national economies changes over
historical time periods (radically so where technological change over
the last two centuries is concerned): new observations may turn up
"other things" that are not equal, which may overturn previously
unfalsified theories.
>
> Doesn't that interpretation of economics place bounds on its use as a
> predictive science?
>
Yes. For example the testability of economic theories may be bounded by
relatively brief historical time periods. A nineteenth century
economist named Jeavons predicted the end of England's coal supply to
come near the turn of the twentieth century. Given the data,
technology, and state of economic theory in his day, his calculations
were as correct as could be. Of course, his prediction was not, since
England is still producing coal at the turn of the twenty first century.
So his theory must be modified to take account of the "other things"
that he had assumed would be "equal" over long historical time periods,
such as technical change and the availability of substitutes.
DJR80
>make the two equal, we must multiply the MP of capital for the price of
>output and divide by the price of capital.
Try looking at the marginal product of a unit of capital that produces capital.
Dan
in Philly
Chasna1
The rate of interest is not a pure number and this is not the definitive
economic definition capital.
Robert Vienneau
> Try looking at the marginal product of a unit of capital that
> produces capital.
Dan seems to be confused between the ill-defined concept of "a unit
of capital" and the equilibrium condition that the price of a
specific capital good be equal to the value of its marginal product.
Consider an economy that produces wheat and corn in yearly production
cycles. At the start of the year, a firm producing wheat buys inputs
of labor, corn, and wheat. The production process takes a year, so the
firm's output of wheat is available at the end of the year. Likewise, a
firm buying corn purchases inputs of labor, corn, and wheat at the
start of the year and has outputs of corn at the end of the year.
In neoclassical theory, commodities are distinguished by their
availability at different times. So there will be five prices to
consider for a yearly production cycle:
w, the wage, which I arbitrarily assume here is paid at the
beginning of the year.
P(1) = (p11, p21), the vector of spot prices of wheat and corn
for immediate delivery at the beginning of the year.
P(2) = (p12, p22), the vector of forward prices of wheat and
corn for delivery at the end of the year. For example, p12
is the price that must be paid at the start of the year for a
contract in which the buyer will receive a bushel of wheat
at the end of the year.
Now consider a competitive firm producing wheat. Assume the firm faces
a constant returns to scale production function
Q1 = f1( L01, X11, X21 )
where Q1 is the output of bushels wheat, L01 is inputs of labor, X11 is
inputs of wheat, and X21 is inputs of corn. Since CRS are assumed, we
can separate questions of scale and relative proportions:
Q1 = Q1 f1( a01, a11, a21 )
where a01 = L01/Q1, a11 = X11/Q1, a21 = X21/Q1.
Also assume the usual diminishing marginal returns. If the firm produces
wheat, it must solve the following problem:
Given w, P(1), P(2)
choose a01, a11, a21 to
max p12 - w a01 - p11 a11 - p21 a21
such that 1 = f1( a01, a11, a21 )
The solution will give the resulting equations (these are meant to be
partial derivatives):
w = p12 df1/da01
p11 = p12 df1/da11
p21 = p12 df1/da21
In competitive equilibrium, the price of every input will be equal to
the value of the marginal product.
Pure economic profit must be nonnegative, for if it were negative the
firm would have chosen not to produce at all. It works out that pure
economic profit cannot be positive either. So we have:
p11 a11 + p21 a21 + w a01 = p12
An analogous set of equations arise for a firm producing corn.
Now, consider the following definitions:
r1 = p12/p11 - 1
r2 = p22/p21 - 1
These are known as the own rates of interest of wheat and corn,
respectively.
In a long run equilibrium, the quantities of corn and wheat inputs are
not given. Assume they have been adjusted such that relative spot prices
of corn, wheat, and labor remain unchanged from year to year. Almost all
economists up until the late 1920s, as far as I am aware, thought of this
constancy of relative prices, or an equivalent condition, as a defining
property of long run equilibrium.
(It was about then that short-run notions of temporary and intertemporal
equilibrium were introduced, and the economists' conceptions became more
complex. Mistakes were made by the early neoclassicals. Walras thought
he could take endowments of produced goods as given, but still consider
an equilibrium with steady-state prices. Others mistakenly wanted to take
the quantity of "capital" as given, but have its form, in terms of
composition of wheat and corn, be endogeneously determined.)
Certainly, we need to introduce some condition relating industries.
Anyways, If you think about the condition of stationary spot prices, you
will see that if no pure economic profits are possible, relative forward
and relative spot prices must be equal:
p11/p21 = p12/p22
Otherwise I could buy or sell wheat or corn in the forward market for
a year and make a profit on the spot market at the end of the year.
Therefore,
p22/p21 = p12/p11
Or
r2 = r1 = r
where r is the common own rate of interest for all goods. It is not a
parameter of some unobservable utility function, although it may become
equal to some such parameter in equilibrium in special cases. Such a
special case would be created by closing this model with
utility-maximization by a infinitely-lived representative agent.
The condition of unchanging relative spot prices allows us to remove P(2)
from our equations. We have
P(1) = [ 1/(1+r) ] P(2)
The condition of no economic profit gives the following system of two
equations:
[ P A + w a0 ](1 + r) = P (*)
where I have dropped the time index on the price vector as being no longer
needed.
We can rewrite (*)
w a0 (1 + r) = P [ I - (1 + r) A ]
Or:
w (1 + r) a0 [ I - (1 + r) A]^(-1) = P
The matrix inverse exists for all r between 0 and some maximum, inclusive,
for the chosen technique if both goods are basic and the economy is
viable.
Let e be a column vector denoting the numeraire. Multiplying, one obtains:
w (1 + r) a0 [ I - (1 + r) A]^(-1) e = P e = 1
Hence, the w-r curve for the chosen technique is:
w = 1/{ a0 [ I - (1 + r) A]^(-1) e (1 + r) } (**)
This is a downward sloping curve in w-r space, and it cuts both axis.
The marginal productivity equations become:
w (1 + r) = pj dfj/da0j , j = 1, 2 (***)
pi (1 + r) = pj dfj/daij , i = 1, 2; j = 1, 2 ($)
So we have a system of 8 Equations - the 2 price equations (*), and the
6 marginal productivity equations (***) and ($). There are 10 variables
to be determined by the model:
The wage w
The common own rate of interest r
2 prices, P = ( p1 p2 )
And 6 production coefficients a0 and A.
I assume it's obvious that the above model generalizes to an n good model.
There are 2 degrees of freedom. One is closed by selecting the numeraire.
There is no equation equating r to some mystical marginal product of
capital.
Marginal productivity is not a theory of income distribution. Consider
the case of one technique a0, A. Then the marginal productivity
equations would be removed and a0, A would be data. There would be
the same degrees of freedom. That is, one can construct two models
of production, one nested inside the other. One takes coefficients
of production as given parameters, and has no equations equating
prices and marginal products. The other has coefficients of production
determined within the model and introduces marginal productivity
conditions to ensure all variables are determined, given either r
or the wage. Therefore, I consider marginal productivity
to be a theory of the choice of technique. The construction of
the w-r frontier as an outer envelope curve of w-r curves for individual
techniques is a more general method of analyzing the choice of
technique, though. The wage is equal to the marginal product of labor
at every point on the w-r frontier in those special case where it makes
sense to talk about derivatives.
Interestingly enough, Walras understood that marginal productivity
is not a theory of income distribution:
"[The theory of marginal productivity] introduces into the problem
of production a system of equations...in which the number of equations
is equal to the number of coefficients of production and in which
these coefficients are represented as unknowns...[The theory] makes
possible a definitive criticism and refutation of the English theory
of rent, by showing that the consideration of marginal productivity
is relevant to the determination of coefficients of production, but
is not relevant to the determination of the price of services."
-- Leon Walras, _Elements of Pure Economics_, Appendix III,
(Translated by William Jaffe), 1954.
Although the wage is equated to the value of the marginal product of both
wheat and corn, it is not determined by the model above. But if r is given,
the chosen technique, w, and prices P, are determined. So specifying r
will simultaneously result in the determination of the value of the
marginal product of labor in all industries and of the wage w.
Suppose that either no commodity is basic or microeconomic production
functions are not continuously differentiable. Then, the same technique
can be chosen by cost-minimizing firms at discrete intervals of r.
Thus, one cannot even map uniquely from knowledge of the chosen
technique and the set of all possible techniques to a unique distribution
of income. According to Samuelson, in his mid-70s discussion with
Joan Robinson on the unimportance of reswitching, this provides
room for class struggle in neoclassical theory.
--
Robert Vienneau
r
v
i
e m
n o Whether strength of body or of mind, or wisdom,
@ c or virtue, are always found...in proportion to
d . the power or wealth of a man [is] a question
r e fit perhaps to be discussed by slaves in the
e p hearing of their masters, but highly unbecoming
a a to reasonable and free men in search of the
m c truth.
s -- Rousseau
Robert Vienneau
that certain objections apply to a wide variety of neoclassical theories.
Here's a demonstration.
1.0 Introduction
The Cambridge Capital Controversy was a major theoretical controversy
arising out of the work of Piero Sraffa. By use of an example, this
article summarizes some negative consequences of the CCC for mainstream
theory. It concludes with some conjectures on how the CCC has
influenced contemporary directions of mainstream research.
2.0 Technical Data
I created this reswitching example, but there's plenty of other examples
in the literature. Consider a simple economy in which only one consumption
good, corn, is produced. Corn can be produced with either iron or tin.
Both iron and tin are produced goods; one process exists for producing
each.
All production processes require one year to complete. The inputs are
hired at the beginning of the year and render their services throughout
the year. Outputs become available at the end of the year. The
following "fixed coefficient" functions define the processes for
producing corn:
X1 = min[ Q2, L ] (2-1)
X1 = min[ 4 Q3, (2/3) L ] (2-2)
where
X1 is the bushels of corn produced by the process at the end of
the year
Q2 is the tons of iron purchased at the beginning of the year
Q3 is the tons of tin purchased at the beginning of the year
L is the person-years of labor hired at the beginning of the year
The process for manufacturing iron is defined by the following production
function:
X2 = min[ 6 Q2, 3 L ] (2-3)
Finally, here's the production function for tin:
X3 = min[ 4 Q3, 2 L ] (2-4)
3.0 Quantity Flows in Stationary States
The analysis is based on comparing long run positions. When
all non-labor inputs into production are themselves the output of
production processes, a long run position is characterized by
constant (spot) prices. A firm producing iron, for instance, must pay
the same price for their iron inputs at the beginning of the year as
they sell iron at at the end of the year. These prices arise when all
industries in use grow at the same rate. For concreteness, assume the
rate of growth is zero. In other words, compare stationary states. The
general conclusions of this analysis generalize to other rates of
growth, although numerical values differ.
Two stationary states, or linear combinations of these states, are
possible for any given net output of corn. Table 3-1 shows the quantity
flows per bushel corn for the iron technique.
TABLE 3-1: STATIONARY STATE WITH IRON
INPUTS Corn Process Iron Process
Labor 1 Person years 0.4 Person years
Iron 1 Ton 0.2 Tons
OUTPUTS 1 Bushel 1.2 Tons
Net output per head: (5/7) Bushels
Iron per head: (6/7) Tons
Every year, the output of the iron industry replaces the iron used up in
both industries, thereby allowing the same flows to be repeated year after
year. Both the labor and iron constraints implied by the fixed coefficient
production processes in use are met with equality. Otherwise, labor or
iron would be a free good. Table 3-2 shows the corresponding quantity flows
for the tin technique.
TABLE 3-2: STATIONARY STATE WITH TIN
INPUTS Corn Process Tin Process
Labor 1.5 Person years 0.1667 Hours
Tin 0.25 Tons 0.0833 Tons
OUTPUTS 1 Bushel 0.3333 Tons
Net output per head: 0.6 Bushels
Tin per head: 0.2 Tons
4.0 Prices in the Iron System
Let pc be the price of corn, pi the price of iron, w the wage and r the
interest rate. The interest rate is also known as the rate of profits in
some of the literature. A long run position using the iron technique
is characterized by the following system of price equations:
( pi ) (1 + r) + w = pc (4-1)
[ (1/6) pi ] (1 + r) + (1/3) w = pi (4-2)
These equations show that wages are paid at the end of the year, and that
the rate of profits is the same in both processes in use, that producing
corn and that replacing iron.
Let corn be the numeraire. Then the price equations imply a tradeoff
between the wage and the rate of profits when comparing long run positions:
w/pc = ( 5 - r )/(7 + r) (4-3)
As with all viable pure circulating capital techniques, this trade off
shows a higher wage is associated with a lower rate of profits. The
maximum wage is (5/7) bushels of corn, corresponding to a rate of
profits of 0%. The maximum rate of profits is 500%, corresponding
to a wage of zero. Figure 4-1 shows the wage-rate of profits curve for
the iron technique.
5/7 +
| x
| x
w/pc | x
| x
| x
| x
+--------------------------------+-----
500%
r
FIGURE 4-1: THE IRON WAGE-RATE OF PROFITS CURVE
One can also find the price of iron in any long run position employing
the iron technique. Equation 4-4 is needed to find the value of capital.
pi/pc = [ 1 + (w/pc) ]/6 (4-4)
5.0 Prices in the Tin System
A system of equations also exists to define long run prices for the
tin technique. Let pt be the price of tin. Then Equations 5-1 and 5-2
give the price system:
[ (1/4) pt ] (1 + r) + (3/2) w = pc (5-1)
[ (1/4) pt ] (1 + r) + (1/2) w = pt (5-2)
Equation 5-3 gives the corresponding wage-rate of profits curve for
the tin system:
w/pc = ( 3 - r )/( 5 - r ) (5-3)
As shown in Figure 5-1, the maximum wage is 3/5 bushels corn, and the
maximum rate of profits is 300%.
|
|
3/5 +
w/pc | x
| x
| x
| x
+--------------+----------
300%
r
FIGURE 5-1: THE TIN WAGE-RATE OF PROFITS CURVE
Equation 5-4 shows the price of tin as a function of the wage.
pt/pc = 1 - w (5-4)
6.0 Reswitching
A long run position is not consistent with a suboptimal choice of
technique. Accordingly, the technique chosen at a given rate of profits
is the one that maximizes the corn wage. Likewise, given the corn wage,
the selected technique maximizes the rate of profit. This rule implies that
the wage-rate of profits frontier for long run position, allowing for
the choice of technique, is the envelope curve formed out of the wage-rate
of profits curves for all available techniques (Figure 6-1).
5/7 +
| x
| + (100%, 1/2)
w/pc | x
| + (200%, 1/3)
| x
| x
+-------------------------------+-----
500%
r
FIGURE 6-1: THE WAGE-RATE OF PROFITS FRONTIER
The frontier between 100% and 200% is from the tin technique. The frontier
at the extremes outside this interval is from the iron technique. Reswitching
is the phenomenon in which a technique is chosen at at least two
different ranges of the rate of profits, with other techniques chosen at
intermediate rates of profits. Figure 6-2 shows the technique chosen
for any exogeneously given income distribution.
r 500% 200% 100% 0%
+-- Iron Technique --|-- Tin Technique --|-- Iron Technique --|
w/pc 0 1/3 1/2 5/7
FIGURE 6-2: THE CHOICE OF TECHNIQUE AT DIFFERENT FACTOR PRICES
7.0 Some Implications
This simple example has some surprisingly wideranging and disturbing
implications. These counterintuitive conclusions can arise in much
more complicated models with many techniques, many more commodities,
land-like natural resources, and fixed capital. In fact, these
complications create even more difficulties for traditional Neoclassical
theory. For example, depreciation allowances and the economic life of
machines are not determined by technical data; they must be solved
simultaneously with prices and the choice of technique. A higher
interest rate need not be associated with a choice of technique that
extends the economic life of machines. The ordering of land from
high rent to low rent land is not determined by technical data on
fertility; even with unchanged net output the order of rentability can
differ for different exogeneously given income distributions. Different
types of factors cannot be treated symmetrically in this theory, but
must be handled by models with different structures.
7.1 Marginal Productivity Theory of Distribution
An important negative implication of this analysis concerns the marginal
productivity theory of distribution - there is no such thing. This analysis
could be recast in the form of inequalities and marginal productivity
relationships. Such a recasting would yield no new results. The location
on the envelope curve forming the wage-rate of profits frontier is still
unspecified. The distribution of income must be given from outside the
marginal productivity relationships. Notice that this implication does
not rely on reswitching and holds even with a continuum of continuous
functions for available processes.
Once either the wage or the rate of profits is known, the preferred
technique, the other distributive variables, and all prices are
determined. Reswitching shows this relationship is not invertible.
Suppose the technique actually in use in a long run position and all
possible techniques are known. That technique may be compatible with
widely separate discrete intervals for the distributive variables and
different price systems. In the example, the choice of the iron
technique is compatible with both high and low wages, but not
intermediate wages. The distribution of income is not determined
by physical data about the technique employed.
This conclusion may not be surprising. The determinates of final demand
have not yet been specified in the model. A traditional response is to
add utility functions relating consumption and the disutility of labor.
Closing the model in this way, though, is questionable. Suppose the wage
or the rate of profits is given. In a pure circulating capital model,
such as the example, the level and composition of final demand has no
influence on prices. In a model with more than one consumption good, long
run prices are uninfluenced by whether consumers want more cloth and
less corn. In models with land, the level of demand for each good will
influence final prices, but may not exhibit well-behaved substitution
relationships. Likewise, different wages or rates of profits can be
associated with equilibria in which labor and capital are not
substituted in a manner consistent with traditional theory. Luckily
alternative theories of distribution exist for closing the model that do
not depend on substitution.
7.2 "Demand" for Labor
The relationship between wages and the "demand" for labor in the example
illustrates the possibility of behavior incompatible with traditional
theory. The person years of labor required per bushel of corn can be
computed for each available technique. Which technique will be preferred
at each wage has already been determined. Consequently, the person years
of labor per bushel corn can be graphed against the wage, as shown in
Figure 7-1.
|
5/7 +------+
| |
| |
1/2 + +-----+
| |
w/pc | |
| |
1/3 + +-----+
| |
+------+-----+----------
1.4 1.7
Person years per bushel
FIGURE 7-1: THE "DEMAND" FOR LABOR
For wages above 1/3 bushels, this curve looks like a discrete approximation
to the traditional demand curve. But the switch at 1/3 bushels appears
"perverse" from the standpoint of traditional theory. A lower wage is
associated with a less labor-intensive profit-maximizing technique.
7.3 "Demand" for Capital
Another traditional belief in some Neoclassical models is that the demand
and supply are equated in the market for capital. The interest rate is
thought to be the price of capital. This belief can be investigated by
this model as well. Capital is irretrievably a value quantity. So first
the equilibrium price of iron and tin must be determined. Table 7-1
was constructed based on Equations 4-4 and 5-4.
TABLE 7-1: PRICES OF CAPITAL GOODS
Interest
Rate Iron Tin
0% 2/7 Bushels
100% 1/4 1/2 Bushels
200% 2/9 2/3
500% 1/6
Once prices are given, the value of capital can be determined for
each technique. Table 7-2 shows the results, while Figure 7-2 shows the
graph of capital intensity against the interest rate.
TABLE 7-2: VALUE OF CAPITAL PER BUSHEL
Interest Iron Tin
Rate System System
0% 12/35 Bushels
100% 3/10 1/6 Bushels
200% 4/15 2/9
500% 1/5
|
500% +-----------+
| +
| +
200% + +-----+
| +
r | +
100% + +-------------------------+
| +
| +
0% +---+-------+-----+-----+-----+-----+--
0.17 0.20 0.22 0.27 0.30 0.34
Capital per unit output (Bushels)
FIGURE 7-2: THE "DEMAND" FOR "CAPITAL"
Figure 7-2 cannot be reconciled with the traditional view. With rates of
profits between 100% and 200%, the tin technique is preferred. In this region
a higher interest rate is associated with a higher value of the capital used
in producing corn. Furthermore, the switch point at 200%, once again,
is "perverse" from the viewpoint of traditional theory. A higher interest
rate is associated with a switch to a more capital-intensive technique.
Clearly the interest rate is not a "scarcity index" for "capital."
The point of the example is "capital-reversing," not reswitching. Imagine
a third technique is available, and that this technique dominates at rates
of profits below a value slightly above 100%. Then the wage-rate of
profits frontier formed from the envelope curve corresponding to the
three techniques will not exhibit reswitching. Each technique will
appear once and only once. Still, a "perverse" switch will exist at a
rate of profits of 200%.
7.4 Aggregate Production Functions
The Cambridge Capital Controversy developed other insights into capital
theory. Consider Eugen von Bohm-Bawerk's theory. He thought lower
interest rates were associated with a switch towards techniques with
a longer "period of production." The period of production was intended to
be a physical measure of capital intensity. The example shows that no
such measure is available in the general case. Techniques may not be
capable of being ordered uniquely by a capital intensity that varies
monotonically with the interest rate. Around interest rates of 100%,
the iron technique is preferred at lower interest rates. On the other
hand, the tin technique is preferred at lower interest rates around
200%. Bohm-Bawerk's theory is mistaken. At least Knut Wicksell realized
he never got it completely right.
Another approach to capital theory is associated with the concept of
aggregate production functions:
Y = F( K, L ), (7-1)
where Y is net output, K is "capital," and L is total labor. Constant
returns to scale are assumed, so the aggregate production function can
be expressed on a per capita basis:
y = Y/L = F( K/L, 1 ) = f( k ), (7-2)
Other typical assumptions are that more capital per head is associated with
more output per head:
df/dk > 0, (7-3)
and that capital exhibits diminishing marginal returns:
2 2
d f/dk < 0 (7-4)
Figure 7-3 illustrates a conventional aggregate production function.
| x
| x
Output | x
per | x
head | x
(y) | x
| x
| x
+----------------------------------
Capital per head (k)
FIGURE 7-3: A CONVENTIONAL PRODUCTION FUNCTION
Profit is assumed to be maximized, where profit is defined as in
Equation 7-5:
profit = F( K, L ) - r K - w L (7-5)
Ignoring the dependence of the value of capital on the interest rate, the
first order conditions for a maximum are that the wage equal the
marginal product of labor:
w = dF/dL, (7-6)
and that the interest rate equal the marginal product of "capital:"
r = dF/dK = df/dk (7-7)
These conditions are supposed to ensure that the factor payments exhaust
the value of the output:
y = w + r k (7-8)
The reswitching example shows that the assumptions on which this
traditional story are based are without foundation in a multicommodity
world. Table 7-3 shows the value of capital per head at selected interest
rates for the example. One can also calculate output per head at
different interest rates. The resulting production "function" is shown
in Figure 7-4.
TABLE 7-3: VALUE OF CAPITAL PER HEAD
Interest Iron Tin
Rate System System
0% 12/49 Bushels
100% 3/14 1/10 Bushels
200% 4/21 2/15
500% 1/7
| F E B A
0.7 + +------+ x------+
Output | + x
per | + x
head | x +
(y) 0.6 + x------+
| C D
|
+----+------+-----+------+-----+------+---
0.10 0.13 0.14 0.19 0.21 0.25
Capital per head (k)
FIGURE 7-4: THE EXAMPLE PRODUCTION "FUNCTION"
Point A corresponds to the long run position associated with an interest
rate of 0%. Equilibria with interest rates between 0% and 100% lie along
the segment between A and B. There is a switch point at 100%, and the
equilibrium values of output and capital per head are shown by point C.
Equilibria associated with the tin technique lie along the segment
between C and D. Finally, the iron technique is preferred again at
interest rates above 200%, as shown by the segment between E and F.
Figure 7-4 is hardly a step function approximation to a well-behaved
production function. In fact, Figure 7-4 does not show a function at all.
It is almost as if any scribble in y-k space could be a production
function. Thus, the conventional story, in which the wage is the
marginal product of labor and the interest rate is the marginal product
of capital, is invalid.
The failure of the traditional story to hold is particularly conspicuous
if reswitching and capital reversing occur. However, even assuming a
continuum of continuous functions characterizing production possibilities
and the absence of both phenomena, the traditional story does not hold.
The problem is that capital intensity depends parametrically on the
interest rate. A vicious circle arises if the interest rate is then said
to be determined by the marginal product of capital.
To see this, consider once again the wage-rate of profits frontier for
a single technique, as in Figure 7-5. The dotted line is supposed to be
a concave wage-rate of profits frontier for a single technique, the solid
line is the tangent at Point B. Let the net product be the numeraire.
|\
| \
| \
Ax \
| x \
w | \B
| \
| x\
+-------++---
r
FIGURE 7-5: A WAGE-RATE OF PROFITS FRONTIER
Equation 7-8 expresses the condition that factor payments exhaust the
net product. A simple manipulation of Equation 7-8 yields Equation 7-9:
w = - k r + y (7-9)
Suppose the interest rate is as at Point B in Figure 7-5. Then Equation
7-9 shows the capital intensity at this point is the absolute value of
the slope of a secant connecting the intercept of the frontier with the
wage axis (Point A) and Point B. On the other hand, take total
differentials of Equation 7-8:
dy = dw + r dk + k dr (7-10)
Dividing Equation 7-10 through by dy yields Equation 7-11:
1 = dw/dy + r dk/dy + k dr/dy (7-11)
Now suppose the traditional aggregate Neoclassical story was true and
the interest rate was the marginal product of capital, as expressed by
Equation 7-7. Then, Equation 7-12 must hold:
k = - (dw/dy) / (dr/dy) = - dw/dr (7-12)
But Equation 7-12 shows that the value of capital per head is the absolute
value of the slope of the tangent line at Point B.
In general, capital intensity can hardly be the additive inverse of the
slopes of both the tangent and the secant at point B. Except for
uninteresting special cases, the traditional story requires that the
wage-rate of profits frontier be a straight line for each individual
technique on the envelope curve. A smooth differentiable frontier can be
created as the envelope curve of a continuum of individual frontiers. If
all techniques had straight line frontiers, both Equations 7-9
and 7-12 would hold. Marginal products would explain income
distribution.
What is needed to ensure linear frontiers? The answer is that the
capital intensity be the same in all processes. For the simple two good
example considered here, the ratio of iron and labor inputs in producing
corn would need to be the same as the ratio in producing iron. Similarly,
the ratio of tin and labor inputs in producing corn would need to be the
same as the ratio in producing tin. If the example was so modified, the
result would be a discrete approximation to the traditional story. Those
familiar with Marx have pointed out that this assumption of equal
capital intensity also validates the labor theory of value as a theory of
relative prices. But just as the labor theory of value is insufficiently
general, so marginal productivity theory based on aggregate production
functions relies on too restrictive assumptions to have any hope of
being descriptive of capitalist reality.
Even if all wage-rate of profits frontiers were linear, the traditional
story would still be sensitive to a criticism due to Joan Robinson. The
resulting production function is constructed by comparing equilibria
constructed out of the same available technical knowledge. The economy is
not capable of moving along a production function. If the interest rate
dropped, the array of capital goods in existence would no longer be
appropriate. Iron might be wanted instead of tin. Unless one assumes
capital goods can costlessly change their form, a long disequilbrium
process would result. In no way would this process be captured by a
movement from one adjacent point to another on the production function.
7.5 Interest as A Reward for Waiting
Once Robert Solow began to realize the negative consequences of the
Cambridge criticism for his eponymous growth model, he proposed an
alternative basis for capital theory. He argued that the central concept
of capital theory should not be capital, but the rate of interest as
expressing a rate of return. Interest reflects a payment for deferring
present consumption. By deferring present consumption, one can redirect
the resources set free to produce tools that will result in a greater
stream of consumption in the future. Interest rates measure this supposed
return on investment.
Consider a stationary state in which one consumption good is produced by
a multitude of capital goods and in which a multitude of alternate
techniques are available. Let
C( 0 ) = C( 1 ) = C( 2 ) = ... (7-13)
denote the quantity of the consumption good that is available at the end
of years 0, 1, 2, ... Now consider a slight displacement from this
position. Suppose h less units of the consumption good are produced in
year zero. Instead, the resources released are used to construct capital
goods that, with maintenance, will ensure an additional perpetual
future stream of g units of the consumption good. So the new stream of
the consumption good will be:
C( 0 ) - h, C( 1 ) + g, C( 2 ) + g, C( 3 ) + g, ... (7-14)
Solow defines the rate of return as follows:
r = g / h, (7-15)
and claims that the market rate will converge to this value in long
term equilibrium. (Note that the present values of the infinite stream
of g units of the consumption good and the h units abstained from
consumption are equal at the interest rate given by Equation 7-15.) No
aggregate measure of capital seems to appear in this formulation of
interest rate theory. The interest rate appears to be purely a
technocratic notion independent of all considerations of pricing.
Luigi Pasinetti has argued that this conception founders on reswitching
just as badly as the aggregate production function/Solow growth model. The
above reswitching example can be used to illustrate Pasinetti's argument.
To determine the rate of return, consider a switch from the tin technique to
the iron technique. Each year the tin technique produces a net output
of 3/5 bushels corn per head. In the year in which the switch occurs, the
labor force is no longer hired to work up 1/5 tons of tin per head. Instead,
they combine their labor with 6/7 tons iron per head. As a consequence, the
net output in the future will be 5/7 bushels per head. A perpetual
additional stream of 4/35 bushels per head is the return from "deferring
consumption" in the year in which the switch occurs.
The return on investment can only be found after determining how much corn
is immediately given up by switching from the tin technique to the iron
technique. But this quantity can only be found by valuing iron and tin in
terms of corn. So questions of valuation are necessary to calculate the
return on investment, after all. If there were only one set of prices at
which this switch would occur, no problem would arise for the
technocratic conception of the rate of interest. The return on investment
would then be uniquely determined by the technical data. But this is not
the case.
Recall Table 7-3 expresses the value of capital per head in bushels of corn.
At a switch point of an interest rate of 100%, the iron technique
requires 4/35 bushels of corn per head more than the tin technique. Thus,
in Solow's jargon the additional perpetual net output of 4/35 bushels is
obtained by sacrificing 4/35 bushels per head in the first year.
The rate of return is then:
r = [ (5/7) - (3/5) ]/[ (3/14) - (1/10) ] = 100% (7-16)
Now consider the switch point at an interest rate of 200%. In this case,
the iron technique requires an additional 2/35 bushels of corn per head,
as compared with the tin technique. Solow's rate of return is given by
Equation 7-17:
r = [ (5/7) - (3/5) ]/[ (4/21) - (2/15) ] = 200% (7-17)
The same physical quantity flows are associated with a lower interest rate
in the neighborhood of 100%, and a higher interest rate in the neighborhood
of 200%. Both cases are associated with a switch from the tin technique to
the iron technique. But the calculation of the rate of return is vastly
different in both cases because of the need to value heterogeneous capital
goods in terms of the single consumption good. This shows the "abstention
from consumption" used in calculating the rate of return is not determined
by purely technical data. Luigi Pasinetti argues that the above definition
of the rate of return is a tautology. The rate of interest can always be
expressed as a ratio in which the denominator is called "current abstention
from consumption," and the numerator is called "a perpetual future
increase in consumption." Such an expression casts no light on what
determines the rate of interest.
8.0 Conclusion
The Cambridge Capital Controversy showed that an abundance of traditional
models implicitly relied on special and unstated assumptions. Generally,
these models are mistaken in a multicommodity world. One response of
mainstream theorists was to retreat to disaggregated theory. It is still
open to debate whether Neoclassical long-run equilibrium theories can
survive without a centralized capital market equating investment and
savings or the demand and supply of capital. It is also a subject of
discussion what, if anything, has been abandoned in such models.
Reswitching examples lead one to doubt whether prices in such models can
be interpreted as "scarcity indices."
There are also short run equilibrium models. But these models are
disequilibrium models from the standpoint of the long run. The given
quantities of produced commodities in existence at the beginning of
the period reflect mistaken past expectations about the current
situation. The disequilibrium nature of short run models raises the
issue of their adequacy for economic theory. Perhaps what is needed
are models in which the modeled agents are conscious of their
disequilibrium nature. Furthermore, how are expectations formed? What
happens if agents are aware of their strategic interdependence? How
can agents coordinate their strategies if multiple equilibria exist?
How should stability issues be handled? These questions have all
become topics of current research, and an abundance of models have
been developed to investigate them. The result seems to be a world
in which "anything can happen, and nothing need happen."
The nature of the questions posed by these developments is also unclear.
Are these questions matters of logic to be answered by mathematical
modeling? Will the answers be universal or vary with the institutional
structure of the societies to which they are applied? How do empirical
considerations enter? One thing is clear though - there exists a
reading of contemporary trends in which the work of Piero Sraffa is
central. As the leader of a school of thought, he can be said to have
redirected the whole tendency of mainstream theory.
Chris Auld
Rob wrote:
> This essay demonstrates that the existence of "price Wicksell effects"
>can lead to the inequality of the marginal product of capital and the
>interest rate. The equality being challenged here should be understood
>as it is used in macroeconomic models with aggregate production functions.
>That is, macroeconomic modeling with aggregate production functions is
>inadequately grounded in microeconomic theory. I conclude with some
>rather far-reaching possibilities.
Wait, wait, you mean to tell us there are *aggregation problems* in
macroeconomics!? Oh my god, stop the presses! Thank you, thank you,
Rob for bringing this startling new fact to the attention of the
economics profession!
> I have explained this before. Several economists have mistakenly
>asserted this argument has a simple technical flaw, although they don't
>all agree where that flaw lies. In fact, the length of my exposition
>here results from my attempting to clarify several points of confusion
>exhibited by economists responding to previous versions.
To be clear here: no one has ever denied that there are problems aggregating
capital. The issue is whether Rob's little model demonstrates that fact.
Anyone who wishes can look up my post of June 7, 1996 (Rob has been feverishly
working on this for a little while) demonstrating that the original version
of this essay showed that, under the assumptions Rob claimed, the interest
rate equaled the value of the marginal product of capital in the model Rob
posted. Shall we press on and see if, in three years, Rob has managed to
come up with a correct exposition of some elementary economics first
expounded when my grandfather was a lad?
> I claim this argument is not about index number problems or the
>aggregation of capital [3]. I also do not see how it relates to the
>aggregation of production functions. Those who believe otherwise are
Since the argument (when given correctly) only holds in economies with
more than one capital good, it is indeed about aggregation problems in
certain macroeconomic models. Since this paragraph hangs alone and Rob
everywhere else discusses the issue as an aggregation problem, perhaps
it is he should be more clear.
Rob goes on to consider an economy with the technology:
> a01 person years & a11 tons steel PRODUCE 1 ton steel
> a02 person years & a12 tons steel PRODUCE 1 bushel wheat
And explicitly says:
>capital good might be used at a different set of prices. We certainly
>haven't assumed a Leontief fixed-coefficients technology.
And derives an implication of perfect competition:
> w = [ 1 - a11 (1 + r) ] / d( r ) (19)
He then goes on:
>interest rate [6]. The factor price frontier is thus formed from
>the outer-envelope curve of the factor price curves corresponding to
>each individual technique. Points on this frontier that lie on two or
>more curves for individual techniques are known as "switch points."
>The optimal cost-minimizing technique is unique at interest rates
>for non-switching points.
And here is where the problems begin. For smooth production functions,
*every* point in price space is a "switch point." Generally, the proportion
of inputs varies continuously with ratios of input prices. So when Rob
goes on and assumes:
> Assume the observed technique is a non-switching point.
In other words, assume we are at a point on the production function with
a "kink:" a small change in factor prices will produce no substitution
effect. Also note that at such a point the production function is not
differentiable.
So when Rob goes on with:
dw/dr = - a12 a01 / [ d( r ) d( r ) ] (20)
His result obtains because only because of the special assumptions on
technology. Generally, one couldn't treat factor ratios as parametric
with respect to factor prices, as Rob does above.
So, despite the fact the some of Rob's exposition gets the ideas right, he's
yet again blown the math, since his math doesn't, in fact, apply under the
assumptions typical in neoclassical theory. Now, Rob, being Rob, goes on
to make a lovely sequence of political implications and a whole heap of
snide, sneering jabs at professional economists:
>Neoclassical theory [17]. In particular, it was shown, I think, that
>Neoclassical economists cannot consistently maintain in their equilibrium
>framework that owners of capital goods make any contribution to production.
Since one can demonstrate the same aggregation problems exist if labor is
actually heterogeneous, does that mean we can also conclude that labor makes
no contribution to the production process? (For god's sake, Rob, trying
to claim capital "makes no contribution to production" is just so silly
and so transparently a desperate attempt to maintain a certain political
ideology, it's just pathetic.)
> Finally, it is curious that economists continue to use aggregate
>production functions despite the clear warnings of this traditional
[ Yadda yadda yadda ]
Well, Rob, you're always welcome to relax that modeling assumption, produce
new models that outperform the old ones, and gain publishing success.
> What explains this apparent continuation of the miseducation of
>economists that Joan Robinson decried over forty years ago [19]? My
>hypothesis is partly ideological. Any advanced treatment of capital
>theory and the appropriate analytical tools [20] would expose the student to
>the Cambridge Capital Controversy. The student would then learn about some
>serious questioning of the internal consistency of many claims of
>neoclassical economists. There are obviously normative overtones to this
>controversy, for example, over the exploitative nature of profits and the
>capitalist system as a whole. Neoclassical economics might be claimed to
>currently fill the social role of "hired prize fighters" for capital, what
>Marx characterized as "vulgar economics" [21]. This social role is
>threatened by the CCC.
Yeah, more advice on advanced training in economics from Rob Vienneau. For
one thing, aggregation problems are a key issue in micro and macro theory
at the first year level. For another, I guess I'll just ask Rob once again
why he thinks he's qualified to comment on what should or shouldn't be taught
to graduate students. Correct me if I'm wrong, Rob, but it seems to me that
at least some of the following criteria should hold if someone wishes to
make comments about the content of graduate training in economics:
- person has some graduate training in economics
- person holds BA in economics
- person holds MA in economics
- person holds Ph.D in economics
- person has graduate training in another relevant discipline
- person has taught courses at the graduate level in economics
- person does research in economics
- person understands basic economic tools and theories
None apply to Rob Vienneau. Rob, it's a big, big world of economics out there,
and wasting time in a grad theory course discussing ancient debates over capital
theory just has an opportunity cost that exceeds whatever benefits the students
would receive. I hate to shatter your Evil Conspiracy Theory (you and Jay have
been comparing notes, haven't you?), but the reasons this stuff isn't taught to
graduate students are that mundane: it's just not that important, relative to
all the other stuff they must learn.
--
Chris Auld (403)220-4098
Economics, University of Calgary <mailto:au...@ucalgary.ca>
Calgary, Alberta, Canada <URL:http://jerry.ss.ucalgary.ca/>
Robert Vienneau
> >interest rate [6]. The factor price frontier is thus formed from
> >the outer-envelope curve of the factor price curves corresponding to
> >each individual technique. Points on this frontier that lie on two or
> >more curves for individual techniques are known as "switch points."
> >The optimal cost-minimizing technique is unique at interest rates
> >for non-switching points.
> And here is where the problems begin. For smooth production functions,
> *every* point in price space is a "switch point."
Chris is mistaken. I showed him where to look in the literature for
discussion of this exact point in the long essay to which he is
responding. The mathematics of the continuum and of limits can be
counterintuitive. He might also try some of the exercises in Kurz
and Salvadori.
> Generally, the proportion
> of inputs varies continuously with ratios of input prices. So when Rob
> goes on and assumes:
> > Assume the observed technique is a non-switching point.
> In other words, assume we are at a point on the production function with
> a "kink:" a small change in factor prices will produce no substitution
> effect. Also note that at such a point the production function is not
> differentiable.
Given Chris' above mistake, Chris is just continuing a mistaken line
of reasoning.
> So when Rob goes on with:
>
> dw/dr = - a12 a01 / [ d( r ) d( r ) ] (20)
>
> His result obtains because only because of the special assumptions on
> technology. Generally, one couldn't treat factor ratios as parametric
> with respect to factor prices, as Rob does above.
Same comment.
I'd much rather hear Chris' opinion of the new Dead boxed set.
Chris Auld
Subject: Re: Economics is not science
Summary:
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Robert Vienneau <rv...@see.sig.com> wrote:
>> And here is where the problems begin. For smooth production functions,
>> *every* point in price space is a "switch point."
>Chris is mistaken. I showed him where to look in the literature for
>discussion of this exact point in the long essay to which he is
>responding. The mathematics of the continuum and of limits can be
>counterintuitive. He might also try some of the exercises in Kurz
>and Salvadori.
<sigh>
I see Rob still hasn't figured out the basics of production theory, as
taught to second-year undergraduates. But it's just so cute when Rob
tries to condescend to others! You know, Rob, if you ever actually go to
grad school, you'll learn all sorts of advanced mathematical techniques
and how they can be applied in economic problems! And then perhaps
you would learn how foolish you look when you refer to the simple little
toy models you post as "mathematical economics" (if you want to see what
economists consider "mathematical economics," open, say, an issue of
JET).
What's interesting here is that Rob does actually get the point right in
some of his discussion, he just blows the math. More on this below.
>Given Chris' above mistake, Chris is just continuing a mistaken line
>of reasoning.
>
>> So when Rob goes on with:
>>
>> dw/dr = - a12 a01 / [ d( r ) d( r ) ] (20)
>>
>> His result obtains because only because of the special assumptions on
>> technology. Generally, one couldn't treat factor ratios as parametric
>> with respect to factor prices, as Rob does above.
>
>Same comment.
OK, Jay, oops, Rob, think *real hard*: the parameters in the expression
above give ratios of inputs. If production technologies are smooth, can
you differentiate with respect to factor prices and hold factor ratios
constant? Why do think you think that whatever source your plagiarising
this stuff from insisted that the analysis holds if and only if the initial
equilibrium is at a kink?
The intuition underlying the "lengthy post" Rob has been scribbling away
at these last four years can be adequately expressed in a couple of sentences,
but for some reason it takes Rob pages of poorly expressed text to express
his little model, which fails to provide that intuition. And since Rob
doesn't understand the issues, he draws all sorts of ludicrous conclusions
from his sophomore exercise. How one manages to draw political conclusions
from an aggregation difficulty in economic theory is something beyond me,
best left for amateur ideologues such as our pal Rob.
>I'd much rather hear Chris' opinion of the new Dead boxed set.
Skip the studio crap, stip to bootlegs.
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >> And here is where the problems begin. For smooth production functions,
> >> *every* point in price space is a "switch point."
> >Chris is mistaken. I showed him where to look in the literature for
> >discussion of this exact point in the long essay to which he is
> >responding. The mathematics of the continuum and of limits can be
> >counterintuitive. He might also try some of the exercises in Kurz
> >and Salvadori.
[ stupidities deleted]
> >Given Chris' above mistake, Chris is just continuing a mistaken line
> >of reasoning.
> >> So when Rob goes on with:
> >>
> >> dw/dr = - a12 a01 / [ d( r ) d( r ) ] (20)
> >>
> >> His result obtains because only because of the special assumptions on
> >> technology. Generally, one couldn't treat factor ratios as parametric
> >> with respect to factor prices, as Rob does above.
> >Same comment.
[more stupidities]
> Rob, think *real hard*: the parameters in the expression
> above give ratios of inputs. If production technologies are smooth, can
> you differentiate with respect to factor prices and hold factor ratios
> constant? Why do think you think that whatever source your plagiarising
> this stuff from insisted that the analysis holds if and only if the initial
> equilibrium is at a kink?
Since Chris has seen me write this essay here over time, his incorrect
accusation of plagiarism seems to reveal some sort of mental problem.
Consider a given interest rate and wage compatible with a long run
equilibrium. Consider the case of smooth production functions. Chris is
claiming that at least two combinations of values of inputs are
cost-minimizing at this interest rate for a given output. That is, that
cost-minimization does not yield an unique answer for coefficients of
production for a given interest rate in the continuous case. Needless
to say, Chris remains mistaken.
The next question is whether the so-called factor-price curve is tangent
to the outer envelope curve - the so-called factor-price frontier - at
a non-switching point. The answer is obviously "yes" for the linear
programming case that Chris, for some reason, seems to think is excluded
from neoclassical economics. The case of "smooth" production functions
is found by taking the limit of the linear programming case.
Non-zero price Wicksell effects clearly provide the indicated problem
for defining a "quantity of capital," independent of the interest rate,
in either case.
[ more stupidities deleted. ]
If mistakes are constant and systematic, one begins to suspect there
might be a reason.
Chris Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>> Rob, think *real hard*: the parameters in the expression
>> above give ratios of inputs. If production technologies are smooth, can
>> you differentiate with respect to factor prices and hold factor ratios
>> constant? Why do think you think that whatever source your plagiarising
>> this stuff from insisted that the analysis holds if and only if the initial
>> equilibrium is at a kink?
>
>Since Chris has seen me write this essay here over time, his incorrect
>accusation of plagiarism seems to reveal some sort of mental problem.
Well, I'm sorry Rob. Could you please clearly identify your original
contributions to the literature?
>Consider a given interest rate and wage compatible with a long run
>equilibrium. Consider the case of smooth production functions. Chris is
>claiming that at least two combinations of values of inputs are
>cost-minimizing at this interest rate for a given output. That is, that
No, I'm not. I'm asserting Rob cannot differentiate with respect to
factor prices and hold factor ratios constant if production functions
are smooth. Rob, curiously, has not addressed this point in his
response (is anyone reminded of the months and months of stonewalling
Rob undertook to avoid admitting that he's never actually proved that
a labor demand curve can slope up?)
>a non-switching point. The answer is obviously "yes" for the linear
>programming case that Chris, for some reason, seems to think is excluded
>from neoclassical economics. The case of "smooth" production functions
>is found by taking the limit of the linear programming case.
Rob explicitly, repeatedly claimed that his analysis holds for smooth
production functions -- recall his point was to provide analysis under
the usual neoclassical assumptions. It is true that sometimes neoclassical
models assume away substitution affects for convenience, but that is the
rare case, and done in order to deliberately avoid substitution effects
obscuring some other phenomenon of interest. Rob is also wrong
in asserting that one can generally take solutions to linear programming
models and claim that those solutions become the solutions to nonlinear
problems in the limit: the mathematics of the continuum are indeed
strange, and sometimes any finite solution is fundamentally different --
even in the limit -- than a solution under continuity (game theory is
full of curious results arising from this fact). Rob's equation is
correct for any locally non-differentiable technology (no matter how many
"techniques" exist -- even a _countable_ infinity of them) but it is not
correct once differentiability obtains, because then he cannot treat factor
ratios as parametric.
>Non-zero price Wicksell effects clearly provide the indicated problem
>for defining a "quantity of capital," independent of the interest rate,
>in either case.
I agree. An aggregation problem (the same problem exists with respect
to heterogenous labor). I'm simply pointing out yet another technical
error in Rob's exposition. How many more years before you get it right,
Rob? By the way, since you don't believe this is an aggregation problem
(or, more accurately, you sometimes claim it is, and sometimes claim
it isn't), here's a challenge: develop a model with one capital good,
the usual assumptions, and show that the value of the marginal product
of capital differs from it's rental price in equilibrium.
>If mistakes are constant and systematic, one begins to suspect there
>might be a reason.
Quite.
con...@inow.com
> domain evidently could be *falsified* in that domain. Falsifiability is
> Karl Popper's well-known criterion for distinguishing scientific from
> nonscientific theories. A falsifiable theory, however, need not be
> capable of becoming strongly overdetermined, for it may not be able to
> generate enough testable predictions. Economic theories--at least those
> that are testable--belong to this category. By Popper's criterion, they
> are scientific; but they are not Archemedian. (p. 57)
>
Then, depending on how economic theory is applied, it could lead to an
incorrect solution to a problem, as opposed to an indeterminate
solution, right Don?
What I am really asking is: is the objective of economic theory to
minimize contradictions, or maximize completeness?
Robert Vienneau
> Robert Vienneau <rv...@see.sig.com> wrote:
> >> Rob, think *real hard*: the parameters in the expression
> >> above give ratios of inputs. If production technologies are smooth, can
> >> you differentiate with respect to factor prices and hold factor ratios
> >> constant? Why do think you think that whatever source your plagiarising
> >> this stuff from insisted that the analysis holds if and only if the initial
> >> equilibrium is at a kink?
> >Since Chris has seen me write this essay here over time, his incorrect
> >accusation of plagiarism seems to reveal some sort of mental problem.
> Well, I'm sorry Rob. Could you please clearly identify your original
> contributions to the literature?
The long essay that Chris is responding to is my original expression
of some well-known ideas. References are provided in the essay.
> >Consider a given interest rate and wage compatible with a long run
> >equilibrium. Consider the case of smooth production functions. Chris is
> >claiming that at least two combinations of values of inputs are
> >cost-minimizing at this interest rate for a given output. That is, that
> No, I'm not.
That's a curious way for Chris to admit he was wrong when he wrote:
"For smooth production functions, *every* point...is a 'switch point.'"
-- Chris Auld
And the above quote was in response to a post in which I defined a
"switch point:"
"Points on this frontier that lie on two or more curves for
individual techniques are known as 'switch points.' The optimal
cost-minimizing technique is unique at interest rates for
non-switching points."
-- Robert Vienneau
For smooth production functions, every point on the so-called factor
price frontier is a non-switching point.
> I'm asserting Rob cannot differentiate with respect to
> factor prices and hold factor ratios constant if production functions
> are smooth.
I can and do differentiate the factor price *curve* for a given
technique, where the technique is defined by coefficients of
production, i.e. a point on a unit isoquant. It matters not if the
production functions are smooth or linear combinations of fixed
coefficient processes.
The derivative of this curve is certainly relevant to my point
about price Wicksell effects.
> Rob, curiously, has not addressed this point in his
> response...
Chris' continual strawmen cannot force me to repeat nonsense.
> >a non-switching point. The answer is obviously "yes" for the linear
> >programming case that Chris, for some reason, seems to think is excluded
> >from neoclassical economics. The case of "smooth" production functions
> >is found by taking the limit of the linear programming case.
> Rob explicitly, repeatedly claimed that his analysis holds for smooth
> production functions.
I certainly claim the use of factor price frontiers to analyze the
choice of technique applies to smooth production functions. Can Chris
find a claim that he disagrees with, other than strawmen?
> recall his point was to provide analysis under
> the usual neoclassical assumptions. It is true that sometimes neoclassical
> models assume away substitution affects for convenience, but that is the
> rare case, and done in order to deliberately avoid substitution effects
> obscuring some other phenomenon of interest.
It seems to be true that Chris is unable or unwilling to acknowledge
the differences in logic and structure between long run models and
models of intertemporal and temporary equilibrium. This talk of
substitution doesn't make much sense in long run models.
Note that Chris acknowledges that the case of linear combinations of
fixed coefficient processes should be covered by neoclassical theory.
So he admits I provide an analysis under usual neoclassical
assumptions.
Linear programming is not rare.
> Rob is also wrong
> in asserting that one can generally take solutions to linear programming
> models and claim that those solutions become the solutions to nonlinear
> problems in the limit: the mathematics of the continuum are indeed
> strange,
Of course, I did not make that claim. I did, of course, claim that
the mathematics of the continuum and of limits can be counterintuitive.
> and sometimes any finite solution is fundamentally different --
> even in the limit -- than a solution under continuity (game theory is
> full of curious results arising from this fact).
Von Neumann and Morgenstern assume, in their interesting analysis
of bluffing, that the ranks of poker hands comprise a continuum.
> Rob's equation is
> correct for any locally non-differentiable technology (no matter how many
> "techniques" exist -- even a _countable_ infinity of them) but it is not
> correct once differentiability obtains, because then he cannot treat factor
> ratios as parametric.
The case of linear combinations of fixed coefficient processes is useful
for understanding price Wicksell effects. With the above, Chris has
pretty much acknowledged my essay does not contain a technical flaw. At
best, he can quarrel with the wording in certain places.
The construction of factor price frontiers can be used to analyze the
choice of technique in long run models, whether production functions
are smooth or not.
In this thread, I am concerned with price Wicksell effects, not a
combination of price and real Wicksell effects.
> >Non-zero price Wicksell effects clearly provide the indicated problem
> >for defining a "quantity of capital," independent of the interest rate,
> >in either case.
> I agree.
Here Chris explicitly admits my point holds for smooth production
functions.
Let's review:
Consider the tangent to the so-called factor price frontier at a
non-switching point. Consider a secant connecting this point and
the intersection with the wage axis of the so-called factor price
curve for the technique chosen at this non-switching point. This
tangent and secant are not necessarily identical due to price
Wicksell effects.
The additive inverse of the slope of the tangent must be equal to
the value of capital per worker if the interest rate is to be equal
to the marginal product of capital, as that equality is understood
in models with aggregate production functions. But the additive
inverse of of the slope of the secant is the value of capital per
worker.
Thus, the value of capital cannot generally be defined independently
of the interest rate, and the interest rate is generaly not equal to
the marginal product of capital.
The above correct argument applies to "smooth" production functions,
sometimes referred to as the "continuous substitution" case. Once
again, in this case, all points on the frontier are non-switching
points.
> An aggregation problem (the same problem exists with respect
> to heterogenous labor).
It doesn't:
"This enforces the point that it is not heterogenity as such that
makes capital difficult and labor easy to measure; it is rather
that labor is only hired and hence that the value of its stock
never figures in theories involving one- or two-sector models."
-- Mark Blaug, _Economic Theory in Retrospect_, 4th Edition, p. 526.
(See, Chris, that's how somebody living up to academic standards avoids
charges of plagiarism - when they quote Mark Blaug, they say so.)
> I'm simply pointing out yet another technical
> error in Rob's exposition. How many more years before you get it right,
> Rob?
But Chris' charge itself was an example of a technical error. How many
years before you get it right, Chris?
> By the way, since you don't believe this is an aggregation problem
> (or, more accurately, you sometimes claim it is, and sometimes claim
> it isn't),
Anybody not ignorant of the literature relevant to this discussion has
seen the claim that the question is the meaning of capital, not how to
measure it. They may have even seen this claim in some of my quotes
somewhere or another.
> here's a challenge: develop a model with one capital good,
> the usual assumptions, and show that the value of the marginal product
> of capital differs from it's rental price in equilibrium.
Chris deliberately obfuscates the distinction between capital and a
capital good; between the marginal product of capital, as that
expression is understood in models with aggregate production functions,
and the value of the marginal product of a capital good; between the
interest rate and the rental price of a capital good. There's only two
choices here: either Chris is extremely confused or he is unwilling to
admit the marginal productivity theory of distribution is all bosh.
(On the other hand, the unidentified quote in the previous sentence is
an allusion to the literature.)
Chris seems to have acknowledged the following above:
(1) The construction of the so-called factor price frontier can
be used to analyze the choice of technique in long run models
with smooth production functions.
(2) Production functions constructed from linear combinations of
fixed coefficient processes are compatible with neoclassical
economics.
(3) The derivative of the factor price curve for a non-switching
point on the frontier is also the derivative of the frontier
for that point, for the latter case.
(4) The nonequality of this derivative with the slope of the
relevant secant points out that price Wicksell effects cause
difficulties for capital theory.
(5) These difficulties also arise for the case of smooth production
functions.
The only issue left seems to be a matter of personalities or a question
of what he thinks of my writing style. I'm not concerned with his
opinion of either.
Don Libby
> > that implicitly or explicitly define the theory's basic notions, such as
> > mass and equilibrium in the theory of the Archimedian balance; (2) a set
> > of well-defined procedures for testing the theory's predictions; and (3)
> > the ability to become strongly overdetermined in some well-defined
> > domain.
> What I am really asking is: is the objective of economic theory to
> minimize contradictions, or maximize completeness?
The internal consistency (freedom from self-contradiction) should be
taken care of by the first criterion (1) above. The external
consistency (freedom from contradiction by empiric data) is taken care
of in the second criterion (2) above. The completeness should be taken
care of by the third criterion -- the generalizability of the theory
beyond a number of observations limited in historic or geographic scope
would require strong overdetermination. Since this is exceedingly
difficult, I would say that econometricians are usually content to
settle for internal and external validity with limited
generalizability. Theoreticians may strive for a more complete view, at
the risk of undertermination and untestabiltiy.
> >
> > "A theory that could become strongly overdetermined in a well-defined
> > domain evidently could be *falsified* in that domain. Falsifiability is
> > Karl Popper's well-known criterion for distinguishing scientific from
> > nonscientific theories. A falsifiable theory, however, need not be
> > capable of becoming strongly overdetermined, for it may not be able to
> > generate enough testable predictions. Economic theories--at least those
> > that are testable--belong to this category. By Popper's criterion, they
> > are scientific; but they are not Archemedian. (p. 57)
> >
>
> Then, depending on how economic theory is applied, it could lead to an
> incorrect solution to a problem, as opposed to an indeterminate
> solution, right Don?
>
If there are sufficient data to test a theory, then the solution is at
least determinate, or even overdetermined, if not strongly
overdetermined. Assuming a model passes the internal and external
validity tests, then I suppose the theory could still be "incorrect" if
the data are fit equally well by a competing theory. It would then
require a critical experiment, or observations over a broader range in
the parameter space of the models to determine if one or the other more
generally fits the additional observations. Whichever is least
contradicted by the most data wins the "best explanation science
currently has to offer" contest.
con...@inow.com
> con...@inow.com wrote:
> >
> > Don Libby writes:
> > >
> > > "An Archemedian theory has: (1) a set of mathematical axioms or laws
> > > that implicitly or explicitly define the theory's basic notions, such as
> > > mass and equilibrium in the theory of the Archimedian balance; (2) a set
> > > of well-defined procedures for testing the theory's predictions; and (3)
> > > the ability to become strongly overdetermined in some well-defined
> > > domain.
>
> > What I am really asking is: is the objective of economic theory to
> > minimize contradictions, or maximize completeness?
>
> The internal consistency (freedom from self-contradiction) should be
> taken care of by the first criterion (1) above. The external
> consistency (freedom from contradiction by empiric data) is taken care
> of in the second criterion (2) above. The completeness should be taken
> care of by the third criterion -- the generalizability of the theory
> beyond a number of observations limited in historic or geographic scope
> would require strong overdetermination. Since this is exceedingly
> difficult, I would say that econometricians are usually content to
> settle for internal and external validity with limited
> generalizability. Theoreticians may strive for a more complete view, at
> the risk of undertermination and untestabiltiy.
>
Thanks, Don. That just seems like a pretty assertive statement to
me. Perhaps I don't understand, but how does economics keep from
stepping on Godel's toes-I mean it is probably safe to say that
economics is as complex as the arithmetic, yet somehow has transcended
the contradiction and/or completeness issues of formal systems.
If I am not mistaken, Morgenstern raised the same issue, which has
been addressed more recently by Gregory Chaitin,
"Information-Theoretic Incompleteness", World Scientific, London,
England, 1992, ISBN 981-02-1208-9, pp. 129-189, which shows that of
all possible conjectures about a system, the vast majority are not
provably true, or false, and their validity will, forever, remain
uncertain.
A lot of the other sciences are struggling with the implications
presented by Chaitin, and seem to be adopting a strategy of using
abstract mathematical models, and demanding consistency, at the
expense of completeness-since both are not attainable.
As I read your paragraph above, it seems to me that you are saying
economics has transcended these issues-am I wrong?
John
BTW, FYI, Chaitin's method is straight forward in concept-just place
no bounds on how overdetermined things are-assume infinitely so. Then
number all possible conjectures with the real number system, the more
complex the conjecture, the more complex the real number that it maps
to. Those conjectures represented by the irrationals are forever
undecided, those represented by the rationals are, in principle,
provable. In some sense, it is kind of a Godelian method, with the
Peano integers, (or Turing's with the Cantor diagonal,) replaced. Note
that it does not claim that science is wrong-it only places bounds on
what it can do, (at least that is one interpretation of the
story-depending on who is telling it, of course.)
j_t...@my-deja.com
cha...@aol.com (Chasna1) wrote:
> >>For one thing, there is a problem with units. The rate of interest
is a
> >>pure number and the MP of capital is measured in units of output.
To
> >>make the two equal, we must multiply the MP of capital for the price
of
> >>output and divide by the price of capital.
> >
produces
> >capital.
> >
> >Dan
>
> The rate of interest is not a pure number and this is not the
definitive
> economic definition capital.
>
Here are several comments on the discussion so far. First of all, the
problem posed has nothing to do with aggregation or the Cambridge
capital controversy. I mentioned two ways of measuring capital, in
dollars or in physical units. If we measure capital in physical units,
then the VMP of capital must be divided by the price of capital goods,
and recognizing that the price of capital goods equals the present value
of future VMPs, then the MP cancels out and the rate of interest is
determined by the life of capital goods and the rate of interest assumed
in finding the present value of the VMPs. This makes the
determinatiion of interest circular.
If capital is measured in dollars, then the problem is simply buried in
the production function.
Chasna keeps insisting that the rate of interest is not a pure number.
If it is not a pure number, what are its units? And I haven't said
anything about the definition of capital, so my comments can hardly be
blamed on Boehm-Bawerk.
There is one point that no one has commented on, that in the real world
capital depreciates. When we introduce depreciation into the model, we
radically change the nature of the problem. This is one point where I
agree with Boehm-Bawerk, but it has nothing to do with the definition of
capital.
By the way, I have been to graduate school in economics and I can play
games with fancy models and higher mathematics. I am old enough to know
better.
Don Libby
>
> Don Libby writes:
> > con...@inow.com wrote:
> > >
> > > Don Libby writes:
> > > >
> > > > "An Archemedian theory has: (1) a set of mathematical axioms or laws
> > > > that implicitly or explicitly define the theory's basic notions, such as
> > > > mass and equilibrium in the theory of the Archimedian balance; (2) a set
> > > > of well-defined procedures for testing the theory's predictions; and (3)
> > > > the ability to become strongly overdetermined in some well-defined
> > > > domain.
> >
> > > What I am really asking is: is the objective of economic theory to
> > > minimize contradictions, or maximize completeness?
> >
> > The internal consistency (freedom from self-contradiction) should be
> > taken care of by the first criterion (1) above. The external
> > consistency (freedom from contradiction by empiric data) is taken care
> > of in the second criterion (2) above. The completeness should be taken
> > care of by the third criterion -- the generalizability of the theory
> > beyond a number of observations limited in historic or geographic scope
> > would require strong overdetermination. Since this is exceedingly
> > difficult, I would say that econometricians are usually content to
> > settle for internal and external validity with limited
> > generalizability. Theoreticians may strive for a more complete view, at
> > the risk of undertermination and untestabiltiy.
> >
>
> A lot of the other sciences are struggling with the implications
> presented by Chaitin, and seem to be adopting a strategy of using
> abstract mathematical models, and demanding consistency, at the
> expense of completeness-since both are not attainable.
>
> As I read your paragraph above, it seems to me that you are saying
> economics has transcended these issues-am I wrong?
No, economics has not transcended the issue. Some economists opt for
practical solutions to practical problems -- econometricians settle for
consistency at the expense of completeness. Other economists opt for
grand theoretical solutions to theoretical problems -- theoreticians may
settle for completeness at the expense of consistency.
For example, Marx's theory of the rise of capitalism has as data a
single observation -- the historic rise of capitalism -- although it has
more than one parameter: modes of production, relations of production,
immiseration of the working class, etc. It is therefore underdetermined
and untestable (except by proving the pudding in the eating of it),
though it claims to provide a comprehensive explanation for poverty and
strife. Max Weber's theory of the rise of capitalism, on the other
hand, takes a comparative approach, comparing the technological and
organizational development of several cultures, including the advanced
cultures of Asia, and by virtue of having more observations arrives at a
determinate answer to a somewhat more limited question: why do some
advanced cultures give rise to capitalism and others not?
What I am saying is, whether economics maximizes completeness or
consistency depends on the economist: personally I tend to favor the
consistency camp, at the risk of being labelled a reductionist, or even
a "chrematist" by the unhappy campers in the comprehensiveness camp.
Chris Auld
Robert Vienneau <rv...@see.sig.com> wrote:
>au...@jerry.ss.ucalgary.ca (Chris Auld) wrote:
>> Well, I'm sorry Rob. Could you please clearly identify your original
>> contributions to the literature?
>
>The long essay that Chris is responding to is my original expression
>of some well-known ideas. References are provided in the essay.
I see. So, in other words, there is no original contribution. Unless, of
course, we count the wonderful addition of mathematical errors to sixty
year old models as a "contribution."
>> >Consider a given interest rate and wage compatible with a long run
>> >equilibrium. Consider the case of smooth production functions. Chris is
>> >claiming that at least two combinations of values of inputs are
>> >cost-minimizing at this interest rate for a given output. That is, that
>
>> No, I'm not.
>
>That's a curious way for Chris to admit he was wrong when he wrote:
>
> "For smooth production functions, *every* point...is a 'switch point.'"
> -- Chris Auld
>
>And the above quote was in response to a post in which I defined a
>"switch point:"
>
> "Points on this frontier that lie on two or more curves for
> individual techniques are known as 'switch points.' The optimal
> cost-minimizing technique is unique at interest rates for
> non-switching points."
> -- Robert Vienneau
That's not a definition of a "switch point," it's a property of "switch
points" when production technologies are piecewise linear. A "switch point"
is a point on the production function such that an infinitessimal change
in the factor price ratio produces a "switch" in technique. If the function
is smooth, every such point is such a technique. If Rob wants to define
"switch points" such that they are only applicable to non-differentiable
functions, the concept is undefined for smooth technologies. Of course,
as he is wont to do, Rob is trying to divert attention from his technical
errors by getting all caught up in semantics.
>> I'm asserting Rob cannot differentiate with respect to
>> factor prices and hold factor ratios constant if production functions
>> are smooth.
>
>I can and do differentiate the factor price *curve* for a given
>technique, where the technique is defined by coefficients of
>production, i.e. a point on a unit isoquant. It matters not if the
>production functions are smooth or linear combinations of fixed
>coefficient processes.
Rob just doesn't understand the point. Rob, you can't treat the
"technique" as parametric and assert that your result is applicable
to smooth technologies. *You* even assert in your essay that you're
considering an initial equilibrium at a kink. Why do *you* say that
if it's an assumption you don't need?
>I certainly claim the use of factor price frontiers to analyze the
>choice of technique applies to smooth production functions. Can Chris
>find a claim that he disagrees with, other than strawmen?
Talk about strawmen. Did I claim otherwise? For the fifth time: I
want you to acknowledge *your* explicitly stated (albeit contradictory,
and obviously not understood) assumption that your result obtains only
at a non-differentiable point on the production function (which, of course,
means the analysis is pointless in the first place, since the marginal
product of capital is not even defined at such a point). I have no doubt
one could redo the analysis correctly. And, yet again, I'm not denying
the general result is true (eek, *aggregation problems* in macroeconomics).
I certainly do deny the laughable implications about politics and graduate
training in economics Rob manages to draw.
>It seems to be true that Chris is unable or unwilling to acknowledge
>the differences in logic and structure between long run models and
>models of intertemporal and temporary equilibrium. This talk of
>substitution doesn't make much sense in long run models.
Rob, *your model* has substitution, even with the piecewise linear
technology. It's just that we need "large enough" changes in factor
prices to get substitution, whereas with smooth technologies an
arbitrarily small change in factor price ratios produces a substitution
effect. The above is totally irrelevant, even if it were true.
>Note that Chris acknowledges that the case of linear combinations of
>fixed coefficient processes should be covered by neoclassical theory.
>So he admits I provide an analysis under usual neoclassical
>assumptions.
Actually, I explicitly stated that piecewise linear functions are not
"the usual neoclassical assumptions." Perhaps I should have quoted Rob
saying the same thing in his little essay. (It's funny how Rob is so
desperate to try to contradict everything I say that he winds up
contradicting himseld. Let's try an experiment: "hey Rob, the sky
is blue.")
>> and sometimes any finite solution is fundamentally different --
>> even in the limit -- than a solution under continuity (game theory is
>> full of curious results arising from this fact).
>
>Von Neumann and Morgenstern assume, in their interesting analysis
>of bluffing, that the ranks of poker hands comprise a continuum.
How interesting! I remember when Rob admitted he knew nothing about game
theory, then shortly thereafter announced he was reading VnM's 50 year
old book, then proceeded to lecture us for months on VnM, including some
of VnM's assertions that have been known to be incorrect since before I
was born. Hey Rob, have you read any game theory that was written since
WW2 yet? (I don't mean to dissaude Rob from doing so: perhaps a discussion
of what's wrong with game theory would be interesting, and Rob and I
might be able to agree on something for once).
>The case of linear combinations of fixed coefficient processes is useful
>for understanding price Wicksell effects. With the above, Chris has
>pretty much acknowledged my essay does not contain a technical flaw. At
>best, he can quarrel with the wording in certain places.
Huh? Rob, your equation for dw/dr is wrong for continuous technologies.
Yes or no?
>> >Non-zero price Wicksell effects clearly provide the indicated problem
>> >for defining a "quantity of capital," independent of the interest rate,
>> >in either case.
>
>> I agree.
>
>Here Chris explicitly admits my point holds for smooth production
>functions.
No kidding. I've done so several times.
>It doesn't:
>
> "This enforces the point that it is not heterogenity as such that
> makes capital difficult and labor easy to measure; it is rather
> that labor is only hired and hence that the value of its stock
> never figures in theories involving one- or two-sector models."
> -- Mark Blaug, _Economic Theory in Retrospect_, 4th Edition, p. 526.
>
>(See, Chris, that's how somebody living up to academic standards avoids
>charges of plagiarism - when they quote Mark Blaug, they say so.)
More lectures on adademia from Rob Vienneau. Contrary to what you
might have inferred as an undergraduate, Rob, plagiarism occurs if
one swipes ideas from other authors unacknowledged, not just if one
quotes verbatim unacknowledged. (Oh, and by the way Rob: this forum
is entertainment, not a serious academic venue. Read my research if
you want rigorous academic standards, and lighten up here -- you're
posts might become more readable if you acknowledged this.)
Now, let's see what else Blaug has to say:
The famous or rather infamous theorem that the rate of interest
is in equilibrium equated to the marginal product of capital only
applies to one-sector models [my point that this is an aggregation
problem -CA] [...] In that world, the rate of wages is also equated
to the marginal product of labor, which for some strange reason, is
a proposition that wins assent even if the equivalent proposition
about capital is denied [my point exactly! -CA] [...] There is no
such thing as _the_ marginal product of the total stock of capital
in the economy, just as there is no such thing as the marginal
product of the labor force. -- Blaug 4th ed, p468.
That is, the "marginal product of labor" is at best ill-defined when
labor is heterogeneous, and as such will not generally be equal to the
wage rate. Exactly the point Rob is tediously making with respect to
capital. In the case of capital, other problems arise as well, which
is what Blaug is referring to in Rob's quote. But since Rob's stated
purpose here is to show that the interest rate isn't equal to the
marginal product of capital, he is very much mistaken in asserting the
same problem doesn't occur with respect to heterogeneous labor.
Of course, Blaug is the right sort of reference for this discussion:
history of thought. This is a debate which was old and uninteresting
when I was born. Rob, why don't you acquaint yourself with some
current issues in capital theory?
>> I'm simply pointing out yet another technical
>> error in Rob's exposition. How many more years before you get it right,
>> Rob?
>
>But Chris' charge itself was an example of a technical error. How many
>years before you get it right, Chris?
For the fourth time: can you or can you not differentiate with respect
to factor prices and hold input ratios fixed in the presence of
continuously differentiable production functions, Rob?
>> here's a challenge: develop a model with one capital good,
>> the usual assumptions, and show that the value of the marginal product
>> of capital differs from it's rental price in equilibrium.
>
>Chris deliberately obfuscates the distinction between capital and a
>capital good; between the marginal product of capital, as that
>expression is understood in models with aggregate production functions,
>and the value of the marginal product of a capital good; between the
>interest rate and the rental price of a capital good. There's only two
>choices here: either Chris is extremely confused or he is unwilling to
>admit the marginal productivity theory of distribution is all bosh.
I do? Wow! Will you be writing to Mark Blaug to tell him he's
similarly confused, Rob? (Why do you feel this need to hopelessly
embarrass yourself so very often, Rob? Why not just omit the overblown
rhetoric and sweeping insults?)
>The only issue left seems to be a matter of personalities or a question
>of what he thinks of my writing style. I'm not concerned with his
>opinion of either.
<yawn>
Rob just won't admit he's made a technical error. It seems from his
discussion he doesn't understand these antiquated issues either, which
isn't surprising since he doesn't have a good grasp of intermediate
microeconomics (the approximate level of sophistication of this
discussion). So, in short, we have Rob, as usual, expounding on issues
that economists were interested in thirty or forty years ago, and doing
so replete with technical errors and silly political posturing. Rob,
are you never going to find a more interesting topic to regale us with?
Chasna1
>Chasna keeps insisting that the rate of interest is not a pure number.
>If it is not a pure number, what are its units? And I haven't said
>anything about the definition of capital, so my comments can hardly be
>blamed on Boehm-Bawerk.
Your statement was that the rate of interest is a pure number, meaning it is
dimensionless. This is not true. The dollar dimensions cancel each other, but
the time dimension is retained.
con...@inow.com
Then we have answered the question "Subject: Re: Economics is not science",
haven't we?
John
Don Libby
>
>
> Then we have answered the question "Subject: Re: Economics is not science",
> haven't we?
Yes, falsifiable economic theories are scientific by Popper's criterion,
but not necessarily Archemedian by Layzer's, to the best of my
understanding.
con...@inow.com
> con...@inow.com wrote:
> >
> >
> > Then we have answered the question "Subject: Re: Economics is not science",
> > haven't we?
>
> Yes, falsifiable economic theories are scientific by Popper's criterion,
> but not necessarily Archemedian by Layzer's, to the best of my
> understanding.
>
I would tend to agree, and propose that Popper's criterion does not
necessarily violate information-theoretic incompleteness, (although it
is subservient to it in the sciences-but not necessarily so in other
human endeavors.)
As you say, under Popper's criterion, it is possible to have two
theories, both of which are rationally defensible, that can lead to
mutually exclusive conjectures.
How is that situation addressed?
Don Libby
>
>
> As you say, under Popper's criterion, it is possible to have two
> theories, both of which are rationally defensible, that can lead to
> mutually exclusive conjectures.
>
> How is that situation addressed?
>
*shrug*... Mud wrestling? It's the stuff scientific controversies (and
newsgroup threads) are made of.
David Lloyd-Jones
<con...@inow.com> wrote >
> BTW, as a simple, though not practical, example, suppose that a theory
> states that equity prices are determined, in the aggregate, by P/E
> ratios. If everyone believes it, it will be true.
John,
It is one of the rules of logic that you can prove anything from a false
premise. Since it is never the case that "everyone believes it" for any
"it," you are giving us an example here.
> Such recursive/circular/self-referential constructions are not unique
> to economics-they pervade most of science, (there are some formal
> arguments that Heisenberg Uncertainty is an information-theoretic
> issue-depending on who is telling the story, of course.) In economics,
> it probably occurs at a much higher level in the theoretical
> architecture than the other sciences, (IMHO, and I could be wrong.)
A self-referential construction is not the same thing as a belief held by
all; rather it is known generally as a circular argument, and is
specifically excluded from science.
You are correct on your last point, however. You are wrong. :-)
-dlj.
con...@inow.com
> con...@inow.com wrote:
> >
> >
> > As you say, under Popper's criterion, it is possible to have two
> > theories, both of which are rationally defensible, that can lead to
> > mutually exclusive conjectures.
> >
> > How is that situation addressed?
> >
>
> *shrug*... Mud wrestling? It's the stuff scientific controversies (and
> newsgroup threads) are made of.
>
The reason I ask the question is that it is possible to manufacture
truth if it is a self-referential system, (and that is not precluded
by information-theoretic incompleteness formalities, either-it can
still be a science.)
John
BTW, as a simple, though not practical, example, suppose that a theory
states that equity prices are determined, in the aggregate, by P/E
ratios. If everyone believes it, it will be true.
Such recursive/circular/self-referential constructions are not unique
to economics-they pervade most of science, (there are some formal
arguments that Heisenberg Uncertainty is an information-theoretic
issue-depending on who is telling the story, of course.) In economics,
it probably occurs at a much higher level in the theoretical
architecture than the other sciences, (IMHO, and I could be wrong.)
--
RArmant
>>John Tyler
>
>>Chasna keeps insisting that the rate of interest is not a pure number.
>>If it is not a pure number, what are its units?
Percent per unit of time -- %/year as an example.
con...@inow.com
>
> <con...@inow.com> wrote >
> > BTW, as a simple, though not practical, example, suppose that a theory
> > states that equity prices are determined, in the aggregate, by P/E
> > ratios. If everyone believes it, it will be true.
>
>
> It is one of the rules of logic that you can prove anything from a false
> premise. Since it is never the case that "everyone believes it" for any
> "it," you are giving us an example here.
>
> > to economics-they pervade most of science, (there are some formal
> > arguments that Heisenberg Uncertainty is an information-theoretic
> > issue-depending on who is telling the story, of course.) In economics,
> > it probably occurs at a much higher level in the theoretical
> > architecture than the other sciences, (IMHO, and I could be wrong.)
>
> all; rather it is known generally as a circular argument, and is
> specifically excluded from science.
>
> You are correct on your last point, however. You are wrong. :-)
>
Oh, David, you miss the point entirely. Its verifiable empirically,
too. So, it can not be a false premise.
Look at the context of the discussion.
John
Robert Vienneau
[ stupid libels deleted ]
[ denial of standard definition of "switch point," nonstandard ]
[ definition and further semantic manipulations - all so Chris ]
[ can avoid admitting that he made a mistake. ]
Concludes with:
> Rob is trying to divert attention from his technical
> errors by getting all caught up in semantics.
Clearly, projection.
"The points on the wage-profit frontier at which two techniques
are cost minimizing are called *switch points.*"
-- Kurz and Salvadori (1995)
Kurz and Salvadori include Garegnani's example of reswitching with
a continuum of techniques along the so-called factor-price
frontier (exercise 8.23).
> >> I'm asserting Rob cannot differentiate with respect to
> >> factor prices and hold factor ratios constant if production functions
> >> are smooth.
> >I can and do differentiate the factor price *curve* for a given
> >technique, where the technique is defined by coefficients of
> >production, i.e. a point on a unit isoquant. It matters not if the
> >production functions are smooth or linear combinations of fixed
> >coefficient processes.
> Rob just doesn't understand the point. Rob, you can't treat the
> "technique" as parametric and assert that your result is applicable
> to smooth technologies. *You* even assert in your essay that you're
> considering an initial equilibrium at a kink. Why do *you* say that
> if it's an assumption you don't need?
I understand what I am differentiating - the factor price curve. That
derivative exists in any case. If I am considering an initial
equilibrium at a "kink," this derivative is also the derivative of
the factor price frontier at that point. The result of price Wicksell
effects in the case of "smooth" production functions also results in
the indicated problem of circularity, as Chris agreed in his last
post. On Chris' reading, there is no mathematical error. I have put
a few words in my essay to be even clearer that I am considering
a nonswitching point in some interval in which the observed technique
is cost-minimizing.
I understand that the derivative of the frontier will reflect a
combination of price and real Wicksell effects in the "smooth" case.
Since I am not interested in real Wicksell effects, the appropriate
assumptions are the linear programming case, more or less for the
reasons Chris gave in his last post.
I explicitly never stated in my posts on this thread that the derivative
of a factor price curve is the derivative of the frontier in the smooth
case. This was deliberate.
> >I certainly claim the use of factor price frontiers to analyze the
> >choice of technique applies to smooth production functions. Can Chris
> >find a claim that he disagrees with, other than strawmen?
> Talk about strawmen. Did I claim otherwise?
Personally, I took Chris to be referring to a whole bunch of claims
when he referred to my analysis - the applicability of the so-called
non-substitution theorem to the "smooth" case; the possibility of
capital-reversing in the "smooth" case; the possibility of reswitching
in the "smooth" case, assuming no basic goods; etc.
Can Chris find a claim that he disagrees with, other than strawmen?
> For the fifth time: I
> want you to acknowledge *your* explicitly stated (albeit contradictory,
> and obviously not understood) assumption that your result obtains only
> at a non-differentiable point on the production function (which, of course,
> means the analysis is pointless in the first place, since the marginal
> product of capital is not even defined at such a point).
No, to the pointlessnes. Price Wicksell effects cause problems in
the "smooth" case. The linear programming case clarifies what these
problems are.
> I have no doubt
> one could redo the analysis correctly. And, yet again, I'm not denying
> the general result is true (eek, *aggregation problems* in macroeconomics).
Chris' mere assertions are laughable. Why cannot he acknowledge that
there is still contemporary debate about the point of these analyses?
He illustrates the conclusions that he wants to deny:
> I certainly do deny the laughable implications about politics and graduate
> training in economics Rob manages to draw.
Chris did not read my essay carefully. I was explicit that my ending
was speculative. Furthermore, I stated that since one could make the
point about the unit of capital depending on the interest rate in
a vicious circle without even considering reswitching and capital-reversing,
the CCC must be about additional considerations. It is in that context
that I indicated those implications.
> >It seems to be true that Chris is unable or unwilling to acknowledge
> >the differences in logic and structure between long run models and
> >models of intertemporal and temporary equilibrium. This talk of
> >substitution doesn't make much sense in long run models.
> Rob, *your model* has substitution, even with the piecewise linear
> technology. It's just that we need "large enough" changes in factor
> prices to get substitution, whereas with smooth technologies an
> arbitrarily small change in factor price ratios produces a substitution
> effect. The above is totally irrelevant, even if it were true.
It seems to be true that Chris is unable or unwilling to acknowledge
the differences in logic and structure between long run models and
models of intertemporal and temporary equilibrium. Long run models
don't necessarily have well-behaved substitution relationships.
[ Silliness deleted. ]
[ Random stupidities about game theory in which Chris either misremembers ]
[ my statements or remembers his incorrect conclusions drawn from poor ]
[ reading. ]
> >The case of linear combinations of fixed coefficient processes is useful
> >for understanding price Wicksell effects. With the above, Chris has
> >pretty much acknowledged my essay does not contain a technical flaw. At
> >best, he can quarrel with the wording in certain places.
> Huh? Rob, your equation for dw/dr is wrong for continuous technologies.
> Yes or no?
It is not incorrect for the derivative of factor price curves.
> >> >Non-zero price Wicksell effects clearly provide the indicated problem
> >> >for defining a "quantity of capital," independent of the interest rate,
> >> >in either case.
> >> I agree.
> >Here Chris explicitly admits my point holds for smooth production
> >functions.
> No kidding. I've done so several times.
Chris cannot make up his "mind."
[ More bad reading and stupidities. ]
Chris, you might have reflected on what I did not say in that comment
about Blaug. I expect you alone to fully understand my point. And if
anybody else has been reading enough to understand it, they've already
made a judgement on personalities.
Furthermore, I explicitly said I included references.
And I'm being quite amused.
[ Mere assertions. ]
Actually, I think Blaug has published a number of confused statements.
That doesn't mean I think he's not worth reading. Anybody that would
name his son after David Ricardo, if I understand correctly, is not
likely to be among my list of villians.
You ought to read Blaug's recent HOPE article. He has the Sraffians
either doing bad history or arguing contemporary theory. Roy
Weintraub would also include in contemporary theory a lot of work
you seem to think is in the history of economic thought.
[ Redundant silliness - the redundancy is probably my fault. ]
[ Chris's unwillingness to admit to his obfuscation. ]
> Why not just omit the overblown
> rhetoric and sweeping insults?)
More projection. Can Chris really not see that he's open to the same
charge?
David Lloyd-Jones
<con...@inow.com> wrote
> David Lloyd-Jones writes:
> > <con...@inow.com> wrote >
> > > BTW, as a simple, though not practical, example, suppose that a theory
> > > states that equity prices are determined, in the aggregate, by P/E
> > > ratios. If everyone believes it, it will be true.
> > John,
> > It is one of the rules of logic that you can prove anything from a false
> > premise. Since it is never the case that "everyone believes it" for any
> > "it," you are giving us an example here.
> Oh, David, you miss the point entirely. Its verifiable empirically,
> too. So, it can not be a false premise.
> Look at the context of the discussion.
I don't miss the point at all, and your claim is not remotely verified by
experience.
*Some* people believe that stocks should get their prices from p/e ratios.
Others believe in present discounted value of future cash flows -- with a
variety of discount rates and a universe of different ways of divining
future cash flows. Others keep Wall Street astrologers in business...
The difference between this picture, the actual one, and yours, the false
one, is the difference between having a market and not having a market. If
everyone believed the same theory of valuation there would be no buyers, no
sellers, or both.
-dlj.
j_t...@my-deja.com
cha...@aol.com (Chasna1) wrote:
> >John Tyler
>
> >Chasna keeps insisting that the rate of interest is not a pure
number.
> >anything about the definition of capital, so my comments can hardly
be
> >blamed on Boehm-Bawerk.
>
> Your statement was that the rate of interest is a pure number, meaning
it is
> dimensionless. This is not true. The dollar dimensions cancel each
other, but
> the time dimension is retained.
>
My apologies to Chasna. He is quite right, the time dimension is
retained. This is one of the virtues of sci.econ, we learn something.
j_t...@my-deja.com
dj...@aol.com2 (DJR80) wrote:
> >For one thing, there is a problem with units. The rate of interest
is a
> >pure number and the MP of capital is measured in units of output. To
> >make the two equal, we must multiply the MP of capital for the price
of
> >output and divide by the price of capital.
>
> Try looking at the marginal product of a unit of capital that produces
capital.
>
> Dan
> in Philly
>
This is a very interesting point. If we are talking about a capital
good that reproduces itself, then the rate of interest equals the
MP; that is, if we ignore depreciation, which can never be done in the
real world. However, a capital good that reproduces itself is more
likely to be found on the farm than in the factory. This is where
interest theory began, with talk about the natural increase of crops
and flocks. This is also the world of Frank Knight's Crusonia, a rather
mysterious substance that multiplied all by itself. Talk about a free
lunch! Crusonia was meant to be a model for all capital, but it is
hardly credible.
Chris Auld
>[ denial of standard definition of "switch point," nonstandard ]
>[ definition and further semantic manipulations - all so Chris ]
>[ can avoid admitting that he made a mistake. ]
<yawn>
I don't really care, Rob. If you want to stick with a definition
of "switch point" such that the concept is not applicable to smooth
technologies, be my guest (you will have to rewrite much of your
essay, alas). It seems to me that a "switch point" should be a
point such that the technique "switches," and a _property_ of such
points with quasi-linear technologies is that the factor price
ratio is not unique. I will note that even under the multiple
equilibria definition, one could get "switch points" with smooth
technologies -- Rob, can you tell us how that might occur?
>I understand what I am differentiating - the factor price curve. That
>derivative exists in any case. If I am considering an initial
>equilibrium at a "kink," this derivative is also the derivative of
>the factor price frontier at that point. The result of price Wicksell
>effects in the case of "smooth" production functions also results in
>the indicated problem of circularity, as Chris agreed in his last
>post. On Chris' reading, there is no mathematical error. I have put
>a few words in my essay to be even clearer that I am considering
>a nonswitching point in some interval in which the observed technique
>is cost-minimizing.
Fine, then don't claim your result holds for under the usual neoclassical
assumptions. Also note that the simplification comes at a great cost:
under your assumptions, "the marginal product of capital" isn't defined,
which makes the exercise of showing the marginal product of capital isn't
equal to the interest rate pointless before the analysis even begins. Why
not try to do it with smooth production functions, Rob?
>> Talk about strawmen. Did I claim otherwise?
>
>Personally, I took Chris to be referring to a whole bunch of claims
>when he referred to my analysis - the applicability of the so-called
>non-substitution theorem to the "smooth" case; the possibility of
>capital-reversing in the "smooth" case; the possibility of reswitching
>in the "smooth" case, assuming no basic goods; etc.
Perhaps Rob ought to respond to what I actually write.
>Can Chris find a claim that he disagrees with, other than strawmen?
Yes. I claim you have not fulfilled your stated goal of undertaking the
analysis under the usual neoclassical assumptions. I claim in particular
that your formula for dw/dr is wrong under the usual neoclassical assumptions,
and I think you agree. I claim this issue is just an aggregation problem,
well known to economists and taught to every graduate student, and that it
applies to any aggregated input, not just capital. Finally, I claim that
the implications Rob manages to draw about training in economics and certain
political issues do not follow, and reflect Rob's own insecurities and
ideologies rather than scholarly inquiry.
>> I have no doubt
>> one could redo the analysis correctly. And, yet again, I'm not denying
>> the general result is true (eek, *aggregation problems* in macroeconomics).
>
>Chris' mere assertions are laughable. Why cannot he acknowledge that
>there is still contemporary debate about the point of these analyses?
<yawn>
There is not contemporary debate about these issues. The point of *this*
exercise (not "these*, Rob again seems to be confusing all sorts of issues) is
that there are problems with aggregating capital and other inputs. Known and
boring since before I was born.
>> I certainly do deny the laughable implications about politics and graduate
>> training in economics Rob manages to draw.
>
>Chris did not read my essay carefully. I was explicit that my ending
>was speculative. Furthermore, I stated that since one could make the
>point about the unit of capital depending on the interest rate in
>a vicious circle without even considering reswitching and capital-reversing,
>the CCC must be about additional considerations. It is in that context
>that I indicated those implications.
And I deny those implications, in that context. I'm not sure why Rob thinks
that adding that he's being "speculative" changes the fact that his implications
are silly.
>> Rob, *your model* has substitution, even with the piecewise linear
>> technology. It's just that we need "large enough" changes in factor
>> prices to get substitution, whereas with smooth technologies an
>> arbitrarily small change in factor price ratios produces a substitution
>> effect. The above is totally irrelevant, even if it were true.
>It seems to be true that Chris is unable or unwilling to acknowledge
>the differences in logic and structure between long run models and
>models of intertemporal and temporary equilibrium. Long run models
>don't necessarily have well-behaved substitution relationships.
No kidding, Rob (and I'll once again point out that even the terminology
Rob employs is antique). In *this model*, *your model,* there exists
well-behaved substitution effects. In other contexts, one can sometimes
show "reswitching" and such. Can you try to focus, please?
>[ Random stupidities about game theory in which Chris either misremembers ]
>[ my statements or remembers his incorrect conclusions drawn from poor ]
>[ reading. ]
<yawn>
Anyone can look up the amusing history of Rob on game theory in dejanews.
Notice Rob's arrogant assumption that he couldn't possibly have been wrong
at any point, it must have been "misreading" on my part. Rob, if you
insist on using primary sources that are better than fifty years old, you
are somtimes going to start repeating fifty year old errors.
>> Huh? Rob, your equation for dw/dr is wrong for continuous technologies.
>> Yes or no?
>
>It is not incorrect for the derivative of factor price curves.
<sigh>
It is incorrect, Rob, as a matter of pure math. I guess I was wrong in stating
that Rob had realized this. For the n-th time: you cannot differentiate with
respect to factor prices and hold factor ratios parametric if technologies are
smooth. That's why the source you're plagiarizing this stuff from had you
assume you were at a "non-switching" point. Understand? You plagiarized the
correct interpretation above: how did you manage to forget in just a few
paragraphs?
>> >Here Chris explicitly admits my point holds for smooth production
>> >functions.
>
>> No kidding. I've done so several times.
>
>Chris cannot make up his "mind."
Huh? I think I've said that in every post, Rob. {Talk about reading
difficulties. This is pathetic.)
>[ More bad reading and stupidities. ]
For those keeping score at home who've forgetten their Vienneau-to-English
dictionaries: "stupidities" means "a point I can't respond to," and "bad
reading" means "a point I don't understand."
>Chris, you might have reflected on what I did not say in that comment
>about Blaug. I expect you alone to fully understand my point. And if
>anybody else has been reading enough to understand it, they've already
>made a judgement on personalities.
If anyone knows what Rob is trying to say here, could they please email
me? Cheers.
>[ Mere assertions. ]
Oh my, mere assertions!
Here's Rob's response to a quote from his own source which soundly
contradicts his own conclusions (on simple technical issues):
>Actually, I think Blaug has published a number of confused statements.
Very compelling, Rob. Here's an exercise for you: rewrite your model
with one capital good and two types of labor. Show the marginal
product of the labor force doesn't equal the wage rate. Show that
in that model, the value of the marginal product of capital equals
it's rental price. If you can do this, you've just proven yourself
wrong on several issues, and you owe an apology to Blaug and myself.
If you can't, go down to your nearest community college and take a
course in intermediate micro theory (which would be a wise idea
anyways, of course).
I guess I'll also ask Rob once again what we're to make of his
conclusion from this model that "capital does not contribute to
the production process" when one can redo the analysis with
"labor" substituted for "capital" and arrive at the same result.
(This point is a Vienneau Stupidity, as per the definition above.)
>> Why not just omit the overblown
>> rhetoric and sweeping insults?)
>
>More projection. Can Chris really not see that he's open to the same
>charge?
Fine. My point, Rob, is simply that if you omitted that rubbish from
the little essays you're prone to spamming us with constantly, you
wouldn't alienate your audience before discussion even begins.
So, Rob, are you going to take me up on my challenge to tell us about
some contempory issues in capital theory? Are do you intend to spend
another five years focusing on ancient debate over obscure issues in
production theory?
Chasna1
>retained. This is one of the virtues of sci.econ, we learn something.
>
>John Tyler
Please don't apologize, I am always glad to jump in where I can. The subject of
Capital theory is the most difficult area in all of economics. In seems that no
one comes away with much to show for this particular subject area.
DJR80
>then the VMP of capital must be divided by the price of capital goods,
Maybe I'm missing something. If you look at capital that produces capital,
then prices aren't needed. For example, if the unit of capital is a steel
factory, and you find that it can produce the equivalent of a tenth of a steel
factory every year, then the MPK is .1 per year.
Dan
in Philly
Robert Vienneau
> > If we measure capital in physical units,
> >then the VMP of capital must be divided by the price of capital goods,
> Maybe I'm missing something.
Yup.
> If you look at capital that produces capital,
> then prices aren't needed. For example, if the unit of capital is a steel
> factory, and you find that it can produce the equivalent of a tenth of a steel
> factory every year, then the MPK is .1 per year.
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