Reswitching and the Cambridge Capital Controversy
Robert Vienneau
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 the 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" production 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 equilibrium positions. When
all non-labor inputs into production are themselves the output of
production processes, a long run equilibrium 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. A long run equilibrium 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 profit 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 profit when comparing long run equilibria:
w/pc = ( 5 - r )/(7 + r) (4-3)
As with all viable pure circulating capital long run equilibrium
techniques, this trade off shows a higher wage is associated with a lower
rate of profit. The maximum wage is (5/7) bushels of corn, corresponding
to a rate of profit of 0%. The maximum rate of profit is 500%, corresponding
to a wage of zero. Figure 4-1 shows the wage-rate of profit frontier for
the iron technique.
5/7 +
| x
| x
w/pc | x
| x
| x
| x
+--------------------------------+-----
500%
r
FIGURE 4-1: THE IRON WAGE-RATE OF PROFIT FRONTIER
One can also find the price of iron in any long run equilibrium 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 equilibrium 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 profit frontier 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 profit is 300%.
|
|
3/5 +
w/pc | x
| x
| x
| x
+--------------+----------
300%
r
FIGURE 5-1: THE TIN WAGE-RATE OF PROFIT FRONTIER
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 equilibrium position is not consistent with a suboptimal choice
of technique. Accordingly, the technique chosen at a given rate of profit
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 profit frontier for long run equilibrium, allowing for
the choice of technique, is the envelope curve formed out of the wage-rate
of profit frontiers 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 PROFIT 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 interest, with other techniques chosen at
intermediate interest rates. 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 profit 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
production functions for available processes.
Once either the wage or the rate of profit 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 long run equilibrium and all
possible techniques are known. That technique may be compatible with
widely separate discrete intervals for the distributive variables and
different equilibrium 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 profit 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 equilibrium 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 profit
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 equilibrium 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
profit 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 profit below a value slightly above 100%. Then the wage-rate of
profit 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 profit 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 equilibrium 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 production functions 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 profit frontier for
a single technique, as in Figure 7-5. The dotted line is supposed to be
a concave wage-rate of profit 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 PROFIT 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 profit 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 profit 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. (This convergence is fairly obvious; 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."
Unlike the long run, short run equilibrium models exist which exhibit
traditional substitution behavior. 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
reflects 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.
----------------------------------------------------------------
...there is a general theoretical agreement (which is ignored
in a scandalous way by most textbooks) about the untenability of
neoclassical theories that take their point of departure from
aggregate capital.
-- Bertram Schefold
--
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
Shawn Wilson
Robert Vienneau wrote:
>
> 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 the 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" production functions define the processes
> for producing corn:
>
> X1 = min[ Q2, L ] (2-1)
>
> X1 = min[ 4 Q3, (2/3) L ] (2-2)
I was going to actually spend some time responding to this, but once
again the resident fool Robert chooses to use a production function that
doesn't reflect reality in order to beg the point of his argument. I
mean, he's been asked multiple times to show if his argument works with
a production function that reflects reality, but he never has. One is
forced to the conclusion that the ideas he presents are not reflective
of reality, and that spending time reading them would just be a waste.
SUSUPPLY
>The Cambridge Capital Controversy was a major theoretical controversy
>arising out of the work of Piero Sraffa.
Yawn.
Say Robert, what's your opinion on the designated hitter controversy?
Patrick
Robert Vienneau
wrote:
> I was going to actually spend some time responding to this, but once
> again the resident fool Robert chooses to use a production function that
> doesn't reflect reality in order to beg the point of his argument. I
> mean, he's been asked multiple times to show if his argument works with
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> a production function that reflects reality, but he never has. One is
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> forced to the conclusion that the ideas he presents are not reflective
> of reality, and that spending time reading them would just be a waste.
Inasmuch as the above has any meaning, it is untrue and ill-informed.
I have a collection of related arguments, not one. So who knows
what Shawn thinks he's talking about. But let's assume that he
means he wants a demonstration that reswitching and capital reversing
are possible.
"Reflects reality" is one of Shawn's silly phrases that he can never
explain. Let's first assume that Shawn wants to see empirical evidence
related to reswitching and capital-reversing. It's been explained to
Shawn a number of times that this request is misconceived. Before
validating neoclassical theory with empirical data, it's up to neoclassical
economists to present a coherent neoclassical theory of value. If this
is thought to include a (special-case) long run theory of production
with assumptions that are not unduly restrictive and that rule out
capital-reversing, this challenge has never been met.
Anyways, I have given Shawn a list of references for empirical and
applied work illustrating the possibility of behavior related to
reswitching and capital-reversing. This was in a post dated 25 Aug 1998.
Maybe Shawn thinks the logical possibility of capital-reversing depends
on the assumption of fixed coefficients. Although my example in this
thread did use fixed coefficients for each industry, I have *proven* that
capital-reversing is compatible with variable coefficients. I did this
with the example in my post titled "Do Factor Markets Exist?", dated
22 Sep 1998. In a post dated 21 August 1998, I explained to Shawn how
a continuously differentiable production function can be approximated
arbitrarily closely by a set of fixed-coefficient production processes -
a process being different from a production function. In this approach,
coefficents of production vary between processes and along linear
combinations of processes. Shawn has never demonstrated and cannot
demonstrate how even a countable infinity of observations "in reality"
can distinguish between a production function constructed in this manner
and a continuously differentiable production function.
Or maybe Shawn is claiming that a special case assumption of continuosly
differentiable microeconomic production functions rules out reswitching
and capital-reversing. Since this is a positive assertion, it's up
to him to prove it. Even if he could construct and follow an argument,
he could not prove this. Why? Because it simply is false. Tatsuo Hatta
has shown this, and I have provided Shawn with references to Hatta's
work in a post dated 21 August. (See also the Samuelson quote below).
Shawn is also wrong in thinking that the assumption of fixed coefficients
is non-neoclassical, if that's what he thinks. Although some have
expressed this view, I think it unsupportable. Walras used fixed
coefficients in the first few editions of his _Elements_. Economists
of the stature of Frank Hahn have argued that fixed coefficients
are compatible with neoclassical economics. In fact, that is part
of the point of the post-war turn to algebraic and topological
methods of proofs - to use a general approach that applies to
fixed coefficients, linear programming, and more traditional
calculus-based arguments. If Shawn insists on continuously
differentiable production functions, he is rejecting a great
deal of mainstream work, including empirical applications of
linear programming and Leontief input-output analysis. This has
been explained to Shawn before, as well.
In short, Shawn, like many mainstream economists, seems deeply
ignorant of neoclassical economics. I wonder if Shawn considers
Paul Samuelson to be a member of a radical "fringe":
"Something precious I gained from Robinson's work and that of her
colleagues working in the Sraffian tradition. As I have described
elsewhere, prior to 1952 when Joan began her last phase of capital
research, I operated under an important misapprehension concerning
the curvature properties of a general Fisher-von Neumann technology.
What I learned from Joan Robinson was more than she taught. I learned,
not that the general differentiable neoclassical model was special
and wrong but that a general neoclassical technology does not
necessarily involve a higher steady-state output when the interest
rate is lower. I had thought that such a property generalized from
the simplest one-sector Ramsey-Solow parable to the most general
Fisher case. That was a subtle error and, even before the 1960
Sraffa book on input-output, Joan Robinson's 1956 explorations in
_Accumulation of Capital_ alerted me to the subtle complexities of
general neoclassicism.
These complexities have naught to do with *finiteness* of the number
of alternative activities, and naught to do with the phenomenon in
which, to produce a good like steel you need directly or indirectly
to use steel itself as an input. In other words, what is wrong and
special in the simplest neoclassical or Austrian parables can be
completely divorced from the basic critique of marginalism that Sraffa
was ultimately aiming at when he began in the 1920s to compose his
classic: Sraffa (1960). To drive home this fundamental truth, I
shall illustrate with the most general Wicksell-Austrian case that
involves time-phasing of labor with no production of any good by means
of itself as a raw material.
As in the 1893-1906 works of Knut Wicksell, translated in Wicksell
(1934, Volume I), let corn now be producible by combining labor
yesterday, labor day-before-yesterday, etc):
Q( t ) = f( L(t - 1), L(t - 2), ..., L(t - T) ) = f( L ) (1)
Q = f( L(1), L(2), ..., L(T) ) in steady states (2)
Q = L(1) * f( 1, L(2)/L(1), ..., L(T)/L(1) ),
1st-homogeneous and concave (3)
Q = L(1) * del f( L )/del L(1) + ...
+ L(T) * del f( L )/del L(T), Euler's theorem (4)
del f/del L( j ) = fj( L ),
del del f/(del L(i) * del L(j) ) = fij( L )
exist for L >= 0 (5)
fj > 0, (z1, ..., zT)[ fij( L ) ](z1, ..., zT)' < 0
for zj <> b*L( j ) > 0 (6)
[Symbols are somewhat changed because of ASCII limitations - RLV ]
Nothing could be more neoclassical than (1)-(6). *If* it obtained
in the real world, a Sraffian critique could not get off the ground.
Yet it can involve (a) the qualitative phenomena much like
'reswitching', (b) so-called perverse 'Wicksell effects', (c) a
locus between steady-state *per capita* consumption and the interest
rate, a( i, c ) locus, which is *not* necessarily monotonically
negative once we get away from very low i rates. This cannot
happen for the 2-period case where T = 2. But for T >= 3, all
these 'pathologies' can occur, and there is really nothing
pathological about them. No matter how much they occur, the marginal
productivity doctrine does directly apply here to the general
equilibrium solution of the problem of the distribution of income...
...This monotone relation between (W/Pj, i ) was obscurely glimsped
by Thunen and other classicists and by Wicksell and other
neoclassicists. But the *factor-price trade-off frontier* did not
explicitly surface in the modern literature until 1953, as in
R. Sheppard (1953), P. Samuelson (1953), and D. Champernowne (1954).
One can prove it to be well-behaved for (1)-(3), or any
convex-technology case, by modern duality theory. Before Robinson
(1956), I wrongly took for granted that a similar monotone-decreasing
relation between ( i, Q/( L(1) + ... + L(T) ) ) must also follow
from mere concavity - just as does the relation
- del del C(t + 1)/( del C( t ) )^2 = del i(t)/del C(t) > 0. But
this blythe expectation is simply wrong! I refer readers to my
summing up on reswitching: Samuelson (1966).
I realize that there are many economists who tired of Robinson's
repeated critiques of capital theory as tedious and sterile naggings.
I cannot agree. Beyond the effect of rallying the spirits of
economists disliking the market order, these Robinson-Sraffa-
Pasinetti-Garegnani contributions deepen our understanding of how a
time-phased competitive microsystem works."
-- Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and
Modern Economic Theory_ (edited by G. R. Feiwel), New York
University Press, 1989.
Mark Patrick Witte
Robert Vienneau <rv...@see.sig.com> wrote:
>In article <362DEEEA...@worldnet.att.net>, Wils...@worldnet.att.net
>wrote:
>
>> I was going to actually spend some time responding to this, but once
>> again the resident fool Robert chooses to use a production function that
>> doesn't reflect reality in order to beg the point of his argument. I
>> mean, he's been asked multiple times to show if his argument works with
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>> a production function that reflects reality, but he never has. One is
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>> forced to the conclusion that the ideas he presents are not reflective
>> of reality, and that spending time reading them would just be a waste.
In fairness to Robert Vienneau, he does take the time to present a
model, a rarity in this world, let alone on this newsgroup. I think his
model is intended to reiterate the aggregation problems spotted by the CCC
folks. As Milton Friedman would say, we don't criticize assumptions, we
compare models. Statements like "the model fails to reflect reality" are
true but uninteresting; by definition, models abstract from reality which
means that they fail to mirror "reality" in its complexity. As such, all
models are false, yet some are interesting and useful. The work of Kepler
assumed some remarkable and unexplained guiding forces to move the planets
in particular ways, yet this model worked well to explain many issues humans
found interesting. Here I find some agreement with Mr. Wilson, does
Robert's model explain anything interesting about the real world, does it
answer in the affirmative or negative any questions addressed by, say,
the single output neoclassical model? It just may, I haven't looked far
enough into it to answer this to my own satisfaction, but I hope to.
However, I do have to agree with Mr. Wilson's question of
what is to be gained from digging through this model, what question
does it answer? What aspect of what we observe does this model better
fit than its competitors? Robert posts a bit from a memorial to Joan
Robinson where Paul Samuelson makes some polite remarks about
this class of work, but he makes no nod toward any such merit in
this approach.
>Inasmuch as the above has any meaning, it is untrue and ill-informed.
>
>I have a collection of related arguments, not one. So who knows
>what Shawn thinks he's talking about. But let's assume that he
>means he wants a demonstration that reswitching and capital reversing
>are possible.
Or, to reopen an old wound, is this another example of a
pathological case, like a Giffen good?
>"Reflects reality" is one of Shawn's silly phrases that he can never
>explain. Let's first assume that Shawn wants to see empirical evidence
>related to reswitching and capital-reversing. It's been explained to
>Shawn a number of times that this request is misconceived. Before
>validating neoclassical theory with empirical data, it's up to neoclassical
>economists to present a coherent neoclassical theory of value. If this
>is thought to include a (special-case) long run theory of production
>with assumptions that are not unduly restrictive and that rule out
>capital-reversing, this challenge has never been met.
What does "unduely restrictive" mean? Are we criticizing
assumptions here?
>Anyways, I have given Shawn a list of references for empirical and
>applied work illustrating the possibility of behavior related to
>reswitching and capital-reversing. This was in a post dated 25 Aug 1998.
Could you post this list? I recall seeing a list of such references
once upon a time but finding it unsatisfactory.
>Maybe Shawn thinks the logical possibility of capital-reversing depends
>on the assumption of fixed coefficients. Although my example in this
>thread did use fixed coefficients for each industry, I have *proven* that
>capital-reversing is compatible with variable coefficients. I did this
>with the example in my post titled "Do Factor Markets Exist?", dated
>22 Sep 1998. In a post dated 21 August 1998, I explained to Shawn how
>a continuously differentiable production function can be approximated
>arbitrarily closely by a set of fixed-coefficient production processes -
>a process being different from a production function. In this approach,
>coefficents of production vary between processes and along linear
>combinations of processes.
Hmm...this involves an approximation of a continuously
differentiable function with a list of alternative "plans" involving
various fixed coefficient technologies?
>Shawn has never demonstrated and cannot
>demonstrate how even a countable infinity of observations "in reality"
>can distinguish between a production function constructed in this manner
>and a continuously differentiable production function.
>
>Or maybe Shawn is claiming that a special case assumption of continuosly
>differentiable microeconomic production functions rules out reswitching
>and capital-reversing. Since this is a positive assertion, it's up
>to him to prove it. Even if he could construct and follow an argument,
>he could not prove this. Why? Because it simply is false. Tatsuo Hatta
>has shown this, and I have provided Shawn with references to Hatta's
>work in a post dated 21 August. (See also the Samuelson quote below).
>
>Shawn is also wrong in thinking that the assumption of fixed coefficients
>is non-neoclassical, if that's what he thinks. Although some have
>expressed this view, I think it unsupportable. Walras used fixed
>coefficients in the first few editions of his _Elements_. Economists
>of the stature of Frank Hahn have argued that fixed coefficients
>are compatible with neoclassical economics.
Does anyone really care what is or is not neoclassical?
Aren't we really interested in what is or is not useful? Hahn's comments
here just seems to be continuing the pointless argument about assumptions.
>In fact, that is part
>of the point of the post-war turn to algebraic and topological
>methods of proofs - to use a general approach that applies to
>fixed coefficients, linear programming, and more traditional
>calculus-based arguments. If Shawn insists on continuously
>differentiable production functions, he is rejecting a great
>deal of mainstream work, including empirical applications of
>linear programming and Leontief input-output analysis. This has
>been explained to Shawn before, as well.
>
>In short, Shawn, like many mainstream economists, seems deeply
>ignorant of neoclassical economics. I wonder if Shawn considers
>Paul Samuelson to be a member of a radical "fringe":
>
> "Something precious I gained from Robinson's work and that of her
> colleagues working in the Sraffian tradition. As I have described
> elsewhere, prior to 1952 when Joan began her last phase of capital
Wow, 1952? Well, give it time to soak in to the field and
find its usefulness in explaining our world.
Hmm, Robinson was viewed as a tedious and sterile nag? Maybe
Samuelson wasn't being so polite, or maybe even politeness has limits?
> I cannot agree. Beyond the effect of rallying the spirits of
> economists disliking the market order, these Robinson-Sraffa-
> Pasinetti-Garegnani contributions deepen our understanding of how a
> time-phased competitive microsystem works."
Here is looks like Samuelson is saying in 1989 that this work is
on the level of an interesting exercise.
SUSUPPLY
Robert:
>In fairness to Robert Vienneau....
I think this is known as turning the other cheek.
>Or, to reopen an old wound, is this another example of a
>pathological case, like a Giffen good?
Nice choice of adjective.
>Does anyone really care what is or is not neoclassical?
>Aren't we really interested in what is or is not useful?
Hmm. Is that a model or an assumption?
>Wow, 1952? Well, give it time to soak in to the field and
>find its usefulness in explaining our world.
Maybe that explains all those Chevy Bel-Airs in Cuba.
Patrick
Shawn Wilson
Robert Vienneau wrote:
>
> In article <362DEEEA...@worldnet.att.net>, Wils...@worldnet.att.net
> wrote:
>
> > I was going to actually spend some time responding to this, but once
> > again the resident fool Robert chooses to use a production function that
> > doesn't reflect reality in order to beg the point of his argument. I
> > mean, he's been asked multiple times to show if his argument works with
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> > a production function that reflects reality, but he never has. One is
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> > forced to the conclusion that the ideas he presents are not reflective
> > of reality, and that spending time reading them would just be a waste.
>
> Inasmuch as the above has any meaning, it is untrue and ill-informed.
Really? Show me an industry, or even a single factory, that operates
with a Leontieff production function. Show me a plant that can't
possibly increase production by hiring more workers without also renting
additional capital.
Or are YOU 'ill-informed'?
> I have a collection of related arguments, not one. So who knows
> what Shawn thinks he's talking about. But let's assume that he
> means he wants a demonstration that reswitching and capital reversing
> are possible.
C'mon Robert, we're STILL waiting for you to express that other post in
english. It's now FIVE posts since you were asked to do so. I mean,
until you do not one person has the slightest idea what you thought you
were talking about.
> "Reflects reality" is one of Shawn's silly phrases that he can never
> explain.
Ah, so you're cliaming that a Leontieff prodiuction technology is
realistic, give us ONE real world example.
> Let's first assume that Shawn wants to see empirical evidence
> related to reswitching and capital-reversing. It's been explained to
> Shawn a number of times that this request is misconceived.<
No, I, like the vast majority of economists, am an empiricist. If there
isn't empirical evidence there isn't anything. Economists describe how
the reality we are a part of works, our interest in your descriptions of
some other reality is minimal.
Before
> validating neoclassical theory with empirical data, it's up to neoclassical
> economists to present a coherent neoclassical theory of value.<
Ah, well, 'value' to a firm, is the ability to generate profits.
'Value', to an individual, is the abilty to generate utility. Now that
the neo-classical theory of value has been presented, it's your turn.
If this
> is thought to include a (special-case) long run theory of production
> with assumptions that are not unduly restrictive and that rule out
> capital-reversing, this challenge has never been met.
Ah, I guess you're unfamiliar with basic macroeconomic models. I
suggest you read Romer's 'Advanced Macroeconomics', and refrain from
wasting bandwidth with you ignorant prattle until then.
> Anyways, I have given Shawn a list of references for empirical and
> applied work illustrating the possibility of behavior related to
> reswitching and capital-reversing. This was in a post dated 25 Aug 1998.
>
> Maybe Shawn thinks the logical possibility of capital-reversing depends
> on the assumption of fixed coefficients.
It seems to, since you never use any other technology.
Although my example in this
> thread did use fixed coefficients for each industry, I have *proven* that
> capital-reversing is compatible with variable coefficients.
Actually, you haven't. Your belief does not constitute 'proof'.
I did this
> with the example in my post titled "Do Factor Markets Exist?", dated
> 22 Sep 1998. In a post dated 21 August 1998, I explained to Shawn how
> a continuously differentiable production function can be approximated
> arbitrarily closely by a set of fixed-coefficient production processes -
> a process being different from a production function.
And there's the rub, you can't seem to differentiate between an
arbitrarily large set of Leontieff production functions, and the single
one you use in your posts. Do you even know what a Cobb-Douglas
production function is? Here's a hint at the difference between
Leontieff and Cobb-Douglas: the marginal rate of substitution for a
Leontieff production function is always zero. Since we're are basically
dealing with substitution between factors of production, why is it that
you consider a production function with a MRS of zero appropriate?
Could it be..... SATAN!?
In this approach,
> coefficents of production vary between processes and along linear
> combinations of processes. Shawn has never demonstrated and cannot
> demonstrate how even a countable infinity of observations "in reality"
> can distinguish between a production function constructed in this manner
> and a continuously differentiable production function.
If you were actually using an arbitrarily large number of Leontieff
production functions you would be correct. But you aren't. And it is
very easy to see that a single Leontieff production function in no way
resembles reality. I wonder if you actuallly even understand what
you're saying? You've certainly never expressed it correctly. A
Leontieff production function is of the form
Q = A * min [B*L, C*K],
where L is labor, K is capital, and A, B, and C are parameters. A
Cobb-Douglass production function looks like
Q = a * L^b * K^c,
where L and K are as before, and the parameters are a, b, and c.
Usually b + c = 1, but not always.
(deleted from boredom)
Tell us Robert, Wicksell published sixty years ago, why is he so obscure
and neo-classical theory so dominant?
Robert Vienneau
mwi...@merle.acns.nwu.edu (Mark Patrick Witte) wrote:
> In fairness to Robert Vienneau, he does take the time to present a
> model, a rarity in this world, let alone on this newsgroup.
A common reaction of leftist economists to the CCC is, "A pox on both sides."
> I think his
> model is intended to reiterate the aggregation problems spotted by the CCC
> folks.
As Mark knows, I think that aggregation issues miss major points of the
CCC (although perhaps Mark's comment fairly summarizes major points of
my post with which I began *this* thread).
The neoclassical theory of value is that prices are scarcity indices.
Supposedly, if more of a good used in production is available, its
price will fall and producers will be encouraged to produce more
consumption goods that use that input relatively more intensively.
The prices of these consumption goods will fall. Consumers will
substitute consumption of these cheaper goods for more expensive
goods. Producers will also be encouraged to change methods of
production to adopt techniques and processes that use the lower-priced
input relatively more intensively. That is, producers will substitute
the relatively cheaper input for more expensive inputs. If consumers'
tastes change in favor of a particular consumption good, its price
will supposedly rise. So will the prices of goods used relatively
intensively in the production of that good. Producers will
substitute techniques and processes that use those inputs less
intensively.
This neoclassical theory of value is simply wrong, except, perhaps, as
an account of certain dynamic disequilibrium processes. Since the point
of neoclassical economics was to explain short run and long run theory
with a common supply and demand approach, economics took a wrong
turning in the 1870s.
Suppose one accepts that the neoclassical theory of value is mistaken,
as Samuelson and Hahn do. Does it make sense to continue to affirm
neoclassical economics without a theory of value? What holds the
research program together? One might doubt that a commitment to
formalism is not enough.
> As Milton Friedman would say, we don't criticize assumptions, we
> compare models. Statements like "the model fails to reflect reality" are
> true but uninteresting; by definition, models abstract from reality which
> means that they fail to mirror "reality" in its complexity. As such, all
> models are false, yet some are interesting and useful. The work of Kepler
> assumed some remarkable and unexplained guiding forces to move the planets
> in particular ways, yet this model worked well to explain many issues humans
> found interesting.
I find Friedman incoherent on methodology, and the received view among
mainstream economists mistaken. But I certainly will be amused if Mark
tries to expand on these comments to Shawn. Friedman's article does
indeed allow one to criticize assumptions - not on grounds of realism,
but on whether they abstract essential properties or not.
> Here I find some agreement with Mr. Wilson, does
> Robert's model explain anything interesting about the real world, does it
> answer in the affirmative or negative any questions addressed by, say,
> the single output neoclassical model?
Is there a (multiple good) neoclassical theory of value? Is there any
reason to believe that a one-good model is appropriate for understanding
actual economies? If the answer to these questions is negative, then
there's no need to point to something in the U.S. economy explained
by the CCC.
However, as I've told Mark before (and Shawn too), the interesting
*empirical* questions are along other dimensions.
> It just may, I haven't looked far
> enough into it to answer this to my own satisfaction, but I hope to.
> However, I do have to agree with Mr. Wilson's question of
> what is to be gained from digging through this model, what question
> does it answer? What aspect of what we observe does this model better
> fit than its competitors? Robert posts a bit from a memorial to Joan
> Robinson where Paul Samuelson makes some polite remarks about
> this class of work, but he makes no nod toward any such merit in
> this approach.
These musings seem to miss the point and seem to do so deliberately.
There is no coherent neoclassical theory of value and distribution.
I don't count handwaving as coherent. I don't think contemporary
physicists find medieval impetus theory coherent.
[...]
> >"Reflects reality" is one of Shawn's silly phrases that he can never
> >explain. Let's first assume that Shawn wants to see empirical evidence
> >related to reswitching and capital-reversing. It's been explained to
> >Shawn a number of times that this request is misconceived. Before
> >validating neoclassical theory with empirical data, it's up to neoclassical
> >economists to present a coherent neoclassical theory of value. If this
> >is thought to include a (special-case) long run theory of production
> >with assumptions that are not unduly restrictive and that rule out
> >capital-reversing, this challenge has never been met.
> What does "unduely restrictive" mean? Are we criticizing
> assumptions here?
No other science ignores arguments because of these sorts of
beliefs about methodology.
"Unduly restrictive" means assumptions like any one of the following:
o Only one good is produced
o Capital-intensity is the same in all lines of production (given
the ignorance I have found about price Wicksell effects, I wonder
if some mainstream economists understand any longer the usual
objection to the usual formalization of Marx.)
o Suppose many processes are available for producing one good.
For each pair of processes, the process that requires more labor
input per unit output requires no more of each non-labor input
per unit output than the other process does.
It's fine in math to develop theorems with long lists of conditions.
It's not so fine in a supposedly empirical field when neither the
conditions nor the implications have passed falsifying tests.
> >Anyways, I have given Shawn a list of references for empirical and
> >applied work illustrating the possibility of behavior related to
> >reswitching and capital-reversing. This was in a post dated 25 Aug 1998.
> Could you post this list? I recall seeing a list of such references
> once upon a time but finding it unsatisfactory.
<begin quote>
Adam Ozanne, "Do Supply Curves Slope Up? The Empirical Relevance of
the Sraffian Critique of Neoclassical Production Economics,"
_Cambridge Journal of Economics_, Volume 20, pp. 749-762, 1996.
A classic example of the possibility of reswitching, which I have
not read, is:
Peter Albin, "Reswitching: An Empirical Observation," _Kylos_, 1975,
Number 1, 28, pp. 149-54.
I once found this passage:
"...This possibility has been used by Hartwick (1976), Schweizer and
Varaiya (1977), Scott (1979), and Barnes and Sheppard (1984) to argue for
the possibility of "reswitching" of land uses occurring across space, that
is of one use appearing for one zone, disappearing for another, and then
reappearing at a further out location. Such reswitching could arise if
transportation costs are wage-intensive. In such a case the rent-distance
profile will be discontinuous at the switch points. If the intermediate
land use is agricultural, then there will be a discontinuous pattern of
development from the urban perspective."
-- J. Barkley Rosser, Jr., _From Catastrophe to Chaos: A General Theory
of Economic Discontinuities_, Kluwer Academic, 1991, p. 190
I have not read these references, but Barkley Rosser is referring to:
John Hartwick, "Intermediate Goods and the Spatial Integration of Land
Use," _Regional Science and Urban Economics_, V. 6, pp. 127-145, 1976.
U. Schweizer and P. Varaiya, "The Spatial Structure of Production with a
Leontief Technology-II: Substitute Techniques," _Regional Science and
Urban Economics_, V. 7, pp. 293-320, 1977.
A. J. Scott, "Commodity Production and the Dynamics of Land-Use
Differentiation," _Urban Studies_, V. 16, pp. 95-104, 1979.
Trevor Barnes and Eric Sheppard, "Technical Choice and Reswitching in
Space Economies," _Regional Science and Urban Economics_, V. 14,
pp. 345-352, 1984.
Elsewhere in the same book, Barkley Rosser references (I have not
read these either):
Geir B. Asheim, "The Occurrence of Paradoxical Behavior in a Model
where Economic Activity has Environmental Effects," Norwegian School
of Economics and Business Administration Discussion Papers, 1980.
Raymond Prince and J. Barkley Rosser, Jr., "Environment Costs and
Reswitching Between Food and Energy Production in the Western United
States," mimeo, James Madison University, 1984.
Raymond Prince and J. Barkley Rosser, Jr., "Some Implications of
Delayed Environmental Costs for Benefit Cost Analysis: A Study of
Reswitching in the Western Coal Lands, _Growth and Change_, V. 16,
18-25, 1985.
Finally, we need to learn Italian (based on this quote):
"...since I have gathered that the most active discussion, both theoretical
and empirical, on how probable the occurrence of reswitching is, has
recently been taking place in the Italian language journals - one estimate
puts the number of such papers in recent years to around seventy! I did
not have access to any of them."
-- Syed Ahmad, _Capital in Economic Theory: Neo-classical, Cambridge and
Chaos_, Edward Elgar, 1991, p. 250
Through simulation, I have convinced myself that the probability of
reswitching is very low in a two good model with a structure like that
in my example. I think the probability should increase with the number
of goods.
<end quote>
Mark has not criticized Ozanne before. As of last summer, Rosser
is still willing to point to some of these as evidence of "perverse"
behavior. I recently stumbled across a post in another forum arguing
that a textbook view in economic geography is that neoclassical
economics is something like the divine right of kings - a theory
that the student should know about but not take seriously in this
day and age. The reason given for this view is basically the
application of the CCC to geography.
I, of course, consistently maintain that the question of the empirical
likelihood of reswitching is uninteresting. The question neoclassical
economists need to answer before looking at the evidence is, "Do you
have a coherent theory of value and distribution?" The interesting
empirical questions are about which theories of distribution are
better. Possibilities include a classical theory in which wages
are determined by social norms; a monetary theory of distribution
in which the interest rate is determined by the monetary authority
and differences between the interest rate and rates of profits are
stable; and Post Keynesian theories such as Kaldor's, Pasinetti's, and
Robinson's. Interesting theoretical questions revolve around
relationships between these theories and how they fit into
historical time. Notice none of these theories assume the labor
market must clear in equilibrium. These theories are also coherent
when combined with usual models of production.
> >Maybe Shawn thinks the logical possibility of capital-reversing depends
> >on the assumption of fixed coefficients. Although my example in this
> >thread did use fixed coefficients for each industry, I have *proven* that
> >capital-reversing is compatible with variable coefficients. I did this
> >with the example in my post titled "Do Factor Markets Exist?", dated
> >22 Sep 1998. In a post dated 21 August 1998, I explained to Shawn how
> >a continuously differentiable production function can be approximated
> >arbitrarily closely by a set of fixed-coefficient production processes -
> >a process being different from a production function. In this approach,
> >coefficents of production vary between processes and along linear
> >combinations of processes.
> Hmm...this involves an approximation of a continuously
> differentiable function with a list of alternative "plans" involving
> various fixed coefficient technologies?
<begin quote>
An interesting aspect of this approach is that any continuously
differentiable well-behaved neoclassical production function can
be approximated arbitrarily closely by linear combinations of
processes like those in my example. I think a geometric illustration
of two-dimensional isoquants might convince undecided readers of
this point.
Accordingly, consider isoquants of two different processes
for producing gross outputs of some commodity. Let X1 and X2
represent the quantities of inputs. The output produced by
a single process is given by a function of the form:
min( X1/a1, X2/a2 )
where a1 and a2, the coefficients of production, are given
parameters for a process, but vary between processes. The two
diagrams below show isoquants for each process.
/|\
| | |
| | | |
| | .______________ | | | |
| | | | | |
| | | | | .______
| | X2 | | |
X2 | ._________________ | | .__________
| | |
| | ._______________
| |
+--------------------> +-------------------->
X1 X1
The points of the L-shaped isoquants lie along a ray through
the origin with the equation X2 = ( a2/a1) X1.
A firm with these processes available does not need to
choose one or the other for producing all output. The firm
can choose a linear combination. In this case, an isoquant
would then look something like the following:
/|\
| |
| |
| .
| .
| .
| .
X2 | .__________
|
|
|
+-------------------->
X1
An isoquant with linear combinations of pairs selected from three
processes might look like so:
/|\
| |
| |
| .A
| .
| .
| .
X2 | +
| . B
| .____________
|
+-------------------->
X1
Note that by increasing the number of processes, the resulting isoquants
could be arbitrary close to a smooth curve with slopes of the linear
combinations varying for each pair. Also note that there's an
optimization process underlying the construction of these isoquants.
A nonoptimal choice for the firm would be to produce the same level
as shown in the above isoquant along a line connecting A and B.
I cannot draw hyperplanes in N dimensions. I hope the reader can
see, however, that this approximation approach applies to smooth
neoclassical production functions with N arguments, each argument
representing another input.
<end quote>
> >Shawn has never demonstrated and cannot
> >demonstrate how even a countable infinity of observations "in reality"
> >can distinguish between a production function constructed in this manner
> >and a continuously differentiable production function.
[...]
> >Shawn is also wrong in thinking that the assumption of fixed coefficients
> >is non-neoclassical, if that's what he thinks. Although some have
> >expressed this view, I think it unsupportable. Walras used fixed
> >coefficients in the first few editions of his _Elements_. Economists
> >of the stature of Frank Hahn have argued that fixed coefficients
> >are compatible with neoclassical economics.
> Does anyone really care what is or is not neoclassical?
Mainstream economists protecting their turf seem to care. Hahn was
adopting a rhetorical strategy of claiming the Cambridge model as
a special case of neoclassical theory. Given the confusion generated
by Hicks on what Keynes is all about, this strategy sometimes
seems to work well.
Is the following claim of interest?
"A case has been made for the observation that the modern contributions
to economic understanding have not come from marginal economic
analysis, but, on the contrary, they have mainly come out in bitter
polemic with and as a challenge to it. And they deal with problems
of production, not with the optimum allocation of scarce resources.
Here we need only mention the modern (post-Keynesian) theory of
production based on an open Leontief model, the Sraffian production
and value models, and the Harrod-Domar dynamic macro models with the
Kaleckian distribution and price models."
-- Stanley Bober, _Pricing & Growth: A Neo-Ricardian Approach_,
M. E. Sharpe, 1992.
> Aren't we really interested in what is or is not useful? Hahn's comments
> here just seems to be continuing the pointless argument about assumptions.
And is my point below about linear programming not about what is
useful?
> >In fact, that is part
> >of the point of the post-war turn to algebraic and topological
> >methods of proofs - to use a general approach that applies to
> >fixed coefficients, linear programming, and more traditional
> >calculus-based arguments. If Shawn insists on continuously
> >differentiable production functions, he is rejecting a great
> >deal of mainstream work, including empirical applications of
> >linear programming and Leontief input-output analysis. This has
> >been explained to Shawn before, as well.
[...]
> > I realize that there are many economists who tired of Robinson's
> > repeated critiques of capital theory as tedious and sterile naggings.
> Hmm, Robinson was viewed as a tedious and sterile nag? Maybe
> Samuelson wasn't being so polite, or maybe even politeness has limits?
Maybe Samuelson is aware of certain reactions to Robinson?
> > I cannot agree. Beyond the effect of rallying the spirits of
> > economists disliking the market order, these Robinson-Sraffa-
> > Pasinetti-Garegnani contributions deepen our understanding of how a
> > time-phased competitive microsystem works."
> Here is looks like Samuelson is saying in 1989 that this work is
> on the level of an interesting exercise.
No. Samuelson is pointing out that people with Shawn's apparent beliefs
do not understand neoclassical economics. Why cannot it be taught
rigorously at the graduate level?
> > -- Paul A. Samuelson, "Remembering Joan", in _Joan Robinson and
> > Modern Economic Theory_ (edited by G. R. Feiwel), New York
> > University Press, 1989.
Browsing the Web, I find somebody has put up this quote:
"Well, there are few bad moves you could make, and more right ones than
anyone can ever imagine."
- Mark Witte, (everyone's favorite) Northwestern Economics Professor
Robert Vienneau
> C'mon Robert, we're STILL waiting for you to express that other post in
> english.
Does Shawn thinks he's a king? Does he have tapeworms?
> It's now FIVE posts since you were asked to do so. I mean,
> until you do not one person has the slightest idea what you thought you
> were talking about.
Consider the following Web page:
<http://www.econ.jhu.edu/people/fonseca/het/sraffa.htm>
Does Shawn think the person that put up this page doesn't understand
price Wicksell effects?
> Tell us Robert, Wicksell published sixty years ago, why is he so obscure
> and neo-classical theory so dominant?
Wicksell is neither obscure nor non-neoclassical.
Shawn Wilson
Robert Vienneau wrote:
>
> In article <362F45D2...@uic.edu>, swi...@uic.edu wrote:
>
> > C'mon Robert, we're STILL waiting for you to express that other post in
> > english.
>
> Does Shawn thinks he's a king? Does he have tapeworms?
>
> > It's now FIVE posts since you were asked to do so. I mean,
> > until you do not one person has the slightest idea what you thought you
> > were talking about.
>
> Consider the following Web page:
>
> <http://www.econ.jhu.edu/people/fonseca/het/sraffa.htm>
>
> Does Shawn think the person that put up this page doesn't understand
> price Wicksell effects?
No, I think that you couldn't express that other post in english if your
life depended on it. BTW, 'we' refered to everyone who reads this
group.
I think we've seen exactly how limited your intellectual capabilities
really are. You can parrot what others say, but you don't understand
it. If you actually understood that post you would be able translate it
into english. C'mon, this is a relevancy check. I CHALLENGE you to
express that other post in english.
>
> > Tell us Robert, Wicksell published sixty years ago, why is he so obscure
> > and neo-classical theory so dominant?
>
> Wicksell is neither obscure nor non-neoclassical.
And yet he isn't mentioned anywhere in the NINE textbooks I've checked.
I think that's sufficient evidence for the value of his ideas.
Textbooks that bend over backwards to cover all the main ideas leave
Wicksell out. So, now that evidence of his obscurity is firmly
established, if his ideas are so damaging to neo-classical theory, why
has neo-classical theory outlasted him?
Shawn Wilson
> As Mark knows, I think that aggregation issues miss major points of the
> CCC (although perhaps Mark's comment fairly summarizes major points of
> my post with which I began *this* thread).
>
> The neoclassical theory of value is that prices are scarcity indices.
Not surprisingly for something that comes from Robert, the statement is
flat out wrong.
> This neoclassical theory of value is simply wrong, except, perhaps, as
> an account of certain dynamic disequilibrium processes.
And what are YOUR qualifications to distinguish truth from error? So
far all we've seen is your inability to express an argument YOU quoted
(and passed off as your own, BTW) into actual english.
> Since the point
> of neoclassical economics was to explain short run and long run theory
> with a common supply and demand approach, economics took a wrong
> turning in the 1870s.
Gee, and yet is does such a wonderful job of actually predicting what
will happen regardless. Yeah, LTCM went bust, but predicting the stock
(or bond) market is an incredibly trivial fraction of of what real
economists really do.
> > Here I find some agreement with Mr. Wilson, does
> > Robert's model explain anything interesting about the real world, does it
> > answer in the affirmative or negative any questions addressed by, say,
> > the single output neoclassical model?
>
> Is there a (multiple good) neoclassical theory of value? Is there any
> reason to believe that a one-good model is appropriate for understanding
> actual economies? If the answer to these questions is negative, then
> there's no need to point to something in the U.S. economy explained
> by the CCC.
You didn't answer the question, Robert. Does 'your' model explain
anything in the real world? No. Does it answer any questions that
neo-classical theory does? No. Is it a dead sideline to real economic
thinking? Yes.
> > However, I do have to agree with Mr. Wilson's question of
> > what is to be gained from digging through this model, what question
> > does it answer? What aspect of what we observe does this model better
> > fit than its competitors? Robert posts a bit from a memorial to Joan
> > Robinson where Paul Samuelson makes some polite remarks about
> > this class of work, but he makes no nod toward any such merit in
> > this approach.
>
> These musings seem to miss the point and seem to do so deliberately.
> There is no coherent neoclassical theory of value and distribution.
> I don't count handwaving as coherent. I don't think contemporary
> physicists find medieval impetus theory coherent.
And neither do modern economists find capital reswitching coherent
either. Ya gotta be careful about your metaphors, Robert.
Neo-classical theory lives and reswitching died.
> > Here is looks like Samuelson is saying in 1989 that this work is
> > on the level of an interesting exercise.
>
> No. Samuelson is pointing out that people with Shawn's apparent beliefs
> do not understand neoclassical economics. Why cannot it be taught
> rigorously at the graduate level?
Eh? And what economics courses have YOU taken at the graduate level?
For that matter, why is it that ALL the others who manifestly HAVE taken
graduate level economics courses side with me and against you?
SUSUPPLY
>You can parrot what others say, but you don't understand
>it. If you actually understood that post you would be able translate it
>into english. C'mon, this is a relevancy check. I CHALLENGE you to
>express that other post in english.
Yes, I'd like to see that too. Robert CAN write clear and succinct English.
Remember this from a couple weeks ago:
"Smith argues that the merchantilists were mistaken in thinking the
main advantage of foreign trade is the importation of gold and silver.
Rather, foreign trade exports superfluous commodities and brings back
commodities for which there is demand in the home country. In this way,
the division of labor is not limited by the narrowness of the home
market. So foriegn trade leads to dynamic increasing returns and
greater prosperity."
Lets see something like that, Robert. Unless you copied that from someone else
too.
Patrick
Robert Vienneau
> And what are YOUR qualifications to distinguish truth from error? So
> far all we've seen is your inability to express an argument YOU quoted
> (and passed off as your own, BTW) into actual english.
As a matter of fact, I did leave out quotation marks on one recent post.
The quote from the Web page whose URL I did not give should have been:
"'Well, there are few bad moves you could make, and more right ones than
anyone can ever imagine.'
- Mark Witte, (everyone's favorite) Northwestern Economics Professor"
That is, the description of Mark as "everyone's favorite" was his
student's characterization, not mine (although I concur). Otherwise,
Shawn's comment above is a lie, as long time readers of this group
should know.
> > Is there a (multiple good) neoclassical theory of value? Is there any
> > reason to believe that a one-good model is appropriate for understanding
> > actual economies? If the answer to these questions is negative, then
> > there's no need to point to something in the U.S. economy explained
> > by the CCC.
> You didn't answer the question, Robert. Does 'your' model explain
> anything in the real world? No. Does it answer any questions that
> neo-classical theory does? No. Is it a dead sideline to real economic
> thinking? Yes.
The one-good circulating capital model has some logical implications
that are not logical implications of the more general n-good model.
Some logical differences should be apparent from the numerical
examples I have created. For example, if one knows the selected
technique and the set of all possible techniques, one knows the
distribution of income in the one good case. This is not necessarily
true in the n-good case. Another non-generalizable property is the
association of a lower interest rate with a greater value of capital
per worker and higher consumption per head. Still another property is
the equality of the interest rate and the marginal product of the
value of capital. Once again, these are properties of the one good
model that do not generalize to the n-good model. (A property in common
between these models is the association of a greater steady-state
value of capital per head with greater steady-state consumption per
head.)
Are differences in logical implications between these models
empirically testable? If so, what is the evidence for the restrictions
of the neoclassical special case? If there is none, why should
economists not use the general model of the choice of technique when
using long period models of production? Mainstream economists seem to
promote erroroneous beliefs, perhaps for non-cognitive reasons.
> > > Here is looks like Samuelson is saying in 1989 that this work is
> > > on the level of an interesting exercise.
> > No. Samuelson is pointing out that people with Shawn's apparent beliefs
> > do not understand neoclassical economics. Why cannot it be taught
> > rigorously at the graduate level?
> Eh? And what economics courses have YOU taken at the graduate level?
> For that matter, why is it that ALL the others who manifestly HAVE taken
> graduate level economics courses side with me and against you?
I'd like to defend economists against Shawn's charge. Not all graduate
students or economists are as ill-informed as he implies.
Shawn Wilson
>
> In article <362FA0CE...@uic.edu>, swi...@uic.edu wrote:
>
> > And what are YOUR qualifications to distinguish truth from error? So
> > far all we've seen is your inability to express an argument YOU quoted
> > (and passed off as your own, BTW) into actual english.
>
> As a matter of fact, I did leave out quotation marks on one recent post.
> The quote from the Web page whose URL I did not give should have been:
>
> anyone can ever imagine.'
> - Mark Witte, (everyone's favorite) Northwestern Economics Professor"
>
> student's characterization, not mine (although I concur). Otherwise,
> Shawn's comment above is a lie, as long time readers of this group
> should know.
Well? Where's the english version of that post?
> Are differences in logical implications between these models
> empirically testable?
Yes, they are. Capital reswitching is perfectly observable. It is not,
however, observed in the data. Since it should be observed if it
occurs, and it isn't observed, it almost certainly doesn't occur.
Therefore it is not a relevant chain of reasoning. One would then
expect that chain of reasoning to be abandoned. Lo and behold, it has
in fact been abandoned by everyone actually engaged in the profession of
economics.
If so, what is the evidence for the restrictions
> of the neoclassical special case? If there is none, why should
> economists not use the general model of the choice of technique when
> using long period models of production?
Why, exactly, should economists abandon a model that that gives good
empirical results in favor of one that gives poor empirical results?
Mainstream economists seem to
> promote erroroneous beliefs, perhaps for non-cognitive reasons.
There is also another explanation that wins the Occam's razor test-
those promoting erroneous beliefs for non-cognitive reasons are people
like Robert. Robert, after all, is in a decided minority of economic
opinion.
> > > No. Samuelson is pointing out that people with Shawn's apparent beliefs
> > > do not understand neoclassical economics. Why cannot it be taught
> > > rigorously at the graduate level?
>
> > Eh? And what economics courses have YOU taken at the graduate level?
> > For that matter, why is it that ALL the others who manifestly HAVE taken
> > graduate level economics courses side with me and against you?
>
> I'd like to defend economists against Shawn's charge. Not all graduate
> students or economists are as ill-informed as he implies.
That wasn't the question. What economics courses have YOU taken at the
graduate level? You have made accusations against dedicated students
and professors, what is your evidence? Oh, and why is is that you have
been utterly unable to translate that post of yours into english?
SUSUPPLY
>> > And what are YOUR qualifications to distinguish truth from error? So
>> > far all we've seen is your inability to express an argument YOU quoted
>> > (and passed off as your own, BTW) into actual english.
>>
>> As a matter of fact, I did leave out quotation marks on one recent post.
>> The quote from the Web page whose URL I did not give should have been:
>>
>> "'Well, there are few bad moves you could make, and more right ones than
>> anyone can ever imagine.'
>> - Mark Witte, (everyone's favorite) Northwestern Economics Professor"
>>
>> That is, the description of Mark as "everyone's favorite" was his
>> student's characterization, not mine (although I concur). Otherwise,
>> Shawn's comment above is a lie, as long time readers of this group
>> should know.
Follows as night does day. Just who did you think this was going to fool,
Robert?
Patrick
Robert Vienneau
the original order):
> > > And what are YOUR qualifications to distinguish truth from error?
> Lo and behold, [capital reswitching] has
> in fact been abandoned by everyone actually engaged in the profession of
> economics.
> Robert, after all, is in a decided minority of economic
> opinion.
> What economics courses have YOU taken at the
> graduate level?
After going on and on with these sorts of irrelevancies, Shawn is
hardly justified in suggesting I retract my mild suggestion that
some economists hold some beliefs for non-cognitive reasons.
Although it remains irrelevant to my economic argument, Shawn is
wrong about what every economist believes. I have demonstrated that
Paul Samuelson says "there is really nothing pathological" about
reswitching and capital reversing. Frank Hahn agrees.
There are also communities which welcome economists drawing on
theories I find persuasive. I have never seen this journal
in the dead trees version and am not comfortable in French; however,
writers for the _Cahiers d'économie politique_ is one such
group, as judged by their online table of contents:
<http://panoramix.univ-paris1.fr/C-ECO-PO/>
(Perhaps Shawn can find somebody to help him with the French.)
Another journal, the _Review of Political Economy_, has a Web page at:
<http://www.carfax.co.uk/rpe-ad.htm>
This journal, too, is open to articles about some of my favorite
topics. This one, also, I have never had access to in hardcopy.
The Orwellian approach of denying the very existence of certain groups
of economists and scholars seems to be a common non-argument of
certain posters to this newsgroup.
> > Are differences in logical implications between these models
> > empirically testable?
> Yes, they are. Capital reswitching is perfectly observable. It is not,
> however, observed in the data. Since it should be observed if it
> occurs, and it isn't observed, it almost certainly doesn't occur.
There are many curiosities in these unsupported and perhaps
unsupportable assertions.
First, what is Shawn talking about when he mentions "capital
reswitching"? In my explanation of the differences in logical
implications of n-good and one-good models, which, as usual,
Shawn deleted without comment, I only used jargon terms whose
meaning should have been immediately apparent. I am aware of
"perverse capital deepening", "capital reversing", "reswitching",
and "double switching". But Shawn's term is, at best, rarely used.
Second, how can Shawn make these assertions so confidently? As of
a few months ago, he knew nothing about the Cambridge Capital
Controversy. Since he still does not know about Knut Wicksell's
influence on neoclassical economics and still cannot comprehend
a clear explanation of the trivial observation that non-zero price
Wicksell effects usually result in an inequality in the rate of
interest and the marginal product of capital, he obviously still
lacks knowledge of the economic theory of production. So whence
the certainty? Could Shawn be merely repeating authority he does
not comprehend?
Third, how does Shawn propose to observe "capital reswitching",
whatever that is? Is the United States economy, say, always in
a competitive long run equilibrium? How can he tell? How can he
determine what other technique(s) would be cost-minimizing in
some other long run equilibrium? Can he somehow observe all
techniques available at a given point of time? How does
Shawn propose to tell from mere observation that the observed
technique might not be cost minimizing for some other unobserved
distribution of income, with another technique being cost-minimizing
between? The techniques observed in succession in an economy are a
matter of technological improvements, not different techniques
selected out of a given book of blueprints due to price changes.
Fourth, what data has been examined for "capital reswitching"?
Until the first, third, and fourth point are addressed, nobody
should take Shawn's statement above seriously.
> If so, what is the evidence for the restrictions
> > of the neoclassical special case? If there is none, why should
> > economists not use the general model of the choice of technique when
> > using long period models of production?
> Why, exactly, should economists abandon a model that that gives good
> empirical results in favor of one that gives poor empirical results?
Once again, Shawn is not serious in claiming that a model with
neoclassical restrictions has won out against the general model
on empirical grounds. He cannot cite any such empirical contest.
I suspect Shawn does not understand the logical structure of the
models considered in this thread. It is not the case that there are
two competing general non-nested models - one where capital
reversing *must* happen and one where it cannot. Rather, there are
certain general techniques for analyzing the choice of technique in
a long period position [1]. One can show that capital reversing is a
logical possibility in the general case - that is, that capital
reversing does not contradict the axioms. This is shown, for
example, by specific numeric examples.
It is open to question whether there is a general multigood model of
production whose axioms prohibit capital reversing. If there is, it
would be a special case of the general model, formed by including
additional axioms. If neoclassical economists think neoclassical
economics prohibits capital reversing and reswitching, they should
feel obligated to specify those axioms. But they are unwilling
to specify their assumptions. This is not a matter of questioning
the "realism" of assumptions. It is asking to be shown a logically
consistent multigood model. Neoclassical microeconomics, as
understood here, seems to be a failure on grounds of *logical
consistency*. Those who doubt this assertion should specify the
relevant assumptions on technology implying neoclassical
conclusions [2]. If, for example, these assumptions imply equilibrium
prices are equal to labor values, as traditionally understood
in Ricardo and Marx, neoclassical economists should say so.
One special case is a one-good circulating capital model. Since
more than one good is obviously produced in, say, the United
States economy, the United States economy is outside the scope
of this model. The neoclassical economist might reply, though,
that this model works well empirically in the guise of the
Solow growth model or, perhaps, in an alternative of an
overlapping generations model.
However, the empirical data which convinced neoclassical
economists to accept the Solow growth model do not support this
claim. Income distribution between wages and profits were
more or less unchanged in the U.S. between 1940 and 1970.
The ability of a Cobb-Douglas model to fit this data cannot
possibly falsify the Cobb-Douglas model [3]. This fit does
not demonstrate belief in the mechanisms described in the model
has passed falsifying tests.
On the other hand, it has been argued that the using this model
to draw implications from the National Income Accounts misleads
on the sources of technical change. For an empirical use of the
Cambridge Capital Controversy, see:
T. K. Rymes "Fifty Years after the Cambridge Capital Controversy:
Reflections on the Measurement of Capital and Technical Change"
<http://www.ons.gov.uk/data/iariw/iariprog.htm>
(I don't fully understand Rymes paper.)
I think macroeconomists should use models that do not have
stability problems in the context of the general model of
production. Neoclassical models exhibit stability problems
anyways, but reswitching and capital reversing seem to be
an additional source of instabilities.
There are non-neoclassical models of distribution that have
less stability problems. A neoclassical model has lost in one
empirical tournament [4].
> You have made accusations against dedicated students
> and professors, what is your evidence?
Am I permitted to "insult" my fellow amateurs by explaining in great
detail why they are mistaken? Am I allowed to draw any conclusions
from an inability to even recognize an argument or articulate one
in reply? Am I allow to draw any conclusions from continual
distortion, evasion, and avoidance? Given Shawn Wilson's propensity
to post mere abuse, he's obviously not serious in asking such a question.
Notes:
[1] The phrase "long period position" is used in the literature to be
neutral between Classical natural prices and the different neoclassical
theory of long period or long run prices. The Classical theory has
a different view of competition, which is merely a lack of barriers
to entry. Competitive Classical theory is not based on a price-auction
model where firm demand curves are infinitely price-elastic. Classical
theory can also be developed to describe failures of competition. As
a matter of fact, a Classical approach to market structure supposedly
has become more common lately.
[2] Some here have challenged results accepted in the literature (e.g.
by T. Hatta and Paul Samuelson). Those posters have asserted that
neoclassical economics without capital reversing follows from
variable coefficients. By creating an example with variable
coefficients, I have proven this claim mistaken.
[3] Consider the Cobb-Douglas production function:
Y = A * ( K^alpha ) * [ L^( 1 - alpha ) ]
where Y, A, K, and L are all functions of time, "^" denotes exponentiation,
and "*" denotes multiplication. Y and K are measured in the same value
units and L is measured in, say, person-years. The Cobb-Douglas production
function can also be expressed in per capita terms as:
y = A * ( k^alpha )
where y is income per capita and k is capital per worker. Make all of the
neoclassical assumptions, perfect competition, etc. Then the equilibrium
rate of profit, r, is supposedly equal to the marginal product of capital:
r = dY/dK = dy/dk = alpha * A * [ k^( alpha - 1 ) ]
The profit share, x, is
x = r*K/Y = r*k/y = alpha.
So if the neoclassical economist can fit
y = A * ( k^x )
to empirical data, he may think he can claim to have validated this theory.
However, he would be wrong. Given stable income shares, the fit of a
Cobb-Douglas production function to empirical data follows as an little
more than an accounting identity. Such a test fails to demonstrate that
aggregate neoclassical theory can account for income distribution. To see
this, consider the accounting identity
y = w + r k
where w is the wage. Differentiate with respect to time:
dy/dt = dw/dt + k * dr/dt + r * dk/dt
Or
(1/y)*dy/dt =
(w/y)*(1/w)*dw/dt + ( k*r/y )*(1/r)*dr/dt + (r*k/y)*(1/k)*dk/dt
Or
y' = (1 - x)*w' + x*r' + x*k'
where y' is the time rate of growth of y, etc. In other words,
y' = B(t) + x*k'
Assume x is constant with respect to time. Integrate both sides
ln( y ) = x * ln( k ) + C1 + Int B(t) dt
Or
y = C * exp[ Int( B(t) dt ] * k^x
Or
y = A( t ) * k^x
So the ability for data, in which income distribution is roughly stable,
to fit a Cobb-Douglas production function is litte more than an accounting
identity.
Reference:
Anwar Shaikh, "Humbug Production Function," _The New Palgrave:
Capital Theory_, Macmillan, 1990.
[4] Stephen A. Marglin, _Growth, Distribution, and Prices_, Harvard
University Press, 1984.
SUSUPPLY
>There are also communities which welcome economists drawing on
>theories I find persuasive. I have never seen this journal
>in the dead trees version and am not comfortable in French; however,
>writers for the _Cahiers d'économie politique_ is one such
>group, as judged by their online table of contents:
>
> <http://panoramix.univ-paris1.fr/C-ECO-PO/>
>
>(Perhaps Shawn can find somebody to help him with the French.)
While you search for someone to help you with English? And, do these
"communities" have any sharp objects lying around?
>The Orwellian approach of denying the very existence of certain groups
>of economists and scholars seems to be a common non-argument of
>certain posters to this newsgroup.
The Vienneuian--or as an e-mail correspondent suggested to me,
Viennereal--approach (complete fabrication) not being unknown on this newsgroup
either.
> I only used jargon terms whose
>meaning should have been immediately apparent.
You use jargon for exactly the opposite reason, Robert. As is obvious to
everyone.
> Could Shawn be merely repeating authority he does
>not comprehend?
Cute. But speaking of that, how are you doing on the homework assignment Shawn
gave you?
>I suspect Shawn does not understand the logical structure of the
>models considered in this thread.
Then why don't you explain it to him, and us, in clear English?
>One special case is a one-good circulating capital model. Since
>more than one good is obviously produced in, say, the United
>States economy, the United States economy is outside the scope
>of this model.
Which economies are within the scope?
>(I don't fully understand Rymes paper.)
He'd undoubtedly have some problems with you, too.
>Am I permitted to "insult" my fellow amateurs by explaining in great
>detail why they are mistaken?
As I've told you before, this is the internet, you can do anything you like,
including tell lies and make a fool out of yourself. Such as that you confine
your insults to amateurs like Ed Flaherty, Bill Vogt....
> Am I allowed to draw any conclusions
>from an inability to even recognize an argument or articulate one
>in reply?
The rest of us have been doing just that.
> Am I allow to draw any conclusions from continual
>distortion, evasion, and avoidance?
Ditto.
>Given Shawn Wilson's propensity
>to post mere abuse, he's obviously not serious in asking such a question.
Now we know who tutored Bill Clinton for his Grand Jury testimony.
Patrick
Shawn Wilson
Robert Vienneau wrote:
>
> In article <36309781...@uic.edu>, swi...@uic.edu wrote (not in
> the original order):
>
> > > > And what are YOUR qualifications to distinguish truth from error?
>
> > Lo and behold, [capital reswitching] has
> > in fact been abandoned by everyone actually engaged in the profession of
> > economics.
>
> > Robert, after all, is in a decided minority of economic
> > opinion.
>
> > What economics courses have YOU taken at the
> > graduate level?
>
> After going on and on with these sorts of irrelevancies, Shawn is
> hardly justified in suggesting I retract my mild suggestion that
> some economists hold some beliefs for non-cognitive reasons.
If I was wrong, why were you afraid to inclde the remarks I was
responding to? Have you gotten so desperate that you're forced to
resort to out of context quotations?
>
> Although it remains irrelevant to my economic argument, Shawn is
> wrong about what every economist believes.<
Let us refer back to the third quotation of mine that you provided
above. I have been studying economics at an advanced level for many
years. I have read innumerable journel articles on the subject. I
suspect I have an excellent idea of what economists believe. What
exposure have YOU had to the beliefs of economists? Especially, what
exposure have YOU had that allows you to contradict me?
I have demonstrated that
> Paul Samuelson says "there is really nothing pathological" about
> reswitching and capital reversing. Frank Hahn agrees.
It only becomes pathological when it is followed beyond the point at
which it is determined to be a dead end.
>
> There are also communities which welcome economists drawing on
> theories I find persuasive. I have never seen this journal
> in the dead trees version and am not comfortable in French; however,
> writers for the _Cahiers d'économie politique_ is one such
> group, as judged by their online table of contents:
>
> <http://panoramix.univ-paris1.fr/C-ECO-PO/>
>
> (Perhaps Shawn can find somebody to help him with the French.)
> Another journal, the _Review of Political Economy_, has a Web page at:
>
> <http://www.carfax.co.uk/rpe-ad.htm>
>
> This journal, too, is open to articles about some of my favorite
> topics. This one, also, I have never had access to in hardcopy.
>
> The Orwellian approach of denying the very existence of certain groups
> of economists and scholars seems to be a common non-argument of
> certain posters to this newsgroup.
In the last FOURTEEN years the Wilson Social Sciences Index (no
relation) turns up all of FOUR articles on the subject of reswitching,
the last four years ago. How little discourse does there have to be
before a subject is considered dead?
>
> > > Are differences in logical implications between these models
> > > empirically testable?
>
> > Yes, they are. Capital reswitching is perfectly observable. It is not,
> > however, observed in the data. Since it should be observed if it
> > occurs, and it isn't observed, it almost certainly doesn't occur.
>
> There are many curiosities in these unsupported and perhaps
> unsupportable assertions.
>
> First, what is Shawn talking about when he mentions "capital
> reswitching"? In my explanation of the differences in logical
> implications of n-good and one-good models, which, as usual,
> Shawn deleted without comment, I only used jargon terms whose
> meaning should have been immediately apparent. I am aware of
> "perverse capital deepening", "capital reversing", "reswitching",
> and "double switching". But Shawn's term is, at best, rarely used.
Now THAT was funny! After I've been taking you to task, lo these many
posts now, for impenetrable language in one of your posts, YOU take me
to task for using a term which you say is 'rarely used'. Never mind
that it is, in fact, used, or that its meaning was transparent from
context.
BTW, are you even going to admit that you don't actually understand the
stuff you post and pass off as your own?
>
> Second, how can Shawn make these assertions so confidently? As of
> a few months ago, he knew nothing about the Cambridge Capital
> Controversy.
Well, I can use an index. I can observe the lack of unexpected
responses to changes in factor prices in unrelated research. And, I can
observe that the only supporters of the CCC are fools like you who can't
even translate an argument YOU passed of as YOURS into english.
Since he still does not know about Knut Wicksell's
> influence on neoclassical economics and still cannot comprehend
> a clear explanation of the trivial observation that non-zero price
> Wicksell effects usually result in an inequality in the rate of
> interest and the marginal product of capital, he obviously still
> lacks knowledge of the economic theory of production. So whence
> the certainty? Could Shawn be merely repeating authority he does
> not comprehend?
Irony of ironies. Tell us, oh master of the subject, when you will
deign to gift us mere mortals with an explanation of you now famous post
that we can understand?
> Third, how does Shawn propose to observe "capital reswitching",
> whatever that is?
One takes a data series on investment, broken down as far as possible,
and regresses that against a series on interest rates and such other
economic variables as might be relevant. If reswitching exists one
would expect to see a positive response of investment to increases in
the interest rate.
Is the United States economy, say, always in
> a competitive long run equilibrium?
So, what you're saying is that reswitching is only observed in realities
other than this one. Damn, it seems that the relevance of reswitching
just hit zero.
How can he tell? How can he
> determine what other technique(s) would be cost-minimizing in
> some other long run equilibrium? Can he somehow observe all
> techniques available at a given point of time? How does
> Shawn propose to tell from mere observation that the observed
> technique might not be cost minimizing for some other unobserved
> distribution of income, with another technique being cost-minimizing
> between? The techniques observed in succession in an economy are a
> matter of technological improvements, not different techniques
> selected out of a given book of blueprints due to price changes.
You seem to be going to some length to state that reswitching is
entirely irrelevant to the field of economics.
> Fourth, what data has been examined for "capital reswitching"?
See above.
>
> Until the first, third, and fourth point are addressed, nobody
> should take Shawn's statement above seriously.
And until you can provide some reason why reswitching is at all relevant
to descriptions of how the reral economy works...
>
> > If so, what is the evidence for the restrictions
> > > of the neoclassical special case? If there is none, why should
> > > economists not use the general model of the choice of technique when
> > > using long period models of production?
>
> > Why, exactly, should economists abandon a model that that gives good
> > empirical results in favor of one that gives poor empirical results?
>
> Once again, Shawn is not serious in claiming that a model with
> neoclassical restrictions has won out against the general model
> on empirical grounds. He cannot cite any such empirical contest.
What empirical tests have your ideas proved superior in?
>
> I suspect Shawn does not understand the logical structure of the
> models considered in this thread.
It could be, but you have never demonstrated an understanding either.
What is this, post EIGHT in which I've asked you to express that other
post in english?
(snip)
> > You have made accusations against dedicated students
> > and professors, what is your evidence?
>
> Am I permitted to "insult" my fellow amateurs by explaining in great
> detail why they are mistaken? Am I allowed to draw any conclusions
> from an inability to even recognize an argument or articulate one
> in reply? Am I allow to draw any conclusions from continual
> distortion, evasion, and avoidance? Given Shawn Wilson's propensity
> to post mere abuse, he's obviously not serious in asking such a question.
Speaking of avoidance... English?
Finally...
> [3] Consider the Cobb-Douglas production function:
>
> Y = A * ( K^alpha ) * [ L^( 1 - alpha ) ]
>
> where Y, A, K, and L are all functions of time, "^" denotes exponentiation,
> and "*" denotes multiplication. Y and K are measured in the same value
> units and L is measured in, say, person-years. The Cobb-Douglas production
> function can also be expressed in per capita terms as:
>
> y = A * ( k^alpha )
>
> where y is income per capita and k is capital per worker. Make all of the
> neoclassical assumptions, perfect competition, etc. Then the equilibrium
> rate of profit, r, is supposedly equal to the marginal product of capital:
>
> r = dY/dK = dy/dk = alpha * A * [ k^( alpha - 1 ) ]
>
> The profit share, x, is
>
> x = r*K/Y = r*k/y = alpha.
Too bad. You screwed up yet again. That isn't the profit share, its
the capital share. You didn't model profits. It's realy sad how
incapable you are of learning the difference between interest and
profits.
> So if the neoclassical economist can fit
>
> y = A * ( k^x )
>
> to empirical data, he may think he can claim to have validated this theory.
No. When an economist can equate, through empirical data, the marginal
product of capital with the sum of the rate of time preference,
depreciation, and the population growth rate, THEN he can say he has
validated his theory. Yes, it's been done. Actually, it's easy.
> However, he would be wrong. Given stable income shares, the fit of a
> Cobb-Douglas production function to empirical data follows as an little
> more than an accounting identity. Such a test fails to demonstrate that
> aggregate neoclassical theory can account for income distribution. To see
> this, consider the accounting identity
See above.
(snip)
> So the ability for data, in which income distribution is roughly stable,
> to fit a Cobb-Douglas production function is litte more than an accounting
> identity.
Or not.
Mark Patrick Witte
While it's always gratifying to have someone say something nice,
this does strike me as a strange use for an adult's time (to paraphrase
John Panzar).