Rising Interest Rates is Inflationary?
Anil Das
came out, there were several analysts called in by radio stations
etc, to analyse the effect it will have.
According to the guy I heard on radio, who is an
investment analyst or some such, the Fed's action is inflationary.
His argument is that since people know that interest rates are
going up, they will try to buy houses etc, before the rates go
up again, thus increasing the demand for money.
Also, according to him, the rise in inventories is
a consequence of people anticipating interest rate hikes. Again,
the principle of `buy before rates go up', and this inventory
will also lead to inflation.
Is he talking thru his hat? What I learned in my economics
class is that inflation is related to the rate of change in
economic growth, not the rate of change of interest rates.
What he said seemed to make sense at that time though.
--
Anil Das an...@nskernel.tandem.com
Patrick Powers
I would agree that such a tendency exists, particularly with
house buying. I would speculate that this is the motive behind
the much-attacked efforts by the Federal Reserve to raise short-term rates
aggressively. Raising the short term rates rapidly increases
confidence in long-term stability amongst lenders, thus stabilizing or
even lowering long term rates and averting 'must buy NOW' panic.
Raising short term rates cautiously and slowly has the opposite effect.
In my casual estimation the Fed has been very successful with this
policy.
snef
wrote:
well yes it may be that the rate of growth of econ
activity dE/dt is proportional to the rate of increase
of the cost of money dI/dt or (very simplified)
dE/dt = A*dI/dt
At the same time other factors come into play,
that is, the rate of growth is also inversely proportional
to the cost of money,
dE/dt = -BI
As I increases (+ dI/dt) the latter factor becomes larger
at some point, stopping off growth. The factors A and B are
frequency dependent so they have different time lags which, in
fact, push dE/dt negative (i.e. recession). Seems to me that
we have just about reached the point where the boost to
dE/dt from positive dI/dt is spent and that we are headed for
recession in the near future.
s
gn842
>
>
>I would agree that such a tendency exists, particularly with
>house buying. I would speculate that this is the motive behind
>the much-attacked efforts by the Federal Reserve to raise short-term rates
>aggressively. Raising the short term rates rapidly increases
>confidence in long-term stability amongst lenders, thus stabilizing or
>even lowering long term rates and averting 'must buy NOW' panic.
>Raising short term rates cautiously and slowly has the opposite effect.
>
>In my casual estimation the Fed has been very successful with this
>policy.
Let's not forget that raising the cost of capital, while deflationary
in that it slows down demand, also has an inflationary impact because
it is, after all, an increase in a major factor cost. Firms in
non-competitive environments w/inflexible demand curves would simply
pass these costs along to consumers. I suspect therefore that the
use of interest rates to control the economy is a very unwieldy
club which may by itself contribute to "stagflation" (note I
said *contribute*) because rising capital costs would translate into
higher prices in some areas while causing an overall decrease in
economic activity. In other words, the effects can be particularly
brutal because the sectors which are "relatively impervious" to the
increase in capital costs hold their own and the sectors which are
capital sensitive have to do "double penance": the decrease in THEIR
activity must be strong enough not only to counter the "general
inflation" but to counter the "interest-rate caused" inflation. Another
way of saying this is that there is probably a core of "privileged
sectors" who are relatively indifferent to monetary policy while
the others are left holding the bag. It is clear that one of the
principal victims of the policy is the housing/construction market,
which in Olsonian terms makes sense, since the "collective action"
problem of these firms in terms of organizing to defend themselves
politically are much greater than that of more concentrated sectors.
Edward Flaherty
to the marginal product of capital. Rising interest rates could be the
effect of an increase in the marginal product of capital, thereby
increasing the demand loanable funds.
--
Edward Flaherty
Department of Economics
Florida State University
efla...@garnet.acns.fsu.edu
mos...@gate.net
1. The government is a net payer of interest. To the extent that higher rates increases the
deficit, more "money" is being created. However, the new money created is often almost
0 velocity. That is, it has almost no effect on inflation. Many of the receivers of government
interest payments, such as pension funds, insurance companies, etc. actually spend very little
of any new money received in this manner.
2. A transfer between borrowers and lenders takes place. People with savings get more, those
in debt get less. This shift can be disruptive, with some industries doing better and some worse.
The immediate effect, or shock value, of disruption is often a slow down.
3. HIgher rates have a deleveraging effect. Marginal buyers/borrowers fail to qualify for credit, and
may be forced into default on existing loans. This reduces money supply. For Fed policy to have
this effect, 3 must overcome 1.
4. Anticipatory borrowing can increase the money supply. However, that assumes some pent up
demand that is "on the fence" with its borrowing decisions.
5. Speculative money can have an effect, that is offset when the speculator unwinds the position.
This can also be disruptive.
Changing the short term interest rate is a very blunt instrument, but it is about all the Fed has direct
control over. Fiscal policy has a vast amount of options, many of which directly affect the quantity
of money, who gets it, and the very incentives that drive the economy. However, changes must
be debated and voted on by Congress, so the Fed is often carrying the burden with its very limited
tools.
Robert Vienneau
These assertions were shown to be wrong three decades ago during the
Cambridge Capital Controversies. All sides to the debate agreed they
were wrong.
Robert Vienneau
--
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Edward Flaherty
> In article <3h1iob$8...@mailer.fsu.edu> efla...@garnet.acns.fsu.edu (Edward Flaherty) writes:
> > Neither let us forget that the real interest rate is equivalent
> >to the marginal product of capital. Rising interest rates could be the
> >effect of an increase in the marginal product of capital, thereby
> >increasing the demand loanable funds.
>
> Cambridge Capital Controversies. All sides to the debate agreed they
> were wrong.
Tell that to Lucas.
gn842
>
>> @albany.edu (gn842) writes:
>> In article <3gtn2h$s...@bigblue.oit.unc.edu>, pow...@goofy.stat.unc.edu (Patrick Powers) says:
>> >
>> >I would agree that such a tendency exists, particularly with
>> >house buying. I would speculate that this is the motive behind
>> >the much-attacked efforts by the Federal Reserve to raise short-term rates
>> >aggressively. Raising the short term rates rapidly increases
>> >confidence in long-term stability amongst lenders, thus stabilizing or
>> >even lowering long term rates and averting 'must buy NOW' panic.
>> >Raising short term rates cautiously and slowly has the opposite effect.
>> >
>> >In my casual estimation the Fed has been very successful with this
>> >policy.
>>
>> Let's not forget that raising the cost of capital, while deflationary
>> in that it slows down demand, also has an inflationary impact because
>> it is, after all, an increase in a major factor cost. Firms in
>> non-competitive environments w/inflexible demand curves would simply
>> pass these costs along to consumers. I suspect therefore that the
>> use of interest rates to control the economy is a very unwieldy
>> club which may by itself contribute to "stagflation" (note I
>> said *contribute*) because rising capital costs would translate into
>> higher prices in some areas while causing an overall decrease in
>> economic activity. In other words, the effects can be particularly
>> brutal because the sectors which are "relatively impervious" to the
>> increase in capital costs hold their own and the sectors which are
>> capital sensitive have to do "double penance": the decrease in THEIR
>> activity must be strong enough not only to counter the "general
>> inflation" but to counter the "interest-rate caused" inflation. Another
>> way of saying this is that there is probably a core of "privileged
>> sectors" who are relatively indifferent to monetary policy while
>> the others are left holding the bag. It is clear that one of the
>> principal victims of the policy is the housing/construction market,
>> which in Olsonian terms makes sense, since the "collective action"
>> problem of these firms in terms of organizing to defend themselves
>> politically are much greater than that of more concentrated sectors.
>>
>>>>>
>
>1. The government is a net payer of interest. To the extent that higher rates increases the
> deficit, more "money" is being created. However, the new money created is often almost
> 0 velocity. That is, it has almost no effect on inflation. Many of the receivers of government
> interest payments, such as pension funds, insurance companies, etc. actually spend very little
> of any new money received in this manner.
>
You've argued this before and I would like to make sure that I have
your argument right (BTW you write a bit too wide for my screen).
I'm the government, I issue a bond. Someone pays me for the bond.
I take the money and spend it. Those bucks fly out into the economy
and are in essence transferred (hence the term transfer payments).
I give the bond buyer a piece of paper that says IOU. This piece of
paper is itself a negotiable instrument.
Therefore, government debt increase the money supply.
But, $100,000+ denomination bonds are not your most liquid form of
money. They would typically only be used in Very Large Transactions
like buying GM or the Rockefeller Plaza, where participants find it
easier to transfer bond ownership than to liquidate the bond, dump
it in a bank, and then buy another bond. Consequently, I have
learned from other correspondence, the addition to the money supply
is in "L" not in "M1."
I don't see why you raise the issue of interest payments on the bond
as a money supply issue because this is reverse transfer payment
(unless funded by more debt) and should be neutral w/regard to the
money supply.
Thanks again for your help. Please check out the thread on
the myth of the multiplier for more fun requests for clear thinkiing
and clarifications!
P.S. FYI Hamilton in the Report on Manufactures (1793) proposed
bond issuance "funded debt" as a means to retore liquidity to a
chronically imbalanced economy. It was clear that he thought the
bonds could circulate as exchange instruments even though the trade
imbalance was sending gold to England. Hamilton argued that the
gain in liquidity TODAY was wortth more than the loss of liquidity
TOMORROW (since many bonds were held in England), because liquidity
TODAY meant economic growth that would better prepare one for tomorrow.
Robert Vienneau
>Robert....@launchpad.unc.edu (Robert Vienneau) writes:
>> In article <3h1iob$8...@mailer.fsu.edu> efla...@garnet.acns.fsu.edu (Edward Flaherty) writes:
>> >capital...
>> These assertions were shown to be wrong three decades ago...
> Tell that to Lucas.
Dr. Flaherty is almost certainly more familiar with the writings of
Robert Lucas than I am. But as far as I know Lucas has never commented
on findings accepted or discovered by, say, Samuelson, F. Fisher,
Bliss, or Hahn. Instead he just uses models and techniques known
to have no valid theoretical or empirical foundation. This disregard
of established results is hardly likely to increase respect for
(schools of) economics.
Mark Witte
Robert Vienneau <Robert....@launchpad.unc.edu> wrote:
>efla...@garnet.acns.fsu.edu (Edward Flaherty) writes:
>>Robert....@launchpad.unc.edu (Robert Vienneau) writes:
>>> In article <3h1iob$8...@mailer.fsu.edu> efla...@garnet.acns.fsu.edu (Edward Flaherty) writes:
>>> >...the real interest rate is equivalent to the marginal product of
>>> >capital...
>>> These assertions were shown to be wrong three decades ago...
>> Tell that to Lucas.
>
>Dr. Flaherty is almost certainly more familiar with the writings of
>Robert Lucas than I am. But as far as I know Lucas has never commented
>on findings accepted or discovered by, say, Samuelson, F. Fisher,
>Bliss, or Hahn. Instead he just uses models and techniques known
>to have no valid theoretical or empirical foundation. This disregard
>of established results is hardly likely to increase respect for
>(schools of) economics.
> Robert Vienneau
Your first sentence seems correct but after that you seem to get in some
trouble. Lucas is a macro economist and I really can't think of any
contributions to modern macro from Bliss or F. Fisher. Checking both sides of
the isle, I looked in Sargent and in Blanchard and Fischer and find no
references for either of them. I've read papers by Bliss but for the life of
me, I can't think of who F. Fisher is. Stan Fischer? Irving Fisher? Lucas
is a busy guy, he doesn't have time to comment on everyone, even on every
economist.
His work has touched on that of (Paul) Samuelson and (Frank, not Robert) Hahn.
Lucas used an uncertainty over information structure similar to Samuelson's
asset pricing paper (1965) for his "Some international evidence..."(1973)
paper. I'm pretty sure he had plenty of other references as well.
Lucas has certainly done Hahn related work with his growth models and
asset pricing literature which examined issues in unstable equilibria like in
Hahn's 1968 "Growth Path" paper.
Criticising Lucas for being unfamiliar with the literature is like accusing
his work of lacking theoretical or empirical support. It's OK not to like
him, but you have to work pretty hard to discredit him. It's worth doing
though, you would get tenure and probably an endowed chair out of it, and
change the way modern macroeconomists think about the world.
Edward Flaherty
> Dr. Flaherty is almost certainly more familiar with the writings of
> Robert Lucas than I am. But as far as I know Lucas has never commented
> on findings accepted or discovered by, say, Samuelson, F. Fisher,
> Bliss, or Hahn. Instead he just uses models and techniques known
> to have no valid theoretical or empirical foundation. This disregard
> of established results is hardly likely to increase respect for
> (schools of) economics.
First, I'm not a phd, only a lowly phd candidate. Second, while I'm
not familiar with the body of literature that discredited a crucial
pillar of classical microeconomics, Lucas, Romer, Cooley, et al, have
enjoyed quite a bit of empirical success with their endogenous growth
models that include the 'flawed' condition that MPk = r.
Robert Vienneau
common knowledge if economics were properly taught.
To begin in the middle, Paul Samuelson attempted to justify applying
marginal productivity theory to aggregate production functions in
"Parable and Realism is Capital Theory: The Surrogate Production
Function" (Review of Econ. Stud., Vol. 39, Number 3, 1962). At this
point, he was addressing Joan Robinson and did not understand the
implications of Sraffa. He made some assumptions - basically that a
simple labor theory of value holds - whose extreme restrictiveness he
did not understand.
Amit Bhaduri contributed two of the more insightful demonstrations that
the interest rate does not equal the marginal product of capital, "The
Concept of the Marginal Productivity of Capital and the Wicksell
Effect" (Oxford Econ. Papers, V. 18, No. 3, 1966) and "On the
Significance of Recent Controversies on Capital Theory: A Marxian View"
(Econ. Journal, V. 79, 1969).
For those who have read my posts on this theme before, I note that
Bhaduri's argument depends on neither reswitching nor capital
reversing. Pierangelo Garegnani showed what was wrong with Samuelson's
framework along these lines in "Heterogeneous Capital, the Production
Function, and the Theory of Distribution" (Rev. Econ. Studies., V.37,
No. 3, 1970). Paul Samuelson accepted the logic of these criticisms of
aggregated Neoclassical theory in his contribution to the symposium on
paradoxes in capital theory - "A Summing Up" (Quarterly Journ. on
Econ., V. 80, No. 4, 1966.)
The Cambridge Capital Controversy was a complex and multifaceted
affair. Two important Neoclassical summaries are Christopher Bliss'
book "Capital Theory and the Distribution of Income" (1975) and Frank
Hahn's paper "The Neo-Ricardians" (Cambridge Journal of Economics, V.
6, No. 4, 1982). Although Bliss and Hahn are not in total agreement,
they both argue that disaggregated Neoclassical theory is sound and
does not need an equation equating the demand and supply of "capital."
Franklin M. Fisher had an interesting contribution. He showed, via
simulation, that a Cobb-Douglas aggregate production function could fit
data generated by any process, provided only that income distribution
remained roughly constant. Since income distribution is very stable in
the real world, the ability of a Cobb-Douglas function to fit empirical
time series is no demonstration that such a function provides any
insight into actual mechanisms determining income distribution.
Macroeconomics can proceed forward without assuming that the interest
rate is equal to the marginal product of "capital." Paul Davidson shows
that in his new book "Post Keynesian Macroeconomic Theory" (Edward
Elgar, 1994). (I wonder which "side of the aisle" Mark Witte would
place this. Perhaps he's in the wrong church.)
Steven E. McIntosh
: According to the guy I heard on radio, who is an
: investment analyst or some such, the Fed's action is inflationary.
: His argument is that since people know that interest rates are
: going up, they will try to buy houses etc, before the rates go
: up again, thus increasing the demand for money.
: Also, according to him, the rise in inventories is
: a consequence of people anticipating interest rate hikes. Again,
: the principle of `buy before rates go up', and this inventory
: will also lead to inflation.
: Is he talking thru his hat? What I learned in my economics
: class is that inflation is related to the rate of change in
: economic growth, not the rate of change of interest rates.
: What he said seemed to make sense at that time though.
This is a relatively weak argument because not only does buying a house
relate to long-term interest rates (not the short-term rates the Fed is
raising) but interest rate hikes and cuts are based on the economic
growth rate and the inflationary expectation. Holding growth constant,
interest rates rise when inflation is expected to rise. Interest rates
also rise when inflation is constant but growth rises. Higher interest
rates have the effect of slowing down economic growth because increased
capital costs and decreasing inflationary EXPECTATIONS because of a
greater incentive to save, as well as discouraging short-term borrowing.
If what he was saying was true, the Fed would attack inflation by
lowering interest rates, but that could only be done if they expected
inflation and/or growth to decrease in the first place. Even if what
hesaid was true (assuming that the people are mistaken in their
knowledge about monetary dynamics) it wouldn't be repeated too many
times because long term rates such as mortgages could very well go down
as short term rates go up during tight money inverted rate curves.
The number of people who would try to "take advantage" of such perceived
"bargain basement" money prices are relatively few. Most people aren't
speculators, and even if they were, they would find better opportunities
elsewhere. Such an effect, if it exists, would not be felt by the
economy or the market.
The Fed is raising rates because they see commodity prices rising and
they view this as the first sign of rising inflation. Because of this,
they expect inflation to rise, so they raise interest rates, since they
forecast a constant economic growth rate. If economic growth were
falling they wouldn't raise interest rates and would lower them if it
were falling enough. But since it is rising, they are raising rates.
It's not inflation that really worries the Fed right now, except in
relation to commodity prices, because inflation was only 2.7% last year.
What really worries them is too much growth, which would really raise
interest rates, even if inflation remained constant. They are raising
rates now so they don't have to raise them more down the road. You may
believe that growth is always good, no matter how much, but to great of
a growth rate strips out resources. This leads to higher commodity
prices, leading to higher prices for finished goods, leading to a
decrease in the quantity of finished goods demanded, which leads to
a decrease in supply, which is stagflation.
Mark Witte
"Give me that old time religion!"
- Mark Witte
In a math class I once took, a student was doing a proof on the board. He
skipped a step in his presentation and referenced some other known proof as
establishing the validity of this step. The professor would have none of that
and said that if the student could not clearly explain in words what he was
doing there, then he really did not understand.
The interest rate and the investment which determine the marginal product of
capital are both subject to some future uncertainty over realization. You had
a complaint about how Robert Lucas' work neglected (or was contradicted by)
the above economists. Lucas certainly moved the fields' understanding of
modelling expectations forward.
In a world with capital, why wouldn't the currect expected marginal product of
capital over some future interval be equal to the expected interest rate over
that period (ignoring inflation and risk premia)?
Suppose the interest rate were less than the marginal product of capital.
Borrowing and building capital would earn a positive return so simple
arbitrage would drive them together. Suppose the interest rate were above the
marginal product of capital. How could loans to finance capital purchases
then ever be repaid? So investment would fall, allowing depreciation to raise
the marginal product of capital until it reached the interest rate.
Can you explain why the above gentlemen's work would overturn this logic?
Robert Vienneau
between them.
The first story is about a totally disaggregated world in equilibrium:
>>It will be a long time before a broker calls any of us with
>>a deal on a unit of "capital". We can buy bread and clothing.
>>Although I do not have much use for such goods, I could
>>buy pig iron or steel. The market for second-hand factories
>>is thin, but I can easily buy shares in firms that own
>>factories.
>Bread? Clothing? My grandfather chuckles when economists talk
>about the price of apples. He points out that there are so many
>grades and types of apples, each with it's own price, that the
>abstraction ignores much that is important. However, he would
>agree that the abstraction contains a valuable reflection of the
>underlying principle of supply and demand.
I meant to suggest specific qualities of goods. Maybe I should
have written about specific items of clothing or "Number 2 Red
Winter Wheat" available in Minneapolis in a week's time.
>>In Neoclassical competitive equilibrium, shares in firms
>>will not yield profits, for there are no pure profits to
>>be had. Of course, all prices must be discounted to a single
>>instant in time. Interest rates are used in determining the
>>rental price of specific capital goods.
>So in the neoclassical model, competitive forces would drive
>the interest rate and marginal product of capital to equality
>so as to keep the economy at zero economic profit. So....
Wrong. The price of each and every factor service, including
the services of individual "capital goods" can be assumed to
be equal to their values of the marginal product. There is
no economic profit. My claim is there is no good in this model
called "capital." So the interest rate cannot be said to be
equated to the marginal product of anything. That is...
>>But nowhere do I see a good called "capital" whose price is an
>>interest rate and which can have a marginal product.
>This is news to firms and the IRS which concern themselves
>with capital depletion allowances and the like. [misdirected
>sarcasm deleted]
I'm talking about the rigorous logic of a model, not the loose
way of talking in the real world. Anyway, accounting rules
have a large amount of convention that cannot be relied
upon for understanding the logic of profit-maximizing,
especially when it comes to depreciation.
Let's move on explicitly to the second story of an
aggregated world:
>>Perhaps Mark Witte is thinking of certain models with aggregate
>>production functions Y = F( L, K ). But a look at units ought
>>to raise questions here. The price of labor, the wage, is
>>in terms of the numeraire per *person-hour*. No such physical
>I think the usual numeraire is the output good.
Right. But the point is that labor is measured in person-hours,
a different unit than the numeraire. *In what units is "capital"
measured?*
>>dimension enters into the interest rate, the supposed price
>>of "capital." So what are the units for measuring "capital?"
>>Is it purely a value unit? Is the interest rate used for
>>discounting future yields to obtain its measure? If the
>>interest rate must be given to measure capital, how can
>>the marginal product of capital then be said to determine
>>the interest rate?
>I would suggest R.G.D. Allen's _Macro-Economic Theory_. I
>know, I know, it came out in 1967 and so represents this
>wild new approach to economics but it's a nice read. There
>are some simple models in there.
It's weird to suggest to me that logic would be outdated just
because it's old. It's outdated if later developments have shown
it to be wrong or based on unstated arbitrary assumptions. Or,
in economics, if changes in institutions have made it irrelevant.
I assume Allen presents one good models in which labor and a
single good can be used to produce more of that good. The
good can be used either for consumption or as a capital
good.
But what about 2-good models in which labor and an input
can be used to produce either more of that input or a
capital good? How is this story cast into an aggregate
production function? (Remember Mark Witte insisted
that one could not just call on references, and must put
the argument in English.)
Now in trying to explain this aggregate story Mark laspes
back into the disaggregated story without noticing the
difference. He also implicitly assumes with inadequate
justification that dynamics are well-behaved and that
prices are scarcity indices in models with accumulation
of capital goods. This is mistaken. He uses the
term "depreciation" in an unusual fashion.
>Here is a reprise of my simple story. In allocating savings,
>it is nice to pursue the highest risk adjusted rate of return
>possible for a given maturity (an efficient point on that
>frontier). If investing in K5984 drill presses will earn profits
>which are greater than the going return for that level of
>risk, then many K5984 drill presses will be bought until the
>profit on such machine is just about equal to the opportunity
>cost of funds. If the profit on K5984 drill presses were less
>than the risk adjusted going rate of return for a given maturity,
>few K5984 drill presses would be bought until depreciation
>increased their scarcity to the point where the profit of
>investing in them was equal to the opportunity cost of funds,
>which might for simplicity be called "the interest rate"
>although it is closer to being "an interest rate."
For simplicitly, I have been willing to abstract from a structure
of interest rates reflecting different degrees of risk.
>This took me twelve lines, last time I told this story it only took
>me six line. Oh well, inflation I guess. I confess that there
>really is no such thing as the K5984 drill press, it is an
>abstraction like "bread" or "clothes" or "apples." If it makes
>it clearer for you, substitute in Steelcase Model 233 chair
>instead of K5984 drill press. Such chairs actually exist, I'm
>sitting on one.
>So does the interest rate have nothing to do with how much
>firms might spend on different durable inputs? Is there a
>similar indifference to the interest rate when choosing
>financial assets?
Whatever I think about the relationship between the choice
of technique in a state of given technical knowledge and the
real world is irrelevant to my point about the lack of
connection between these two stories.
I do have problems with the claim that in Neoclassical
models, the rate of return is the same in all lines of
production, abstracting from risk. For the sake of
argument, we can assume that endowments just happen
to be such that all own rates of interest are equal for
all produced means of production actually produced.
I hope the above has clarified my point. Now for a polemical
sequel.
>>The miseducation of economists begins with the first page
>>of their first textbook when they are told that the returns
>>to "Land", "Labor", and "Capital" are rent, wages, and interest.
>>How many are told about the apologetic role of that trinitarian
>>formula in the history of economic thought?
>I think the miseducation of economists began with Adam Smith and
>David Ricardo. Smith way oversimplied the workings of a pin factory.
>And what was Ricardo thinking with all these abstractions in his
>models? If only we had a nice methodology like those sociologists
>we are always admiring.
One of my favorite economists Nicholas Kaldor thought economics
went wrong with Book I, Chapter V of the Wealth of Nations where
Smith replaced investigation of "improvements in the productive
powers of labour" with the determinants of price. (Somehow Varian's
text manages to adopt Kaldor's argument of the ubiquity of increasing
returns while dropping his claim that they are subversive of
traditional teaching.)
I do not object to abstractions per se. I do not know what the correct
balance should be between economic sociology and theory, but, with
Schumpeter, think there should be some sociology in economics. I
admire both Smith and Ricardo. I am undecided about who is better,
whether I prefer the pure theoretical abstractions of Ricardo or the
keen sociological insights of Smith. But this has nothing to do with
my argument about the marginal product of "capital."
Robert Vienneau
-------------------------------------------------------------
There is a general theoretical agreement (which is ignored in a
scandalous way about the untenability of neoclassical theories
that take their point of departure from aggregate capital.
-- Bertram Schefold
-------------------------------------------------------------
Mark Witte
Robert Vienneau <Robert....@launchpad.unc.edu> wrote:
>Mark Witte tells two stories without realizing there is no connection
>between them.
Well no, I tell the same story twice hoping that one of them gets through.
Neither seems to.
>
>The first story is about a totally disaggregated world in equilibrium:
>
>>>It will be a long time before a broker calls any of us with
>>>a deal on a unit of "capital". We can buy bread and clothing.
>>>Although I do not have much use for such goods, I could
>>>buy pig iron or steel. The market for second-hand factories
>>>is thin, but I can easily buy shares in firms that own
>>>factories.
>
>>Bread? Clothing? My grandfather chuckles when economists talk
>>about the price of apples. He points out that there are so many
>>grades and types of apples, each with it's own price, that the
>>abstraction ignores much that is important. However, he would
>>agree that the abstraction contains a valuable reflection of the
>>underlying principle of supply and demand.
>
>I meant to suggest specific qualities of goods. Maybe I should
>have written about specific items of clothing or "Number 2 Red
>Winter Wheat" available in Minneapolis in a week's time.
Your point was to ridicule the idea of an aggregated investment good called
capital. I point out that aggregation is so common in economics that we often
lose sight of how much we really use it. Fortunately, we can talk about the
markets for apples and capital without getting confused (or most of us can).
Maybe I should have written about specific items of capital like a "tan
Steelcase Chair Model #233 in my office right now."
>
>>>In Neoclassical competitive equilibrium, shares in firms
>>>will not yield profits, for there are no pure profits to
>>>be had. Of course, all prices must be discounted to a single
>>>instant in time. Interest rates are used in determining the
>>>rental price of specific capital goods.
>
>>So in the neoclassical model, competitive forces would drive
>>the interest rate and marginal product of capital to equality
>>so as to keep the economy at zero economic profit. So....
^^^^^^^^^^^^^^^^^^^^
>
>Wrong. The price of each and every factor service, including
>the services of individual "capital goods" can be assumed to
>be equal to their values of the marginal product. There is
>no economic profit. My claim is there is no good in this model
My eyes widen in disbelief that you don't understand as basic a
concept to our field as "zero economic profit." This may be at
the root of your problems.
>called "capital." So the interest rate cannot be said to be
>equated to the marginal product of anything. That is...
>
>>>But nowhere do I see a good called "capital" whose price is an
>>>interest rate and which can have a marginal product.
>
>>This is news to firms and the IRS which concern themselves
>>with capital depletion allowances and the like. [misdirected
>>sarcasm deleted]
>
>I'm talking about the rigorous logic of a model, not the loose
>way of talking in the real world. Anyway, accounting rules
>have a large amount of convention that cannot be relied
>upon for understanding the logic of profit-maximizing,
>especially when it comes to depreciation.
I'll get to the first line of this paragraph in a moment. The lines following
it seem to indicated that you recognize that "capital" is not quite as
mythological good you first suggested.
I've put forward several versions of the simple neo-classical model where
arbitrage would drive the interest rate and the marginal product of capital to
equality. You may have talked about rigorous models but they have yet to be
seen on this thread. I'll try again.
Hmm, a model. The usual assumptions apply.
(I) Y(t) = F(K(t), N)
(II) Y(t) = C(t) + [K(t+1) - (1-d)*K(t)] d = depreciation rate
(III) U = Sum from 0 to infinity of B^t * u(C(t)) 0<B<1
(IV) Some appropriate transversality condition.
Max (III) st (I) and (II) and (IV) over the K process.
Yields FOC: B^t * (F'(K(t)) + (1-d)) - B^(t-1) = 0
(F' + (1-d)) = 1/B
Net marginal product of capital = 1/(rate of time preference)
= interest rate or return necessary to compensate for the delayed
consumption the capital represents.
This is the standard Ramsey result with discounting, the (net) marginal
product of capital is equal to the interest rate.
>
>Let's move on explicitly to the second story of an
>aggregated world:
>
>>>Perhaps Mark Witte is thinking of certain models with aggregate
>>>production functions Y = F( L, K ). But a look at units ought
>>>to raise questions here. The price of labor, the wage, is
>>>in terms of the numeraire per *person-hour*. No such physical
>
>>I think the usual numeraire is the output good.
>
>Right. But the point is that labor is measured in person-hours,
>a different unit than the numeraire. *In what units is "capital"
>measured?*
It is measured in the same units as the consumption good since in the simple
neo-classical model there is direct convertability between the captial and the
consumption good.
>
>>>dimension enters into the interest rate, the supposed price
>>>of "capital." So what are the units for measuring "capital?"
>>>Is it purely a value unit? Is the interest rate used for
>>>discounting future yields to obtain its measure? If the
>>>interest rate must be given to measure capital, how can
>>>the marginal product of capital then be said to determine
>>>the interest rate?
>
>>I would suggest R.G.D. Allen's _Macro-Economic Theory_. I
>>know, I know, it came out in 1967 and so represents this
>>wild new approach to economics but it's a nice read. There
>>are some simple models in there.
>
>It's weird to suggest to me that logic would be outdated just
>because it's old. It's outdated if later developments have shown
>it to be wrong or based on unstated arbitrary assumptions. Or,
>in economics, if changes in institutions have made it irrelevant.
I would not suggest that logic spoils with age just as I would not suggest
that anything new is worthless. I put forward the Allen book because it is
widely seen as a classic exposition of the types of models which seem to
trouble you so.
>
>I assume Allen presents one good models in which labor and a
>single good can be used to produce more of that good. The
>good can be used either for consumption or as a capital
>good.
>
>But what about 2-good models in which labor and an input
>can be used to produce either more of that input or a
>capital good? How is this story cast into an aggregate
>production function? (Remember Mark Witte insisted
>that one could not just call on references, and must put
>the argument in English.)
You want references to non-reversable investment? Jesus, there's certainly a
huge literature there. For me to answer you question you will have to specify
the shock process to the system. If it is a perfect certainty world, then the
ex ante equivalence between the consumption and investment goods would be
maintained ex post so the relative price and therefore the units would be the
same. In a stochastic model, the price/unit relation between capital and
consumption goods would be the same ex ante, would vary as the shocks moved
the marginal product of capital (assuming lags to adjustment or time to build
technologies), and would tend toward equality in their ergotic distributions.
Anticipating your next post, 3-good models (government or human capital, for
instance) would work the same way.
>
>Now in trying to explain this aggregate story Mark laspes
>back into the disaggregated story without noticing the
>difference.
Well, no. I disaggregate because you complain that there is no such thing as
"capital." So I make up a good which might be considered capital and show how
it obeys the simple dynamics of the neo-classical model. Ah, but this is not
the aggregate capital good, it is a disaggregate capital good. But by
arbitrage, all capital goods would follow the same process so this
"representative" capital good behaves just as the aggregate capital good
(adjusting for differences in risk, depreication, etc).
>He also implicitly assumes with inadequate
>justification that dynamics are well-behaved and that
>prices are scarcity indices in models with accumulation
>of capital goods. This is mistaken. He uses the
>term "depreciation" in an unusual fashion.
I was assuming the usual neo-classical exponential depreciation. Since that's
the model which got us into this discussion, that's the depreciation
formulation I used. Nothing unusual here to economists.
>
>>Here is a reprise of my simple story. In allocating savings,
>>it is nice to pursue the highest risk adjusted rate of return
>>possible for a given maturity (an efficient point on that
>>frontier). If investing in K5984 drill presses will earn profits
>>which are greater than the going return for that level of
>>risk, then many K5984 drill presses will be bought until the
>>profit on such machine is just about equal to the opportunity
>>cost of funds. If the profit on K5984 drill presses were less
>>than the risk adjusted going rate of return for a given maturity,
>>few K5984 drill presses would be bought until depreciation
>>increased their scarcity to the point where the profit of
>>investing in them was equal to the opportunity cost of funds,
>>which might for simplicity be called "the interest rate"
>>although it is closer to being "an interest rate."
>
>For simplicitly, I have been willing to abstract from a structure
>of interest rates reflecting different degrees of risk.
I just added this to head off pointless quibbles (like about a 2-good
model).
>
>>This took me twelve lines, last time I told this story it only took
>>me six line. Oh well, inflation I guess. I confess that there
>>really is no such thing as the K5984 drill press, it is an
>>abstraction like "bread" or "clothes" or "apples." If it makes
>>it clearer for you, substitute in Steelcase Model 233 chair
>>instead of K5984 drill press. Such chairs actually exist, I'm
>>sitting on one.
>
>>So does the interest rate have nothing to do with how much
>>firms might spend on different durable inputs? Is there a
>>similar indifference to the interest rate when choosing
>>financial assets?
>
>Whatever I think about the relationship between the choice
>of technique in a state of given technical knowledge and the
>real world is irrelevant to my point about the lack of
>connection between these two stories.
>
>I do have problems with the claim that in Neoclassical
>models, the rate of return is the same in all lines of
>production, abstracting from risk. For the sake of
>argument, we can assume that endowments just happen
>to be such that all own rates of interest are equal for
>all produced means of production actually produced.
This is straight out of Ricardo's "falling rate of profit." Lines of
production in the neo-classical model which pay a higher rate of return will
attract resouces from other areas until the zero economic profit condition
holds everywhere. The neo-classical model is an allocative general
equilibrium model with mobile factors so that endowments don't really come
into it.
[Fairly off the subject discussion of the history of economic thought
deleted.]
Let's cut to the chase. You said Lucas' work was silly because it depended
upon equating the marginal product of capital with the interest rate. I
replied with an example of why such equality would be expected to hold
in a simple model. I asked for a simple model which would contradict this
logic. Sure the neo-classical model does not have every bell and whistle in
the world, but what important factor overturns its result?
Robert Vienneau
Since Mark Witte seems to identify rigor with math, let's do some math.
Consider an economy which produces a single consumption good, corn,
measured in bushels, and a single capital good, steel, measured in
tons. Suppose firms have selected a profit-maximizing production
technique in which A unassisted person years hired at the beginning of
the year produce one ton of steel available at the end of the year.
Steel lasts forever unchanged. Suppose B person-years, applied to one
ton steel, produce one corn in one year. Let w denote the wage paid to
the workers at the end of the year, r the rate of interest, and p the
price of a ton of steel, all measured in bushels-corn. (I assume a long
term equilibrium in which all spot prices are stationary.)
Consider first, the steel industry. The value of their costs per unit
output, calculated at the start of the year, is A w/(1 + r). The value
of a unit product at the same point in time is p/(1 + r). Thus, the
condition of no economic profit implies:
p = A w (1)
Equation 2 is obtained by equating the present value of costs and
outputs in the production of corn:
p + B w/(1+r) + B w/(1+r)^2 + ... = 1/(1+r) + 1/(1+r)^2 + ... (2)
Some arithmetic yields:
p = A w = (1 - B w)/r (3)
Equation 3 allows one to obtain a curve relating the wage and the rate
of interest, Samuelson's factor price frontier:
w = 1/(A r + B) (4)
The factor price frontier is a hyperbola with a negative slope:
dw/dr = - A/(A r + B)^2 (5)
Substituting from (4), we can find the price of steel in terms of the
interest rate and the chosen coefficients of production:
p = A/(A r + B ) (6)
Note that capital *cannot* be measured in the same units as output
without performing a calculation at a given rate of interest.
Although this is more restrictive than I need, consider a stationary
state. Output consists exclusively of corn. Steel has been built up in
the past, but isn't currently being produced. Since steel has a
positive price, I am considering a corner solution.
Consider the output for one person-year, that is, output per head.
Output per head consists of y = 1/B Bushels corn, and capital per head
is physically comprised of (1/B) tons steel. In value terms,
k = p/B = A/[ B (A r + B) ] (7)
Wages and interest payments completely exhaust the product:
y = w + r k (8)
Differentiate Equation 8 with respect to y:
1 = dw/dy + r dk/dy + k dr/dy (9)
Now let's make the mystical assumption that the interest rate is equal
to the marginal product of "capital:"
r = dy/dk (10)
Equations 9 and 10 yield:
k = - ( dw/dy )/( dr/dy ) = - dw/dr (11)
We have already calculated the slope of the factor price frontier.
Thus, if the interest rate is equated to the marginal product of
"capital:"
k = A/(A r + B)^2 (12)
In general, this does not agree with the value of capital per head
already determined in Equation 7. So the interest rate is generally not
equal to some nebulous marginal product of capital for any positive
interest rate.
See why I do not become a professional economist? No progress in
understanding seems to be possible among the mainstream.
Robert Vienneau
Mark Witte
Robert Vienneau <Robert....@launchpad.unc.edu> wrote:
>Edward F., if you care about these matters, I request your attention.
>
>Since Mark Witte seems to identify rigor with math, let's do some math.
Actually I posted there intuitive examples of why the marginal product of
capital and the interest rate would be equal. Robert Vienneau ignored them
so I wrote out a mathematical model which he seems to have ignored as well.
At the end of my last post, I asked him to cut to the chase and state what
important objection to the neo-classical model overturned its relation between
the interest rate and the return on investment.
>
>Consider an economy which produces a single consumption good, corn,
>measured in bushels, and a single capital good, steel, measured in
>tons. Suppose firms have selected a profit-maximizing production
>technique in which A unassisted person years hired at the beginning of
>the year produce one ton of steel available at the end of the year.
>Steel lasts forever unchanged. Suppose B person-years, applied to one
Perhaps I was too strong in claiming that Robert Vienneau ignored my
descriptive models. He did say that my use of exponential depreciation was
"unusual." I didn't understand what was unusual about it but now I see that
he prefers zero depreciation. As Tom Jones sings, "It's not unusual...."
I was having fun up until this point.
Your model seems to assume a fixed factor, labor.
On its own, labor can only produce steel.
You've assumed a Leontief production function for corn.
B hours of labor + 1 ton steel = 1 bushel of corn in one year.
I haven't seen much done with Leontief production functions since their
assumptions are quite strong. Let's see what kind of trouble they make here.
I guess one problem would be the lumpiness of production which goes with a
classic Leontief production function, eliminating the use of continuous
function calculus as a tool. You've used it once so far but I'm not sure
matters for your development to this point.
Labor without steel can't do anything but make steel (we have no stated
preferences so I'll assume there is no taste for leisure).
You state that steel is not being produced and market clearing implies that
all labor is employed. Therefore, there must be one ton of steel for every B
units of labor. Your model is isomorphic with a single input fixed factor
model at this point.
The marginal product of capital is not well defined here. If capital were
to increase by one ton of steel, output would not rise at all since all
labor is currently employed and steel produces nothing on its own.
If capital were to fall by one ton, then output would fall by one bushel of
corn. Obviously, continutity of the production function is violated so
calculus will not give us meaningful answers.
Since there is no gain to increasing the capital stock, there is no return for
thrift and thus the interest rate (the return on delayed consumption) is zero.
It's a little past my bedtime so my intuition is a bit foggy on what borrowing
would mean in this model. Without stated preferences, I can't see what you'd
have to give someone to get him or her to give up some consumption now.
Thus, on the margin, for an increase in the capital stock, the interest rate
and the marginal product of capital both appear to be zero in spite of some
admittedly restrictive assumptions.
>
>Consider the output for one person-year, that is, output per head.
>Output per head consists of y = 1/B Bushels corn, and capital per head
>is physically comprised of (1/B) tons steel. In value terms,
>
> k = p/B = A/[ B (A r + B) ] (7)
>
>Wages and interest payments completely exhaust the product:
>
> y = w + r k (8)
>
>Differentiate Equation 8 with respect to y:
>
> 1 = dw/dy + r dk/dy + k dr/dy (9)
>
>Now let's make the mystical assumption that the interest rate is equal
>to the marginal product of "capital:"
>
> r = dy/dk (10)
>
>Equations 9 and 10 yield:
>
> k = - ( dw/dy )/( dr/dy ) = - dw/dr (11)
>
>We have already calculated the slope of the factor price frontier.
>Thus, if the interest rate is equated to the marginal product of
>"capital:"
>
> k = A/(A r + B)^2 (12)
>
>In general, this does not agree with the value of capital per head
>already determined in Equation 7. So the interest rate is generally not
>equal to some nebulous marginal product of capital for any positive
>interest rate.
This result does not hold for the reasons explained above.
I confess, I really do like math. It's wonderful stuff but when misused, it
can lead to all kinds of trouble. My research involves a lot of discontinous
investment modeling and it makes me wish for the simple world were continuity
applies.
>
>See why I do not become a professional economist? No progress in
>understanding seems to be possible among the mainstream.
>
> Robert Vienneau
>
Well, I think that's a little bit strong.
Robert Vienneau
>Actually I posted there intuitive examples of why the marginal product of
>capital and the interest rate would be equal. Robert Vienneau ignored them
>so I wrote out a mathematical model which he seems to have ignored as well.
Given Mark thought my closing statement was a little harsh, it's
probably just as well I don't comment on his conventional
"mathematical" model. What can one say about a claim that two
variables, Y and K, represent quantities of physically different goods,
but have the same units?
>At the end of my last post, I asked him to cut to the chase and state what
>important objection to the neo-classical model overturned its relation
>between the interest rate and the return on investment.
Actually, I'm stating neo-classical theory, not objecting to it. Mark seems
to think the(?) neo-classical model is an outdated approach with aggregate
production functions, value measures of capital, and an equality between
the marginal product of "capital" and the interest rate. I'm showing why
that's wrong.
>...He did say that my use of exponential depreciation was
>"unusual." I didn't understand what was unusual about it but now I
>see that he prefers zero depreciation.
The statement that I object to is
>>>>If the profit on K5984 drill presses were less
>>>>than the risk adjusted going rate of return for a given maturity,
>>>>few K5984 drill presses would be bought until depreciation
>>>>increased their scarcity to the point where the profit of
>>>>investing in them was equal to the opportunity cost of funds
This bit about "depreciation increasing scarcity" I find bizarre. The
assumption of exponential depreciation, although conventional, is
misleading, if not wrong. It depicts depreciation as a natural process.
Walras and Samuelson, Solow, & Dorfman (in 1960) made the same mistake.
However, I want to dodge how to correctly regard depreciation. If Mark
doesn't like capital goods with infinite lifetimes, I'll try the other
obvious simplification below.
>...Your model seems to assume a fixed factor, labor.
>On its own, labor can only produce steel.
>You've assumed a Leontief production function for corn.
Wrong. I assumed constant returns to scale and that coefficients of
production were chosen out of a wider range of choices. In fact, I
explicitly wrote:
>>...Suppose firms have selected a profit-maximizing production
>>technique...
To show that my objection does not depend on Leontief technologies, I
present another model where I go into more detail.
Consider an economy which produces a single consumption good, corn,
measured in bushels, and a single capital good, steel, measured in
tons. Today I assume steel lasts for one year. The production function
for steel is:
Q1 = f1 ( X01, X11 ), (1)
where X01 is person-years of labor hired at the beginning of the year
and paid at the end of the year, X11 is the tons of steel purchased at
the beginning of the year, and Q1 is the tons of steel available at the
end of the year. The production function for corn is:
Q2 = f2 ( X02, X12 ), (2)
where the variables are defined in analogy with Equation 1.
Assume constant returns to scale, diminishing marginal products,
etc. Equations 1 and 2 can be rewritten as:
1 = f1 ( a01, a11 ) (3)
1 = f2 ( a02, a22 ), (4)
where aij represents the quantity of factor i used in producing one
unit output of commodity j.
Consider a balanced growth path in which both industries produce an
output and relative spot prices are stationary. (So relative endowments
of steel and labor are taken as variables determined by the model, not
given data.) Let p denote the price of steel, w the wage, and r the
interest rate.
The firm producing steel solves the mathematical programming problem
given in Display 5:
Choose Q1, a01, a11 to
Maximize Q1 p/(1+r) - a01 Q1 w/(1+r) - a11 Q1 p
Such that 1 = f1 ( a01, a11 ) (5)
Q1 >= 0, a01 >= 0, a11 >= 0.
An analogous problem describes the corn industry.
The solution to these programming problems yields the Sraffian system
of equations 6 and 7:
p a11 ( 1 + r ) + a01 w = p (6)
p a12 ( 1 + r ) + a02 w = 1 (7)
A Neoclassical might be inclined to interpret these equations as
asserting there's no pure economic profit. In this context, I do not
argue. Equations 6 and 7 obtain whether firms have only one
fixed-coefficient Leontief technique available, many fixed-coefficient
processes to choose from, or continuous well-behaved micro production
functions (properly specified in physical terms).
Since I am considering the last case, the solutions also show that
the coefficients of production satisfy the marginal productivity
equations given in Equations 8, 9, 10, and 11:
w = p d f1( a01, a11 )/d a01 (8)
w = d f2( a02, a12 )/d a02 (9)
p ( 1 + r ) = p d f1( a01, a11 )/d a11 (10)
p ( 1 + r ) = d f2( a02, a12 )/d a12 (11)
Equations 8 and 9 show that the wage equals the marginal product of
labor in the steel and corn industries. Similarly, Equations 10 and 11
show the price of steel, taking time discounting into account, is equal
to the marginal product of steel in the steel and corn industries.
The marginal productivity equations only become relevant if the
coefficients of production are free to vary. Thus, I consider marginal
productivity theory, properly understood, to show how profit-maximizing
firms select a production technique. One should also note there are 7
variables (p, w, r, a01, a02, a11, and a12), but only 6 equations. What
is held constant when one defines the marginal product of labor? The
correct answer in a long period context is the interest rate. Since
distribution must be given from outside the system, it is incorrect to
claim marginal productivity is a theory of income distribution.
(Marginal products are part of the determinants of the factor price
frontier, but cannot determine the location on that frontier.)
Equations 8 through 11 are all the marginal productivity conditions
in this model. There is no equation relating the marginal product of
"capital," measured in the same units as output, to the interest rate.
(Anybody inclined to interpret Equations 10 and 11 as about the
marginal product of "capital," should consider what happens if there's
more than one capital good. The price of each capital good will be
equated to - not determined by - the value of its marginal product, but
there's no sense in any aggregate measure of value "capital.")
The remainder of this model parallels my previous model. The factor
price frontier relates the wage and the interest rate:
w = [1 - a11 (1+r)]/[(a01 a12 - a11 a02)(1+r) + a02] (12)
(The notation does not reflect the dependence of the coefficients of
production on the interest rate.) Given the interest rate, one can
determine the value in the consumption good of a physical unit of each
capital good:
p = a01/[(a01 a12 - a11 a02)(1+r) + a02] (13)
Once again, note the dependence on the interest rate.
A special case is of logical importance here, but is too restrictive
to be used in empirical work. Suppose the production functions happened
to be such that the same ratio of capital goods to labor were always
chosen in all lines of production:
a01/a11 = a02/a12 (14)
Then, and only then, would the factor price frontier be a straight line
(in an infinitesimal neighborhood of the given interest rate):
w = ( 1 - a11 )/a02 - r a11/a02 (15)
Furthermore, prices would be proportional to labor values.
p = a01/a02 (16)
(Some slight work is needed to show that Equation 16 asserts prices are
proportional to labor values.)
Mark accepted that the results of a stationary state generalized to
a positive rate of growth g. Since the algebra for positive growth is
more complicated, I will restrict myself to considering quantity flows
in a stationary state. For ease of notation, define the variable
"denom" by Equation 17:
denom = a01 a12 - a11 a02 + a02 (17)
Each year the steel industry produces a12/denom tons steel per worker,
and the corn industry produces (1 - a11)/denom bushels corn per worker.
The output of the steel industry is distributed with (a11 a12)/denom
tons back into steel production and (1 - a11) a12/denom tons being sold
to the corn industry. These quantities entirely use up the output of
the steel industry and just replace the capital goods used up in each
industry. The net output consists entirely of corn, thus defining a
stationary state. Using Equation 13, one can calculate the value of
capital per head in bushels corn:
k = p a12/denom (18)
k = a01 a12/{[(a01 a12 - a11 a02)(1+r) + a02] denom} (19)
Those trying this at home can check that the following identity holds:
y = w + r k (20)
where w, as a function of r is read off of the factor price frontier.
Consider some manipulations of Equation 20. Differentiating by net
income per head yields:
1 = dw/dy + r dk/dy + k dr/dy (21)
Make the outdated mystical assumption that the interest rate equals the
marginal product of capital:
r = dy/dk (22)
So
k = - (dw/dy)/(dr/dy) = - dw/dr (23)
Does Equation 23 yield the same answer as the value of capital
already determined in Equation 19? It's traditional to consider a
factor price frontier with fixed coefficients. The final factor price
frontier is formed as an envelope curve in which the technique chosen
for a given wage (interest rate) maximizes the interest rate (wage).
This envelope curve can be continuous and continuously differentiable.
Adjacent points may differ not only in the coefficients of production,
but even in what capital goods are produced. Under these assumptions,
the derivative in wages with respect to the interest rate, given
coefficients, is:
dw/dr = - a01 a12/[(a01 a12 - a11 a02)(1+r) + a02]^2 (24)
Thus, we see, as before, that the interest rate is unequal to the
marginal product of "capital" for positive interest rates.
How about in the special case of linear factor price frontiers? In
this case,
dw/dr = - a11/a02 (25)
Some manipulation will show that in this special case the interest rate
is the marginal product of capital. Thus, aggregate Neoclassical theory
only holds in a multicommodity world if a simple labor theory of value
also holds. If this condition is too restrictive for Marx, it's too
restrictive for Samuelson, Solow, and Lucas.
(One might object to the traditional procedure for differentiating the
factor price frontier, perhaps because one thinks that derivatives
should treat coefficients of production as functions of the interest
rate. Based on the geometry of the situation, it seems to me that it
makes no difference to the argument, just changes Equation 24 in a
more complicated fashion.)
If Mark wants to continue to defend an orthodox persistence in
fallacious nonsense long since exposed, I quit. I'm not even going to
bother with reswitching or Solow and Pasinetti's argument over the rate
of return.
Mark Witte
>In article <3imed2$g...@news.acns.nwu.edu>, mwi...@casbah.acns.nwu.edu (Mark Witte) says:
>>
>>Dear Robert Vienneau,
>>were to any sophisticated person who had the misfortune of reading your posts.
>>
>> If you are going to rail about the failings of economists, please have
>>something worth saying. If you just like playing with your computer, why
>>don't you stick to sending yourself e-mail.
>>
>>
>> Mark Witte
>
> I always read Witte's comments with great interest and confess that it is a
> time saver for me to see "which thread is interesting" because I need only
> look for his name. Not wishing to intervene in the current matter, I would
> point out that debates in this format are "unwinnable." (Cf. Mosler's
> delusions on demand deposits and the value of money residing in taxation.)
> If we "fight to win" i.e. in trying to get s.o. else to cry uncle then
> we are bound to degenerate from virtuoso performance (e.g., Witte's critiques
> in this thread) to ad hominem attacks.
>
> Of course, there are *fora* in which one can "win": in reviewing a book
> or journal article (post or pre-publication), in making a hiring decision,
> in giving a grade. But for better or for worse this is not that kind of
> forum. The best one can hope for is eviscerating logic. If the opponent
> refuses to acknowledge evisceration, he is free to perpetuate his verison
> of error/truth. No point in getting excited about it. Try to remember
> Kuhn's observation that the perpetuators of false/disproven paradigms have
> to *die* before a field moves on to a new paradigm.
I don't get excited but if someone persists on posting claims that are
demonstrably wrong yet claim that this information is the wisdom of the ages,
he or she should expect to take a few flames. Or he or she can move on to
other subjects. A clear choice.
Mark Witte
Rob Vienneau
>>The interest rate is equal to the
>>marginal product of "capital" iff this secant also happens to be
>>tangent to the frontier at the given point. Although one can think of
>>exceptional cases where this condition holds, (most notably if the
>>frontier for a particular technique is a straight line) it's nothing on
>>which to base a macroeconomic theory.
Markku Stenborg responds:
>Pardon my ignorance, I haven't followed this thread all the time, but
>which macro theory is based on marginal product of "capital" = interest
>rate? I thought this condition pops up as a result under a bunch of
>conditions on investors' behavior such as no irreversibility?
There's an ambiguity in my quoted remarks. I did not mean that any
macroeconomic theory was *based* on the proposition that the
marginal product of capital equals the rate of interest. I meant
that no theoretically progressive current macroeconomic theory
should be based on the special conditions (in heterogeneous
capital models) needed to justify the use of aggregate production
functions with value measures of capital. These models are often
used to derive the proposition about the value measure of capital.
As for actual examples of such theories - I have heard that John
Bates Clark is one example. Certainly Solow's eponymous growth
model is another.
Now I am not very familiar with New Classical models, but Edward
Flahery (sp?) and Mark Witte have produced examples of the sort of
propositions that I think are on very weak logical grounds, to put it
mildly.
So, Markku, do you agree? Is the use of aggregate production functions
with value measures of capital unjustified?
Also, Mark Witte states:
>...Again, you either fail to understand your error or are too craven
>to admit it...
>You claimed in your last post that if I found fault with your
>reasoning, you would give up. I wish you had...
I posted to correct the only errors I acknowledge having made.
>If you'd like to post up your model again, I can try to explain it
>to you again.
Perhaps I will. I've written an exapnsion at home that explains
some points Mark Witte found obscure.
In the meantime, those who have been confused enough by Mark
Witte's post to think he has something like a point might look
up Frank Hahn's paper "The Neo-Ricardians" (Cambridge Journal
of Economics, V. 6, No. 4, 1982). Witte's comments seem to
imply Hahn has an "utter lack of economic intution" and should
"get out a second semester freshman calculus book." Somehow
I doubt both propositions.
Robert Vienneau