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.

Tuesday, October 17, 2017


  • A July 24 Jonathan Schlefer article, "Market Parables and the Economics of Populism: When Experts are Wrong, People Revolt", in Foreign Affairs. Schlefer cites the Cambridge Capital Controversy as a demonstration that the neoliberal political project of remaking the world around unembedded markets is doomed to failure.
  • A September 11 interview with Daniel Kahneman in which he basically credits Richard Thaler with inventing behavioral economics. (In his memoirs, Misbehaving, Thaler is also explicit about the disciplinary boundaries between economics and psychology.)
  • Richard Thaler's anomaly columns in the Journal of Economic Perspectives
  • I have not read Nancy Maclean's Democracy in Chains. Marshall Steinbaum reviews this book in Boston Review. Henry Farrell & Steven Teles respond.

Another ongoing brouhaha is about Alice and Wu's undergraduate paper documenting the sexism on Economic Job Market Rumors.

Wednesday, October 11, 2017

Others With Points Of View Like Sraffa's

In Production of Commodities by Means of Commodities, Sraffa writes:

"others have from time to time independently taken up points of view which are similar to one or other of those adopted in this paper and have developed them further or in different directions from those proposed here." -- P. Sraffa (1960): pp. vi - vii.

Who is Sraffa talking about? I suggest the following, and their works, at least:

  • Tjalling C. Koopmans (1957). Three Essays on the State of Economic Science. New York: McGraw-Hill
  • Wassily W. Leontief (1941). Structure of the American Economy, 1919-1929.
  • Jacob T. Schwartz (1961). Lectures on the Mathematical Method in Economics. New York: Gordon & Breach.
  • John Von Neumann (1945-1946). A Model of General Economic Equilibrium, A Model of General Economic Equilibrium. V. 13, No. 1: pp. 1-9.

I thought about listing David Hawkins and Herbert Simon, given how frequently the Hawkins-Simon condition is cited in expositions of Leontief input-output analysis. I might also mention Nicholas Georgescu-Roegen, the creator of the non-substitution theorem. The work of Ladislaus Bortkiewicz, Georg von Charasoff, Vladimir K. Dmitriev, and Robert Remak, as I understand it, mostly predates Sraffa's long period of preparation of his masterpiece.

Sunday, October 08, 2017

Economic Impact Of Regional Disasters: A Job For Input-Output Analysis?

This post, unfortunately, is inspired by current events.

Economists can provide guidance on disaster recovery - for example, from earthquakes and hurricanes.

Economists, for a long time, have been developing input-output models of local economies and interactions between them. I think of Walter Isard as a pioneer here. Such models are of practical importance to my post topic.

Regional input-output models can describe disasters with either a supply-side or demand-side approach. In a supply-side approach, the output of an industry is reduced because the inputs into that industry are not available at the pre-disaster level. Some of the outputs of that industry are inputs into other industries. Other outputs satisfy final demands, for example, for household consumption. Input-output modeling can help trace these consequences.

In a demand-side approach, an industry's output is constrained because those who purchase its outputs cannot do so at the pre-disaster level. If those industries who purchase your products are suddenly reduced in size, you must need cut back your output, too.

Some issues arise here. Can supply-side and demand-side approaches be combined without double counting? How should one model the effects of external infusions of aid? Multiplier effects seem to sit comfortably with the demand side approach. The assumption of fixed coefficients in the Leontief input-output approach seems to be an important restriction here. When it comes to modeling resiliency, I think of the work of Adam Rose. Apparently, some use Computational General Equilibrium (CGE) models for this reason.

I do not know enough to have a firm opinion of CGE models. I have the impression that "Computational" is a misnomer; it does not relate to computational theory and Turing machines, as studied in computer science. I am also not sure that the GE in CGE is what I understand as GE. Anyways, practical considerations interact here with the ideological demands impacting economic theory. I like to think that economists are useful in the hard problem of what to do when disaster strikes.

  • Walter Isard. 1951. Interregional and Regional Input-Output Analysis: A Model of a Space-Economy. Review of Economics and Statistics. Vol. 33, No. 4: pp. 318-328.

Saturday, September 30, 2017

Dean Baker's Rigged And Robert Reich's Saving Capitalism

Dean Baker has a new book out: Rigged: How Globalization and the Rules of the Modern Economy Were Structured to Make the Rich Richer. It recounts how laws that define property, markets, and so on have been rewritten, over the last fifty years, to accomplish an upward redistribution of income. This bias for the rich contrasts with the effects of the rules of the game in the half-century golden age following World War II. This is the same theme as Robert Reich's Saving Capitalism: For the Many, Not the Few. And both books are targeted for the common reader. Thus, a review of Baker's book can usefully compare and contrast it with Reich's book. (I have previously reviewed Reich's book.)

Both books focus on a few areas in which the rules have been rewritten to distribute income upward. For example, consider intellectual property rights, especially the extension of patents and copyrights to last longer and to cover more. Baker, I think, discusses the international dimension more than Reich. The United States has been trying to ensure that patent laws are consistent throughout the world. The largest impact of this attempt, perhaps, is on the price of drugs in developing countries, and the subsequent consequences for health and life.

Both discuss how changes in laws have provided companies with more market power and have protected monopolies and oligopolies. Baker has more of a focus on upper-class professionals, such as doctors, dentists, and lawyers. Baker especially emphasizes how they are protected from international competition. So called free trade treaties, like the North America Free Trade Agreement (NAFTA) are selective in who they subject to the rigors of international competition.

Both discuss corporate governance and the impact on the pay of Corporate Executive Officers (CEOs) and top managers. CEO pay went from 20 times averages wages in the 1960s to over 250 times average wage nowadays. In general, CEO pay is set by a committee appointed by the board of directors who, in turn, are appointed by the CEO. Stockholders have little say, even after the Dodd-Frank bill gives stockholders the right to have an up-or-down non-binding vote on pay packages. Baker extends his critique of CEO pay to heads of foundations and to university presidents, for example.

Reich writes more about contracts, bankruptcy, and enforcement. Baker, on the other hand, writes more about the macroeconomic setting. For example, the Federal Reserve is overly focused on the threat of inflation and not so much on unemployment. I know something of the importance of macroeconomic policy from James Galbraith, who has been writing on this theme for a long time. Baker follows his chapter on macroeconomics with a chapter on the financial sector.

I find Baker more analytical and less polemical than Reich. Baker adopts an interesting trope for putting in context large numbers. He frequently converts dollar flows into multiples of the yearly cost of welfare, that is, the yearly outlay on the Supplemental Nutrition Assistance Program (SNAP). He doesn't always carry through this conversion. I suppose a comparison of doctors' incomes among specialities is only one illustration of health care costs and may not require this contextualization.

I think both books contain a similar tension. Part of their point is that a contrast between non-government intervention in markets and more regulation is a false choice. I think Reich is better on ideological critique of, say, marginal productivity theory or the exploded theory of skills-biased technological change. Baker seems less interested in abstract economic theory, although he does ask whether one can really believe CEOs have gotten so much more productive since the 1950s so as to justify the increased inequality in their pay. But Baker keeps on contrasting legislated barriers to competition with what a free market would produce, that is, less rent. He is too accepting, at least for rhetorical purposes, of traditional economic theory for my tastes. Reich is more consistent with emphasizing that no such thing as a free market can ever exist, absent laws defining markets. Baker does start and conclude with this point.

Baker proposes any number of innovative policies throughout the book, and gathers them together in the second-to-last chapter. For example, Baker suggests that corporations be given an option of issuing non-voting stock to the government, instead of paying corporate income tax. Inventors could be given the option of competing for contest prizes, where a requirement of signing up is that they cannot receive patents over a number of years. (As far as I am aware, existing prize contests have no such connection to the patent system.) He also suggests that governments can pay for medical tourism, where those needing operations travel to other countries in search of cheaper prices. Baker has thought about how some of his policy proposals could first be implemented on a small scale. In general, I find both Baker and Reich too voluntaristic in policy proposals. But I do not know how to avoid that in today's general dismal climate.

I guess my conclusion is that Reich's book is broader, but that Baker's book is generally better in areas of Baker's focus.

Monday, September 18, 2017

Another Example Of A Real Wicksell Effect Of Zero

Figure 1: A Reswitching Example with a Fluke Switch Point
1.0 Introduction

A switch point that occurs at a rate of profits of zero is a fluke. This post presents a two-commodity example with a choice between two techniques, in which restitching occurs, and one switch point is such a fluke. Total employment per unit of net output is unaffected by the choice of technique. Furthermore, the numeraire-value of capital per unit net output is also unaffected by the mix of techniques adopted at a switch point with a positive rate of profits. This is not the first example I present in a draft paper.

2.0 Technology

Consider the technology illustrated in Table 1. The managers of firms know of three processes of production. These processes exhibit Constant Returns to Scale. The column for the iron industry specifies the inputs needed to produce a ton of iron. Two processes are known for producing corn, and their coefficients of production are specified in the last two columns in the table. Each process is assumed to require a year to complete and uses up all of its commodity inputs. (The coefficients were "nicer" fractions before I started perturbing it. Octave code was useful.)

Table 1: The Technology

This technology presents a problem of the choice of technique. The Alpha technique consists of the iron-producing process and the corn-producing process labeled Alpha. Similarly, the Beta technique consists of the iron-producing process and the corn-producing process labeled Beta.

3.0 Quantity Flows

Quantity flows can be analyzed independently of prices. Suppose the economy is in a self-replacing state, with a net output consisting only of corn. Table 2 displays quantity flows for the Alpha technique, when the net output consists of a bushel of corn. The last row shows gross outputs, for each industry. The entries in the three previous rows are found by scaling the coefficients of production in Table 1 by these gross outputs. Table 3 displays corresponding quantity flows for the Beta technique.

Consider the quantity flows for the Alpha technique. The row for iron shows that each year, the sum (9/356) + (11/356) = 5/89 tons are used as iron inputs in the iron and corn industries. These inputs are replaced at the end of the year by the output of the iron industry, with no surplus iron left over. In the corn industry, the sum 10/89 + 11/89 = 21/89 bushels are used as corn inputs in the two industries. When these inputs are replaced out of the output of the corn industry, a surplus of one bushel of corn remains. The net output of the economy, when these processes are operated in these proportions, is one bushel corn. The table allows one to calculate, for each technique, the labor aggregated over all industries per net unit output of the corn industry. Likewise, one can find the aggregate physical quantities of capital goods per net unit output of corn.

Table 2: Quantity Flows for Alpha Technique
Labor5/89 ≈ 0.0562 Person-Yrs.57,101/51,353 ≈ 1.11 Person-Yrs.
Iron9/356 ≈ 0.0253 Tons11/356 ≈ 0.0309 Tons
Corn10/89 ≈ 0.112 Bushels11/89 ≈ 0.124 Bushels
Output5/89 ≈ 0.0562 Tons110/89 ≈ 1.24 Bushels

Table 3: Quantity Flows for Beta Technique
Labor3/577 ≈ 0.00520 Person-Yrs.671/577 ≈ 1.16 Person-Yrs.
Iron27/11,540 ≈ 0.00234 Tons33/11,540 ≈ 0.00286 Tons
Corn6/577 ≈ 0.0104 Bushels2,519/2885 ≈ 0.873 Bushels
Output3/577 ≈ 0.00520 Tons5,434/2,885 ≈ 1.88 Bushels

4.0 Prices and the Choice of Technique

The choice of technique is analyzed based on prices of production and cost-minimization. Labor is assumed to be advanced, and wages are paid out of the surplus product at the end of the year. Corn is taken as the numeraire. Figure 1 graphs the wage curve for the two techniques. The cost-minimizing technique, at a given rate of profits, maximizes the wage. That is, the cost-minimizing techniques form the outer envelope, also known as, the wage frontier, from the wage curves. In the example, the Beta technique is cost minimizing for high rates of profits, while the Alpha technique is cost-minimizing between the two switch points. At the switch points, any linear combination of the two techniques is cost-minimizing.

One switch point is a fluke; it occurs for a rate of profits of zero. Any infinitesimal variation in the coefficients of production would result in the switch point no longer being on the wage axis. This intersection between the wage curves would then either occur at a negative or positive rate of profits. In the former case, the example would be one with a single switch point with a non-negative, feasible rate of profits, and the real Wicksell effect would be negative at that switch point. In the latter case, it would be a reswitching example, with the Beta technique uniquely cost-minimizing for low and high rates of profits. The real Wicksell effect would be negative at the first switch point and positive at the second.

5.0 Aggregates

In calculating wage curves, one can also find prices for each rate of profits. Table 5 shows certain aggregates, as obtained from Tables 2 and 3 and the price of iron at the switch point with a positive rate of profits. (Table 4 shows this price.) The numeraire value of capital per person-year, for a given technique and a given rate of profits, is the additive inverse of the slope of a line joining the intercept of the technique's wage curve with the wage axis to a point on the wage curve at the specified rate of profits. The capital-labor ratio, for a given technique, varies with the rate of profits, unless the wage curve is a straight line. Since a switch point occurs on the wage axis, the capital-labor ratio for both techniques at the other switch point is identical. As seen in Table 5, it does not vary among the two cost-minimizing techniques at the switch point with a positive rate of profits. The real Wicksell effect is zero at this switch point.

Table 4: Price Variables at Switch Point with Real Wicksell Effect of Zero
Rate of Profits125,483/209,727 ≈ 59.8 Percent
Wage9,226,807/24,957,513 ≈ 0.370 Bushels per Person-Yr.
Wage7,558/595 ≈ 12.7 Bushels per Ton

Table 5: Aggregates at Switch Point with Real Wicksell Effect of Zero
Net Output1 Bushel Corn
Labor674/577 ≈ 1.17 Person-Years
Physical Capital5/89 Tons Iron3/577 Tons Iron
21/89 Bushels Corn2,549/2,885 Bushels Corn
Financial Capitl113/119 ≈ 0.945 Bushels Corn
Capital-Labor Ratio65,201/80,206 ≈ 0.813 Bushels per Person-Yr.

6.0 Implications

A certain sort of indeterminacy arises in the example. For a given quantity of corn produced net, the ratio of labor employed in corn production to labor employed in iron production varies, at the switch point with a positive rate of profits, from around 1/5 to just over 223 to one. A change in technique leaves total employment unchanged, given net output, even as it alters the allocation of labor among industries. At the switch point, a change in technique, given net output, leaves the total value of capital unchanged, while, once again, altering its allocation among industries.

Suppose the economy is in a stationary state with the wage slightly below the wage at the switch point with a real Wicksell effect of zero. The Beta technique is in use. Consider what happens if a positive shock to wages result in a wage permanently higher than the wage at the switch point. The shock might be, for example, from an unanticipated increase in the minimum wage. Prices and outputs will be out of proportion, and a perhaps long disequilibrium adjustment process begins. Suppose that, eventually, after all this folderol, the economy, once more, attains another stationary state. The Alpha technique will now be in use. Labor hired per unit net output will be unchanged. The only variation in the value of capital goods per unit labor is a result of price changes, independent of the change in technique.

Thursday, September 14, 2017

Bifurcation Diagram for Fluke Switch Point

Figure 1: A Bifurcation Diagram

I have previously illustrated a case in which real Wicksell effects are zero. I wrote this post to present an argument that that example is not a matter of round-off error confusing me.

Consider the technology illustrated in Table 1. The managers of firms know of three processes of production. These processes exhibit Constant Returns to Scale. The column for the iron industry specifies the inputs needed to produce a ton of iron. Two processes are known for producing corn, and their coefficients of production are specified in the last two columns in the table. Each process is assumed to require a year to complete and uses up all of its commodity inputs.

Table 1: The Technology

Figure 1 shows two loci in the parameter space defined by the two coefficients of production a0,2α and a2,1. The solid line represents coefficients of production for which the wage curves for the two techniques are tangent at a point of intersection. The dashed line represents parameters for which a switch point exists on the wage axis. The point at which these two loci are tangent specifies the parameters for this example. Figure 2 repeats the graph of the wage curves for that example.

Figure 2: A Fluke Switch Point

Suppose coefficients are as in the example in the main text, but a0,2α is somewhat greater. Then the wage curve for the Alpha technique lies below the wage curve for Beta for all non-negative rates of profits not exceeding the maximum rate of profits. For all feasible rate of profits, Beta is cost-minimizing. On the other hand, if a0,2α is somewhat less than in the example, the wage curve for Alpha is somewhat higher than in Figure 2. The wage curve for Alpha will intersect the wage curve for Beta at two points, one with a negative rate of profits exceeding one hundred percent and one for a switch point with a positive rate of profit. As indicated in Figure 1, this combination of parameters is an example of the reserve substitution of labor

In the region graphed in Figure 1, if the coefficient of production a0,2α falls below the loci at which the two wage curves are tangent, the wage curves will have two intersections. Suppose a2,1 is greater than in the example in the main text. In the corresponding region between the two loci in Figure 1, the rate of profits at both intersections of the wage curves are negative. In this region of the parameter space, Beta remains cost-minimizing for all feasible non-negative rates of profits. If a2,1 is less than in the example, the rate of profits for both intersections are positive in the region between the two loci. The example is one of reswitching. In effect, which intersection of the wage curves is a switch point on the wage axis changes along the locus for the switch point on the wage axis.

Consider the rate of profits at which the wage curves have a repeated intersection, that is, are tangent, for the corresponding locus in Figure 1. Toward the left of the figure, this rate of profits is positive, while it is negative toward the right. By continuity, this rate of profits is zero for a single point in the graphed part of the parameter space. The two loci must be tangent for this set of parameters. The appearance of a switch point with a real Wicksell effect of zero in this post is not a result of round-off error or finite precision arithmetic. Such a point exists for exactly specified coefficients of production.