"Perverse" Price Wicksell Effects Swamping "Normal" Real Wicksell Effects

1.0 Introduction

Capital-reversing can arise in a couple of ways without reswitching. This post steps through a case in which positive price Wicksell effects can dominate negative real Wicksell effects. Around each switch point, firms choose to adopt a more capital-intensive technique of production for slightly lower interest rates. So real Wicksell effects agree, in this example, with the incoherent and outdated intuition of applied neoclassical economics. Nevertheless, due to the re-evaluation of a given set of capital goods at different interest rates, one can find a pair of points such that cost-minimizing firms adopt a more capital-intensive technique, from the given technology, at the higher interest rate. And this pair of points can span at least one switch point. Basically, I created a simple example to replicate graphs like those in Appendix D in Lazzarini (2011).

A case of a positive price Wicksell and negative real Wicksell effect is one case in my suggested taxonomy of Wicksell effects. Burmeister provides one possible neoclassical response to this sort of example. Burmeister advocated the use of David Champernowne’s (unobservable) chain-index measure of capital.

2.0 The Technology

Consider a very simple economy in which a single consumption good, corn, is produced. Entrepreneurs know of the two processes for producing corn shown in the last two columns of Table 1. One corn-producing process produces corn from inputs of labor time and steel. The other corn-producing process uses inputs of labor time and tin. The entrepreneurs know of two other processes, also shown in Table 1. Additional steel can be produced from inputs of labor time and steel. Similarly, labor time and tin can produce more tin.

Table 1: The CRS Technology

Inputs	Steel Industry	Tin Industry	Corn Industry
Labor	1 Person-Year	1 Person-Yr	1 Person-Yr	2 Person-Yrs
Steel	1/2 Ton	0 Ton	1/4 Ton	0 Ton
Tin	0 Kg.	9/20 Kg.	0 Kg.	1/3 Kg.
Output:	1 Ton Steel	1 Kg. Tin	1 Bushel Corn	1 Bushel Corn

All processes exhibit Constant Returns to Scale (CRS). Each process requires a year to complete. Their outputs become available at the end of the year, and they totally use up their inputs of capital goods over the course of the year.

3.0 Quantity Flows

Two techniques are available for producing a bushel of corn as net output.

The first technique, to be called the steel technique, operates the first process to produce 1/2 ton steel and the first corn-producing process to produce one bushel corn. 1/4 ton of the output of the steel-producing process replaces the steel-capital used up in producing steel. The other 1/4 ton output from the steel-producing process replaces the 1/4 ton steel used up in producing corn. In effect, 1 1/2 person-years labor are used in the steel technique for each bushel corn producing in a self-sustaining way.

In the tin technique, 20/33 kilograms tin are produced with the tin-producing process, and one bushel corn is produced with the second corn-producing process. 2 20/33 person-years labor are used in the tin technique for each bushel of corn in the economy’s net output.

Note that the production of corn with the steel system provides more consumption per worker-year than is provided with the tin system. Under the false and exploded neoclassical theory, one would expect the steel system to require more capital per worker. One would also expect it to be adopted at a low interest rate, since the low interest would be signaling a relative lack of scarcity of capital.

4.0 Price Equations

Next, I consider constant prices consistent with the adoption of each technique. Firms will not adopt a technique unless the interest rate (also known as the rate of profits) is earned for each process in use in a technique. For definitiveness, I assume that wages are paid at the end of the year out of output and that a bushel corn is the numeraire.

4.1 Steel Technique

Given these assumptions, the following system of two equations must hold when the steel technique is in use:

(1/2)p_s(1 + r) + w = p_s

(1/4)p_s(1 + r) + w = 1

where p_s is the price of a ton of steel, w is the wage, and r is the interest rate.

Above is a system of two equations in three variables. This system has one degree of freedom. Two variables can be found as functions of the one remaining variable. For example, the wage and the price of steel can be expressed as (rational) functions of the rate of profits. And that price of steel can be used to find the value of capital. The resulting capital-output ratio is:

v_s(r) = 2/(3 - r)

where v_s is the ratio of the value of capital to the value of output in the steel technique.

4.2 Tin Technique

The following system of two equations must hold when the tin technique is in use:

(9/20)p_t(1 + r) + w = p_t

(1/3)p_t(1 + r) + 2 w = 1

where p_t is the price of a kilogram of tin.

The ratio of the value of capital to the value of output in the tin technique, v_t, expressed as a function of the interest rate, is:

v_t(r) = 200/(473 - 187 r)

5.0 Choice of Technique

The trade off between the wage and the rate of profits, for a given technique, is the wage curve for that technique. Figure 1 shows the wage curves for the two techniques, as well as the wage frontier formed as an outer envelope of the wage curves for all the techniques that comprise the technology. Given the interest rate, the cost-minimizing firm adopts the technique whose wage curve is on the frontier at that point. At the switch point, two techniques are simultaneously cost minimizing.

Figure 1: The Wage-Rate of Profits Frontier

The wage curve for a given technique expresses the wage as a function of the rate of profits. The rate of profits at which the switch point occurs is found by equating the wage for two techniques. In the numerical example analyzed in this post, the following quadratic equation arises:

(41/240)(1 + r)² - (13/15)(1 + r) + 1 = 0

The switch point occurs at a rate of profits of approximately 77.46%.

6.0 Conclusion

The above analysis has shown for the example:

• Which technique is cost-minimizing at any given interest rate up to a maximum.
• The ratio of the value of capital to output for each technique for each interest rate.

Thus, as shown in Figure 2, one can find the capital-output ratio for the cost-minimizing technique for each economically feasible interest rate. The price Wicksell effect exhibits the revaluation of given capital goods at different interest rates, while the real Wicksell effect results from the adoption of different capital goods at a given interest rate. Both effects are illustrated in Figure 2.

Figure 2: The Rate of Profits Versus Capital-Intensity

This example has shown that capital-reversing can exist around a switch point even in the absence of reswitching.

References

• Edwin Burmeiser (1980). Capital Theory and Dynamics, Cambridge University Press.
• Andrés Lazzarini (2011). Revisiting the Cambridge Capital Theory Controversies: A Historical and Analytical Study, Pavia University Press.

Pecan Pie

9 inch pie	8 inch pie
3 large eggs	2
2/3 cup sugar	1/2 cup
1/3 teaspoon salt	1/4 teaspoon
1/3 cup butter, melted	1/4 cup
1 cup maple syrup	3/4 cup
1 cup chopped pecans	3/4 cup

Add ingredients in order, stirring thoroughly after each ingredient. Pour into pastry-lined pie pan. Bake at 375 degrees for 40-50 minutes, until set and pastry is nicely browned. Cool. Serve cold or slightly warm.

Elsewhere

• Dan Berrett, in The Chronicle of Higher Education, reports that "Economists push for a broader range of viewpoints". The Institute for New Economic Thinking, Econ4, a couple of professors at the University of Massachusetts at Amherst, and Stephen Marglin are all mentioned.
• Daron Acemoglu recommends five books¹ on inequality in the distribution of income or wealth. Is he basically confused about the logic of the theory of marginal productivity?
• Bryan Caplan parades his ignorance of Keynes on wages. According to Caplan, "nominal wage rigidity is the driving force of the Keynesian model" and if employment increases, wages must fall. But:
• Keynes explicitly argues, in chapter 19 of the General Theory that his analysis applies if money wages are flexible.
• At the time of the publication of the General Theory, Keynes had "always regarded decreasing physical returns in the short period as one of the very few incontrovertible propositions in our miserable subject". So he believed then that less unemployment would be associated with lessened real wages. He changed his mind² in responding to empirical evidence from John T. Dunlop and Laurie Tarshis. Empirical evidence for reverse L-shaped cost curves in industry has held up since then.

Footnotes

1. My list includes, at least:

• James K. Galbraith (1998). Created Unequal: The Crisis in American Pay. Free Press.
• Stephen A. Marglin (1984). Growth, Distribution, and Prices. Harvard University Press

2. References (which I know of from the secondary literature):

• John T. Dunlop (1938). "The Movement of Real and Money Wage Rates", Economic Journal. v. 48 (Sept.): 413-434.
• J. M. Keynes (1939). "Relative Movements of Real Wages and Output", Economic Journal, v. 49 (March): 34-51.
• Lorie Tarshis (1939). "Changes in Real and Money Wages", Economic Journal, v. 49 (March): 150-154.

A Serendipitous Juxtaposition

Tuesday, Peter Dorman, at Econospeak, considers why reactionaries in the United States are not embarrassed when caught at their constant lying. He says the contemporary right-wingers' pride in lying is ultimately derived from Leo Strauss. According to Dorman, Strauss taught:

"The cartoon version of Strauss, which is broadly correct, goes like this: The great philosophers of the past, each in their way, were led by the force of logic and experience to a dangerous insight, that no social or cultural arrangement can substitute for the necessity of virtue, and that only a small minority of individuals are truly virtuous... Those who perceive this truth must write deceptively, since the unworthy masses, if they sense that they are being judged unworthy, will persecute the truth-teller. Strauss provided readings of the canonical texts that claimed to show they functioned on two levels, as decoys for the average reader and secret wisdom for the initiate." -- Peter Dorman

And on Monday, Dani Rodrik, at Project Syndicate notes the difference between discourse among elite economists and what they tell introductory students and the general public:

"As the late great international economist Carlos Diaz-Alejandro once put it, 'by now any bright graduate student, by choosing his assumption...carefully, can produce a consistent model yielding just about any policy recommendation he favored at the start.' And that was in the 1970's! An apprentice economist no longer needs to be particularly bright to produce unorthodox policy conclusions.

Nevertheless, economists get stuck with the charge of being narrowly ideological, because they are their own worst enemy when it comes to applying their theories to the real world. Instead of communicating the full panoply of perspectives that their discipline offers, they display excessive confidence in particular remedies - often those that best accord with their own personal ideologies...

...In my book The Globalization Paradox, I contemplate the following thought experiment. Let a journalist call an economics professor for his view on whether free trade with country X or Y is a good idea. We can be fairly certain that the economist, like the vast majority of the profession, will be enthusiastic in his support of free trade.

Now let the reporter go undercover as a student in the professor’s advanced graduate seminar on international trade theory. Let him pose the same question: Is free trade good? I doubt that the answer will come as quickly and be as succinct this time around. In fact, the professor is likely to be stymied by the question. 'What do you mean by "good?"' he will ask. 'And good for whom?'

The professor would then launch into a long and tortured exegesis that will ultimately culminate in a heavily hedged statement: 'So if the long list of conditions I have just described are satisfied, and assuming we can tax the beneficiaries to compensate the losers, freer trade has the potential to increase everyone's well-being.' If he were in an expansive mood, the professor might add that the effect of free trade on an economy’s growth rate is not clear, either, and depends on an altogether different set of requirements.

A direct, unqualified assertion about the benefits of free trade has now been transformed into a statement adorned by all kinds of ifs and buts. Oddly, the knowledge that the professor willingly imparts with great pride to his advanced students is deemed to be inappropriate (or dangerous) for the general public." -- Dani Rodrik

This bifurcated discourse in economics creates a problem for critics. They can point out that most introductory mainstream teaching and applied policy advice of mainstream economists is self-contradictory and theoretically and empirically unfounded. Defenders of orthodox economists can then accuse the critics of attacking a strawperson. The failure to take their own advanced teaching seriously leads orthodox economists to disappear as a target, in some sense. Maybe the question is one of professional ethics.

On Hayek's Lack Of Impact On Macroeconomics

I'm agreeing with, for example, Brad DeLong, Paul Krugman, and David Warsh. I'm disagreeing with, for example, Peter Klein, Mario Rizzo, Alex Tabarrok, and Steven Horwitz. I suppose I'm also disagreeing with Nicholas Wapshott. Refutations of Austrian Business Cycle Theory (ABCT) are relevant today because of confusions propagated in popular literature.

Keynes argued with many while writing the General Theory. Why not say Keynes versus Dennis Robertson is "the clash that defined modern economics"? I think one could argue that Hayek influenced mainstream macroeconomics through J. R. Hick's exposition of temporary equilibrium in Value and Capital, but this seems a quite attenuated influence.

Keynesians can accept that Hayek had the better of the early 1930s debate with Keynes over Keynes's Treatise on Money. The Treatise is not the General Theory. But Sraffa and Kaldor embarrassed Hayek in his attempt to develop the ABCT. I think the two most important errors in the ABCT are:

• The natural rate of interest is undefined in intertemporal General Equilibria (also known as, more or less, "plan coordination").
• No simple relation exists between the optimal allocation of resources among orders of goods and interest rates.

In short, both Hayek's monetary theory and his capital theory are incorrect.

Qualitative stories about the embodiment in capital goods of misaligned plans are, perhaps, the best one can get from Hayek's capital theory. Ludwig Lachmann and Peter Lewin are my favorite Austrian-school economists to read on this point. (Did Lachmann have any enduring effect on mainstream economics?) But it is hard to quantitatively estimate the effects of such misalignments, and I don't find convincing that recovering from these misalignments are the source of the largest worldwide business cycles that we have seen. Anyways, I prefer Joan Robinson on capital theory in disequilibrium.

The importance one should assign the clash between Hayek and Keynes in the history of macroeconomics seems to me to depend crucially on the impact of Hayek on mainstream views of Keynes' General Theory. But Hayek had no such impact. Hayek tried to address the General Theory in his Pure Theory of Capital. But Hayek's book was ignored at the time and is generally considered a failure. About the only thing else Hayek had to say about Keynes's General Theory occurred in interviews and other transient popular pieces. So, whatever you may think about the worth of Hayek's writings, where can you locate their impact?

Walras's Law Is False

1.0 Introduction

I have asserted that the distribution of income is determined by political power, not by intertemporal utility-maximization. Interest rates are not the result of individual decisions trading off consumption at future dates against consumption now.

Is it not a consequence of this view that Walras's law does not apply to capitalist economies?

2.0 On the Derivation of Walras's Law

Walras's law states that the sum of excess demand across all goods is zero:

p z(p) = p₁z₁(p) + p₂z₂(p) + ... + p_nz_n(p) = 0

The excess demand for the jth good is the difference between the demand and supply of that good at the set of prices at which these functions are being evaluated:

z_j(p) = d_j(p₁, p₂, ..., p_n) - s_j(p₁, p₂, ..., p_n)

And supply and demand functions for each market are found by summing over the supplies and demands for all individuals. But individual supply and demand functions are derived from the theory of utility-maximization, given the initial distribution of the endowments of all goods.

3.0 Macroeconomic Reasoning With Walras's Law

Don Patinkin considered an economy in which n - 1 commodities and "money" are traded.

"For the amount of excess demand for money equals the aggregate value of the amounts of excess supplies of commodities." -- Don Patinkin, Money, Interest, and Prices (2nd edition, Harper and Row, 1965)

I believe Patinkin's approach can be seen as building on J. R. Hicks's Value and Capital (2nd edition, Oxford University Press, 1946). Hicks included demands for both money and other securities in his General Equilibrium approach.

One can argue that the world economy is currently in a disequilibrium; both labor and produced commodities are in excess supply. Thus, by Walras's law, there must be an excess demand for money. And it is the job of monetary authorities, such as the United States's Federal Reserve, to meet that demand, by flooding the market with money while this disequilibrium exists. At least, this is the argument of prominent mainstream "Keynesians", such as Brad DeLong and Paul Krugman (suggestions for links to their blogs here are welcome).

4.0 Conclusion

Keynes's emphasis on fundamental uncertainty is arguably incompatible with the explanation of the demand for money by intertemporal utility-maximizing in a model of General Equilibrium. Thus, the above justification of "Keynesian" monetary policy, based on Walras's law, does not harmonize with Keynes's theory.