Wednesday, January 01, 2020


I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Monday, June 17, 2019

Lewin and Cachanosky on Neo-Ricardian Economics [Citation Needed]

This post is about the misrepresentation of Sraffian capital theory in Lewin and Cachanosky (2019). I cannot recommend this short book. Presumably, it is meant as an introduction. But I do not see it as succeeding. I do not see what a more advanced audience would get out of it that is not available in a few recent papers by Lewin and Cachanosky.

Before proceeding to my main theme, let me note that I agree with some parts of this book, mainly where Lewin and Cachanosky draw on Ludwig Lachmann, to parallel themes in Joan Robinson's emphasis on historical time. They state that no physical measurement of capital exists and that capital is not a factor of production, with a demand function. They state, probably as influenced by Jack Birner, that Hayek never set out a coherent and internally valid theory of capital. His triangles are only useful as an expository device. I am also ignoring certain gaps. For example, the text at the bottom of page 30 suggests, incorrectly, that the economic life of a machine would be the same as its physical life in equibrium, where such disequilibrium phenomena as the introduction of new and better vintages and changes in tastes and technology do not arise.

Citations are needed for these passages:

"Lachmann's capital theory provides the definitive understanding of the nature and working of the capital structure for Austrians today. Rather than conceiving of production as involving a homogeneous mass of 'capital' as a stock (as in both the neoclassical and modern Ricardian conceptions), Lachmann sees it as involving an ordered structure of heterogeneous multispecific complementary production goods. This structure is ever changing as entrepreneurs combine and recombine productive resources in accordance with their assessments of profitability." -- Lewin and Cachanoksy, p. 35.

Where do the neo-Ricardians reject the analysis in Sraffa's book?

"The Keynesian revolution established macroeconomics as [a] legitmate sub-branch of economic inquiry focusing on the relationship betwenn aggregates... [The] neoclassical production function is the workhorse of much of modern literature...

"...its ability, using the marginal productivity theory, to explain the distribution of output (income) between capital and labor... During the 1960s and following, the neoclassical production function was the object of attack by the 'Cambridge Marxists' UK (neo-Ricardians) against the 'Cambridge Massachusetts' neoclassicals, on the presumption that it was essential to the validity of the marginal productivity explanation of the distribution of income ... and that demolishing the notion of capital upon which the aggregate production function depended, they would, at the same time, demolish the marginal productivity theory of distribution." -- Lewin and Cachanoksy, p. 46-47.

Where do the neo-Ricardians assert the non-existence of disaggregated, microeconomic neoclassical theory?

"These paradoxes consist of cases in which it is alleged, for example, ... a fall in the interest rate may first lead to the adoption [of] a more 'capital-intensive' productive technique, and then switch, paradoxically, to a less 'capital-intensive' technique, and then switch back again as the interest rate continues to fall. These are alternative techniques, characterized by their physical capital labor ratios. In other words, switches may occur, as well as reswitches and reversals..." -- Lewin and Cachanoksy, p. 68.

Even Joan Robinson's "real capital" is measured for a given interest rate. Techniques of production are characterized by a complete list of inputs and outputs. These inputs can include produced means of production, unproduced natural resources, and various kinds of labor. When deciding on which technique to adopt, managers of firms, in Sraffian and in any other reasonable analysis of a capitalist system, coompare costs and revenues, with inputs and outputs evaluated at prices.

"The neo-Ricardians identify all 'capital' as intermediate goods, such as machines, tools, or raw materials. They are goods-in-process from the original labor that constructed them, to the emergence of the final consumer good. So all capital goods (can be and) are reduced to dated labor. In this way, we get a purely physical measure of 'capital', one that, by construction, does not vary with the interest rate." -- Lewin and Cachanoksy, p. 69, footnote 3.

Where do the neo-Ricardians assert that, in all interesting cases of joint production, all intermediate goods can be expressed as produced by inputs consisting only of a stream of dated labor? Where do they put forth a measure of capital that does not vary with the interest rate?

"Also important, the neo-Ricardians identify the price of capital as the rate-of-interest which they regard as synonymous with the rate of profit. But neither is correct... The market interest rate is, indeed, the price of capital as we understand it. It is the cost of borrowing 'capital' for the employment of any valuable resource or for any other reason. It is the price of credit and is determined by the time prefernces of borrowers and lenders and the production possibilities available. (The neo-Ricardians have no discussion of what determines interest rates.)" -- Lewin and Cachanoksy, p. 72.

Post Keynesians have considered a theory of growth and distribution in which the interest rate is set by the monetary authorities and the rate of profits exceeds the interest rate by a conventional markup. They have considered other theories in which the wage is given by forces outside the theory of value. They have developed theories of inflation in which conventions on both the rate of profits and wages conflict. In the late 1950s and early 1960s, Richard Kahn, Nickolas Kaldor, Luigi Pasinetti, and Joan Robinson pointed out that savings propensities out of wages and profits constrained functional income distribution along a steady state growth path. Kaldor (1966), in this tradition, developed a model in which the interest rate and the rate of profits are distinguished. I provide two textbooks, in the references, that survey this large body of work.

  • Duncan K. Foley, Thomas R. Micl, Daniele Tavani (2019). Growth and Distribution, Second edition. Harvard University Press.
  • Peter Lewin and Nicolas Cachanosky (2019). Austrian Capital Theory. Cambridge University Press.
  • Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press.

Saturday, June 08, 2019

On Hicks' Average Period of Production

Figure 1: APP Around Switch Points
1.0 Introduction

I take it that the Austrian theory of the business cycle builds on Austrian capital theory. The following two claims are central to Austrian capital theory:

  • Given technology, profit maximizing firms adopt a more capital-intensive, more roundabout technique at a lower interest rate.
  • The adoption of a more roundabout technique increases output per worker.

Originally, Eugen von Böhm-Bawerk proposed a physical measure of the average period of production, but economists of the Austrian school have been distancing themselves from this position for well over half a century. I have argued that the first claim fails, even in a framework without any scalar measure of capital-intensity or the average period of production.

Recently, Nicholas Cachanosky and Peter Lewin, in a series of articles, have championed J. R. Hicks' measure of the Average Period of Production (APP), as a justification of the first claim. They note that the APP, as defined here, is a function of the interest rate. Hence, it cannot fully support Böhm-Bawerk's theory. Saverio Fratini has argued this justification does not work, since the second claim above fails, when this APP is used as a measure of capital-intensity. Lewin and Cachanosky, in reply, argue that Fratini does not properly calculate the APP, since it should be forward looking and apply in disequilibria.

This post re-iterates Fratini's argument, with his example. I more closely follow Cachanosky and Lewin's approach, though.

2.0 Technology

Fratini considers a technology consisting of two techniques of production, Alpha and Beta (Table 1). Each technique requires three years of unassisted labor inputs, per bushel wheat produced at the end of the third year. Labor is advanced and paid at the end of the year. Labor is taken as numeraire. That is, the wage is assumed to be $1 per person-year. The price of a bushel wheat, p, is taken to be $12 dollars per bushel. As I hope becomes apparent, these assumptions generally characterize a disequilibrium.

Table 1: Inputs for Producing A Bushel Wheat
13a3 = 1 Person-Yr.b3 = 2 Person-Yrs.
22a2 = 7 Person-Yrs.b2 = 2 Person-Yrs.
31a1 = 2 Person-Yrs.b1 = 8 Person-Yrs.

The output per worker, in a stationary state, is determined by the chosen technique. Suppose the Alpha technique is adopted. In any given year, 10 person-years are employed per bushel wheat produced. Two person-years are being expended to produce each bushel of wheat harvested at the end of the year, seven person-years are being employed to produce each bushel of wheat available at the end of the next year, and one person-year is employed per bushel wheat harvested even a year later. That is, output per worker, under the alpha technique, yα, is (1/10) bushels per person-year. Similarly, output per worker for the beta technique, yβ, is (1/12) bushels per person-year.

3.0 Net Present Value and the Choice of Technique

Suppose a wheat-producing firm faces a given annual interest rate, r. For convenience, define:

R = 1 + r

The discount factor, f, is defined to be:

f = 1/R = 1/(1 + r)

Consider a decision to choose a technique to adopt for next three years in producing wheat. Powers of the discount factor are used to evaluate the costs and revenues for each technique at the start of the given year. For example, the NPV of the alpha technique is:

NPV(α, f) = -a3 f - a2 f2 + (p - a1) f3

I have assumed that firms expect the given interest rate to remain unchanged for the decision period - a common convention. Revenues are positive, and costs (or outgoes) are negative.

Figure 2 graphs the difference between the NPV for the two techniques. A positive difference indicates that the alpha technique maximizes the NPV, while a negative difference arises when the beta technique is preferred. Which technique is chosen by cost-minimizing firm for each interest rate is shown. At switch points, firms are indifferent between the two techniques.

Figure 2: Difference in NPVs

Under the assumptions, NPV is always positive. (If the beta technique were adopted at an interest rate of zero, its NPV would be zero then.) If markets were competitive, the price of wheat would vary until the NPV was zero, given the interest rate. Fratini does indeed assume equilibrium and analyzes the choice of technique with backwards-looking calculations of costs, as Lewin and Cachanosky claim. But this makes no difference to his argument, so far.

4.0 The Average Period of Production

One might be interested in how NPV varies with the discount factor. The elasticity of the NPV, with respect to the discount factor, is a dimension-less number for assessing such sensitivity. Somewhat arbitrarily, I discount elasticity one period:

APP(α, f) = f [1/NPV(α, f)] [d NPV(α, f)/df]

Elasticity is the variation of NPV with variation of the discount factor, as a proportion of NPV.

APP(α, f) = [-a3 f/NPV(α, f)] x 1
+ [- a2 f2/NPV(α, f)] x 2
+ [(p - a1) f3/NPV(α, f)] x 3

The APP for a technique, at a given discount factor, is the weighted average of the time indices, looking forward, for a given income stream. The weights are the proportion of the income stream received in each period. All income is discounted to the start of the first year.

So the elasticity of the NPV of an income stream, with respect to the discount factor can also be expressed as the average period of production.

Notice that the APP is not defined in equilibrium. The denominators in the above terms are zero, and the APP could be said to be infinite. If only costs are used in the above calculations (thus, no longer of a NPV), the APP is well-defined, at least in the flow-input, point output case. Fratini (2019) does this.

One could also express the APP as a function of the interest rate:

APP(α, r) = [-a3 R2/NPV(α, r)] x 1
+ [- a2 R/NPV(α, r)] x 2
+ [(p - a1)/NPV(α, r)] x 3


NPV(α, r) = -a3 R2 - a2 R + (p - a1)

I skip over some some algebraic manipulations above.

The above is not the definition of the APP in Fratini (2019), for example, in Equation 7. Where I have time indices of 1, 2, and 3, Fratini has indices of 3, 2, 1. I guess one can say that his definition of the APP is backwards-looking.

Fratini's argument still goes forward with Cachanosky and Lewin's (or Hicks') definition. One could present a mathematical proof that the APP is always increased around a switch point with a fall in the interest rate. But here I'll just graph it for the example. See Figure 1, at the top of this post. Around each switch point a lower interest rate is indeed associated with the adoption of a technique with a larger APP. But consider the switch point at an interest rate of 200 percent. The beta technique, adopted at a notionally lower interest rate, has a lower value of output per head.

4.0 Conclusion

The example illustrates that, around a switch point, a lower interest rate is associated with the adoption of a more roundabout technique, where roundaboutness is measured by Hicks' Average Period of Production. Incidentally, the example demonstrates that in a region where one technique is cost-minimizing the APP may decrease with the interest rate. But the adoption of a more roundabout technique can be associated with a decrease in output per worker. So much for Austrian capital theory and the Austrian theory of the business cycle.

Update (14 June 2019): Re-order numbers in table, as they are used in the calculations. References

Thursday, June 06, 2019

Refutation Of Austrian Business Cycle Theory

Those who understand price theory reject the theory of the Austrian Business Cycle (ABC). I am thinking here that its logical invalidity follows from post-Sraffian capital theory. It is also wrong because of its reliance on the concept of the natural rate of interest.

Some years ago, I tried to get published a demonstration that ABC theory was in error. I forget how many journals rejected it. Four or five articles here are from this series of revisions. The rejections from the journals more sympathetic to Post Keynesians generally said that everybody knows that ABC theory is wrong. The rejections from the journals more sympathetic to the Austrian school said that I ought to read more and more obscure literature. Some of this was helpful for my understanding of the history of ABC theory, but none really addressed my points.

Anyways, my favorite revision is the last. I think this is fairly good, but, as of now, do not intend to resubmit it anywhere. I find that recently some articles on the Cambridge Capital Controversies have been published in the Review of Austrian Economics.


Friday, May 31, 2019

Some Reviews of Quiggin's Economics in Two Lessons

I have been thinking of posting a review of Quiggin's book, but this is not it. I suppose I should mention that I am in the acknowledgements.

Quiggin has a response to a couple of the above. By the way, he had a paper, in 1987, on public choice.

I think any reviewer should note that Quiggin is extremely generous to Hazlitt's Economics in One Lesson. Hazlitt does not mention "opportunity cost". By focusing on this concept, Quiggin makes Hazlitt seem more coherent than he is. I agree with Quiggin that this coherence does not require Hazlitt to think the economy is always in equilibrium. It is consistent with prices providing signals, that, when entrepreneurs act on them, move the economy towards equilibrium. It is not consistent, as Quiggin notes in his book, with the economy persisting for a long time within the production possibility frontier, without any tendency to more towards the frontier.

It is no answer to or review of Quiggin's book to rattle on about Keynesianism or the logically incorrect AustrianBusiness Cycle theory. One has to also address Quiggin's points about externalities, information asymmetries, and the continual redefinition of property rights.

Furthermore, a fair reviewer would note that Quiggin does not recommend a mechanical calculation of, say, taxes and subsidies to correct market failures. Although, I guess, he does not mention "government failure" in his book, his consideration of policies is a lot more nuanced than that.

Furthermore, if one thinks the theory of public choice provides an answer to Quiggin, one should note that Hazlitt does not discuss these matters. Hazlitt was a propagandist and, for decades, should have not been taken seriously.

As far as I know, public choice is an application of neoclassical economics. Gloria-Palermo and Palermo (2005), as I recall this paper, argues that the Hayekian argument about the coordinating function of market prices does not provide a welfare criterion alternative to Pareto efficiency. I think I have such criteria in focusing on conditions for the continued reproduction of society, as opposed to the efficient allocation of given resources. One can also point to the Veblenian dichotomy, between instrumental and ceremonial aspects of institutions, as well as to the pragmatism of John Dewey. If I do review Quiggin's book, I want to point out how it is too accepting of Neoclassicism, as well as where it points beyond.

  • Sandy Gloria-Palermo and Giulio Palermo (2005). Austrian economics and value judgements: A critical comparison with Neoclassical Economics. Review of Political Economy 17(1): 63-78.

Saturday, May 25, 2019

All Combinations of Real Wicksell Effects, Substitution of Labor

Figure 1: A Pattern Diagram

Consider an example of the production of commodities, in which many commodities are produced within capitalist firms. Suppose two techniques are available to produce a given net output. These techniques use the same set of capital goods, albeit in different proportions. They differ in process in use for only one industry. Given the qualification about the same capital goods, generic (non-fluke) switch points are the intersection of the intersection of the wage curves for two techniques that differ in exactly one process.

Suppose that, due to technological progress, some coefficients of production decrease in the process unique to the Alpha technique. Figure 1 shows a possible pattern diagram for this generalization of a previous example. Here, switch points and the maximum rate of profits are plotted against the rate of profits. As time goes by, a reswitching pattern leads to a reswitching example. The switch point created at the larger rate of profits exhibits, after t = 1/2, a negative real Wicksell effect and a reverse substitution of labor. A pattern over the axis for the rate of profits then results in the existence of another switch point at an even higher rate of profits. Technological progress can bring about, in a single example, the combination of both non-zero directions of real Wicksell effects with both non-zero directions of the substitution of labor.

The regions in Figure 1 in which reswitching occurs also illustrate process recurrence. Process recurrence is more general, inasmuch as it can arise even without reswitching.

Since all four possible combinations, of nonzero-real Wicksell effects and the substitution of labor, are possible, the direction of real Wicksell effects and the direction of the substitution of labor are independent of one another. The choice of technique results in variation in gross outputs in multiple industries, for given net outputs. (The question of returns to scale is of interest in this context.) These variations in gross outputs also result in variation in the amount of labor firms want to employ. Around a switch point with a positive real Wicksell effect, firms want to employ more labor, per unit of net output, in the aggregate across all industries. A necessary consequence is that they want to employ more labor in at least one industry. This variation in aggregate employment is consistent with any direction in the variation in the labor coefficient of production in the industry with the varying process.

Friday, May 24, 2019

Alfred Eichner's Microfoundations, Or An Open Letter To Marco Rubio

The Growing Importance of Finance in the Post-War U.S. Economy

As I understand it, Marco Rubio takes from Post Keynesians the idea that, during the post-war golden age, investment decisions were dominated by industrial firms. But now, they are dominated by financial corporations. This change has been accompanied by deleterious effects on economic growth, stagnant wages, and an upward shift in the distribution of income and wealth. The increasing importance of finance in the economy in the United States, at least, is illustrated by the above graph. The impact of the global financial crisis is immediately apparent in 2008.

The distinction between having investment directed by finance or by industry might not make any sense to you if you think of every investment as like purchasing a bond. In this sort of way of looking at things, every investment can be evaluated by a Return On Investment, taking suitable account of risk, the payback period, and so on. It does not matter if one is talking about a college degree; research and development in, say, clean energy; a painting by Monet; or a stock option. To the financier, it is all one.

I take some of the most notable work of Alfred Eichner (1937-1988) as a description of the previous era. Eichner learned a lot about how corporations set prices by looking at the results of Senate Committee on the Judiciary, Subcommittee on Antitrust and Monopoly, as chaired by Estes Kefauver. Various corporate executives from the steel industry testified. Rubio, as I understand it, could similarly investigate how American businesses operate now.

Eichner theorized megacorporations. These are corporations that operate multiple plants and produce multiple products and that try to maintain market power. Eichner took aboard the idea, as developed by Gardiner Means and Adolfe Berle (1932), that ownership and control are separate in the modern corporation. In a sense recently explained by Dan Davies, Eichner's approach is microfounded. His theory is consistent with recognizing the principal agent problems that come about when a corporate board is somewhat independent of stock owners, when corporate executives are another group of personnel, and so one. According to Eichner, managers in the megacorp are interested in pursuing a satisfactory rate of growth, not in maximizing economic profits.

Eichner recognizes that corporations set prices as a markup on costs. He builds on the survey findings of R. L. Hall and C. J. Hitch. Eichner's ideas relate to theories of administered or full cost pricing. I guess they are consistent with Robin Marris's managerial theory of the firm.

Markups vary among industries and within an industry over time. How is the markup set? According to Eichner, the markup, at least for industry leaders in price-setting, are put at the level needed to finance investment for planned growth targets. Eichner draws an analogy to a tax, in the Soviet Union, on turnover. This tax was used to finance planned investment.

Eichner had some correspondence with Joan Robinson. He saw his theory of the megacorp as compatible with Post Keynesian theories of growth.

I explicitly do not claim that this theory is descriptive of how investment is determined nowadays in the United States. But I find lots of interesting ideas here.

  • Alfred S. Eichner. 1973. A Theory of the Determination of the Mark-up Under Oligopoly pp. 1184-1200.
  • William Milberg (ed.) 1992. The Megacorp & Macrodynamics: Essays in memory of Alfred Eichner M. E. Sharpe.