Saturday, September 26, 2020

Keynes and Henderson Create A Qualitative Multiplier

In 1929, John Maynard Keynes and Hubert D. Henderson wrote, Can Lloyd George Do It? The Pledge Examined. This was published by The Nation and Athenaeum and is an examination of the pledge by the leader of the Liberal party, if elected, to dramatically reduce the amount of unemployment in Great Britain. (I was inspired to look up this work while reading Zachary Carter's new book.)

Chapter VI of Keynes and Henderson is concerned with "How Much Employment Will the Liberal Plan Provide?" The direct employment for each million pounds can be quantified. The authors divide the resulting indirect employment into two types. The first, in the industries that directly and indirectly supply road-building, housing, and so on, Keynes and Henderson think can be quantified:

VI.2 The Importance of Indirect Employment

"...There is nothing fanciful or fine-spun about the proposition that the construction of roads entails a demand for road materials, which entails a demand for labour and also for other commodities, which, in their turn, entail a demand for labour. Such reactions are of the very essence of the industrial process. Why, the first step towards a right understanding of the economic world is to realise how far-reaching such reactions are, to appreciate how vast is the range of trades and occupations which contribute to the production of the commonest commodities. That a demand for a suit of clothes implies a demand for yarns and tops, and so for wool; that the services of farmers, merchants, engineers, miners, transport workers, clerks, are all involved - this is the A B C of economic science...

Generally speaking, the indirect employment which schemes of capital expenditure would entail is far larger than the direct employment. This fact is one of the strongest arguments for pressing forward with such schemes; for it means that the greater part of the employment they would provide would be spread far and wide over the industries of the country. But the fact that the indirect employment would be spread far and wide does not mean that it is in the least doubtful or illusory. On the contrary, it is calculable within fairly precise limits..."

The second type of indirect employment results from the multiplier effects on aggregate demand of an increase in government spending. At this time, Keynes did not think these indirect effects could be estimated ahead of time, even though he considered them of immense importance:

VI.3 The Cumulative Force of Trade Activity

"But this is not the whole of the story. In addition to the indirect employment with which we have been dealing, a policy of development would promote employment in other ways. The fact that many workpeople who are now unemployed would be receiving wages instead of unemployment pay would mean an increase in effective purchasing power which would give a general stimulus to trade. Moreover, the greater trade activity would make for further trade activity; for the forces of prosperity, like those of trade depression, work with a cumulative effect. When trade is slack there is a tendency to postpone placing orders, a reluctance to lay in stocks, a general hesitation to go forward or to take risks. When, on the other hand, the wheels of trade begin to move briskly the opposite set of forces comes into play, a mood favourable to enterprise and capital spreads through the business community, and the expansion of trade gains accordingly a gathering momentum.

It is not possible to measure effects of this character with any sort of precision, and little or no account of them is, therefore, taken in 'We Can Conquer Unemployment." But, in our opinion, these effects are of immense importance. For this reason we believe that the effects on employment of a given capital expenditure would be far larger than the Liberal pamphlet assumes. These considerations have a bearing, it should be observed, on the time factor in Mr. Lloyd George's pledge. It is a mistake to suppose that a long interval would elapse after, let us say, the work of road construction had been commenced before the full effect on employment would be produced. In the the economic world, 'coming events cast their shadows before,' and the knowledge that large schemes of work were being undertaken would give an immediat fillip to the whole trade and industry of the country."

It would take the work, a few years later, of Richard Kahn and James Meade to formalize these indirect effects and show how to quantify them, in terms of the marginal propensity to consume.

Thursday, September 24, 2020

"When Economists Are Wrong"

In a blog associated with the Frankfurter Allegmeine, Gerald Braunberger criticizes the effects of Sraffian political economy on Italian policy in the 1970s. I rely on google translate and subject matter expertise to make some sense out of this. By the way, Bertram Schefold shows up in the comments. I would like to know more about the motivations behind this. Does Braunberger think the public is increasingly aware that mainstream economics is broken?

Before I disagree, I note Braunberger seems well-informed on some points. I know of grumbles about Garegnani's treatment of Sraffa's archives. And I have heard that the Trieste summer schools were torn between those who emphasized long period logic and Post Keynesians who emphasized uncertainty, money, and historical time. On another point, I do not see why Sraffians giving policy advice should care about whether their advice is consistent with the advice Ricardo had for Britain during and after the Napoleonic war. I would think Sraffians in Italy during the 1970s would be more interested in Marx's views, anyways.

I do not understand what non-Sraffian theory Braunberger thinks exists. All economists should (but do not) recognize no reason exists to think that a lower real wage, in a time of depression, will encourage firms to adopt more labor-intensive techniques and thereby increase employment. In parallel, higher real wages need not decrease employment through the adoption of less labor-intensive techniques. Supply and demand just is not a logically-consistent model, in which conclusions follow from assumptions, of wages and employment.

This does not mean that real wages can be increased willy-nilly, without any consequences. Income effects could be important. And one might want to worry about the possibility of a capital strike. I agree that the political slogan, "The wage as the independent variable" draws directly on Sraffa.

More than economics was involved in the going-ons in Italy in the 1970s. When activists are kidnapping and executing the prime minister and the government is imprisioning leftists without discrimination, firms, government, and unions are unlikely to come to a peaceful agreement about distribution.

Furthermore, Italy was not isolated from the wider world. Were the lira and the mark pegged to the dollar before Nixon ended Bretton Woods? The world-wide rise in oil prices was not the result of Sraffian policy advice. Wage-push inflation arose in many countries; it was not just an Italian problem. Sraffa's colleagues had worked out an explanation of stagflation long before the event. I would think this is an example of when (heterodox) economists are right. (A Tax-based Income Policy (TIP) is a policy idea I associate with American Post Keynesians, like Sidney Weintraub, that might have been worth trying in some countries in the 1970s.)

Saturday, September 19, 2020

Visualizing The Effects Of Markups: A Numeric Example

Figure 1: A Pattern Diagram

This post illustrates the numeric example used here. The example is of an economy in which two commodities, iron and corn, are produced by workers from inputs of iron and corn. Two processes are available for each industry, leading to a choice among four techniques. I analyze stationary states.

I look at prices of production, with a bushel corn as numeraire and wages paid out of the surplus at the end of the year. Prices of production are defined so as to allow for markups in both industries. Figure 1 shows the variation in switch points on the wage frontier with variations in the ratio of markups.

I am interested in how variations in markups can bring about qualitative changes favorable to labor pressing for higher wages. For example, around the switch point between Alpha and Gamma in Region 3 and at the lower wage for such a switch point in Region 4, a higher wage is associated with firms wanting to hire more workers, given the level of net output of corn.

Figure 2: The Solution of the LP in Region 1

I analyze the choice of technique by analyzing the solution of a linear program for a cost-minimizing firm. Figure 2 illustrates. (I have this figure wrong in my working paper.) Above the heavy locus, firms are willing to only produce iron. The regions in which profit-maximizing firms are willing to adopt each iron-producing process are indicated. Below the heavy locus, firms are only willing to produce corn. This region is also partitioned by the two corn-producing process.

Firms are willing to produce both iron and corn only along the heavy locus. The economy is capable of being reproduced only with the indicated combination of wages and prices. This is how the wage frontier appears in this space.

Figure 3: A Pattern over the Axis for the Scale Factor for the Rate of Profits

Figure 3 illustrates the solution to the LP with a higher markup in corn production or a smaller markup in iron production. For a wage of zero, firms are indifferent about the choice of the corn-producing process when prices are such that the economy can be reproduced. Figure 4 shows the case in which relative markups are such that firms are indifferent between the two iron-producing processes at a wage of zero.

Figure 4: Another Pattern over the Axis for the Scale Factor for the Rate of Profits

Figure 4 shows a curious case. Consider the point where firms are willing to operate the first iron-producing process and both of the corn-producing processes. At this combination of the wage and prices, firms are also willing to operate the second iron-producing process. This is a bit more obvious by examining Figures 5 and 6, which are for a slightly higher ratio of the markup in corn production to the markup in iron production. The region in which firms are willing to operate only the second iron-producing process has split up into three subregions. Figure 4 arises for a ratio of markups where the middle subregion is just emerging.

Figure 5: A Four-Technique Pattern
Figure 6: The Solution of the LP in Region 4
Figure 7: An Enlargement in Region 4

Figure 8 illustrates the ratio of markups in which the first and second of the three subregions, in which the firm is only willing to operate the second iron-producing processes are just merging. The middle subregion is such a sliver that it is not really visible on the graph.

Figure 8: A Reswitching Pattern

For the ratio of markups illustrated in Figure 9, firms are willing to operate the second-iron producing process all along the heavy locus. When prices are such that economy can be reproduced, they are willing to operate the first iron-producing process only at the indicated tangent point.

Figure 9: Another Reswitching Pattern

Figure 10 illustrates the solution to the LP for a ratio of markups in right-most region in Figure 1. Markups in the iron industry are much higher than the markups in the corn industry.

Figure 10: The Solution of the LP in Region 6

These diagrams illustrate, for a numerical example, the whole range of relative markups among industries. Qualitative changes in switch points are indicated. And I have demonstrated that the Cambridge capital controversy has implications for non-competitive markets. Can you find this point being made in the literature on industrial organization?

Sunday, September 13, 2020

Visualizing the Effects of Markups on the Choice of Technique

I have a working paper.

Abstract: This article extends to unequal rates of profits a derivation of prices of production from a linear program. A partition of the price-wage space is illustrated in an example with two produced commodities. The variation in the solution of the LP with perturbations of relative markups is illustrated. This analysis provides an intuitive explanation of how the reswitching of techniques and of how capital reversing can emerge in non-competitive markets.

Sunday, September 06, 2020

David Graeber (1961 - 2020) On Usenet A Long Time Ago

I first became aware of David Graeber as a poster on Usenet back in the 1990s.

Many people who have succeeded in this world have no interest in conducting honest discussions. I found some places where one could have cheerful talk, including with harsh disagreement. And I found other places not so much. I probably fit in with the latter.

Sometime in November 1998, a thread arose, "A Donaldism for David Friedman". David Friedman is Milton's son and also promotes plutocracy under the guise of 'liberty'. The thread was about how participants should treat other posters who continually lied and said others secretly wanted to set up a totalitarian dictatorship where they could kill those who disagreed with them. Graeber was not having any of this:

[Dan Clore wrote:]
David [Friedman] wrote:
His basic thesis is that most of the people who claim to be left anarchists are really leninists, or something similar, who mask their views because their true views are unfashionable. If he can demonstrate it about Chomsky, who has the virtue of having written lots of stuff over a long period of time, and if, by forcing people on line to defend Chomsky, he can demonstrate it about them, he can discredit (at least) online left-anarchism--as a movement, and perhaps as a theory. That tactic doesn't appear workable applied to you, since you seem to have no particular interest in defending Chomsky, but it might work for those who do. And, given his beliefs about left-anarchism, it seems to me that it is a reasonable tactic.
Unfortunately for Jimi's "basic thesis", Chomsky has a long historical record in print of attacking Marxism-Leninism and state socialism in general -- including the 1960s, when it was much, much more "fashionable" than anarchism / libertarian socialism. That fact that empirical evidence disproves Jimi's thesis only seems to make him believe in it all the more rabidly: draw what conclusions from that you will.

I am beginning to finally understand what Friedman means by "reasonable". He appears to apply the term only to whether one's actions are consistent with one's premises, and rational in the sense of logically coherent. He does not appear to feel that premises themselves can be unreasonable. One could presumably start from the assumption that David Friedman is indeed a purple-assed baboon and that he ate one's grandmother and as long as one's techniques of argument are consistent with this premise, one is not an unreasonable person.

The question is whether he realizes this  can only confuse everyone else because just about everyone else does not define "reasonable" in this  way. "Reasonable", for most people, implies among other things an ability to compromise, to accomodate other points of view... "Reasonable" implies you are _not_ a fanatic who starts with wild unfalsifiable accusations, not that you have correctly concluded that, if your opponents are evil monsters, then making wild unfalsifiable accusations is best way to make them look bad.

I put forward to Mr. Friedman, then: if you are really a reasonable person ("reasonable" in the common sense, not in your own specialized sense) you will stop using the word in this way because it is obviously deceptive. It allows you to constantly insist to people who do not know you are using the word in a highly idiosyncratic, specialized sense that obvious fanatics who never compromise on anything are "reasonable", and people who are not fanatics and interested in accomodating different points of view are not. At the very least you can shift to a word like "rational". "Reasonable" is an important word with a very rich history and your usage is, to my mind, and I think to others,  just a horrible  perversion of it.


It is very difficult to navigate Google's version of the Usenet archives.

I thought Debt: The First 5,000 Years quite interesting. I probably recall it badly. I learned that money first emerged as the second-hand trading of promises in communities where everybody knew everybody. It was not a matter of solving a problem of the lack of the double-coincidence of wants in a barter system. These debts became more formal, more rigid, when communities became more hierarchical, more structured. The introduction of coins, as tokens, came about when you had outsiders, like an empire's soldiers visit, and they had no interest in participating in a village community as an equal. Debts periodically got out of hand, and a jubilee would be declared. (Yes, I know, Graeber was mistaken about Apple. I know several entrepreneurs who have started their own high tech companies.)

I was vaguely aware of Graeber jeopardizing his career at Yale with his support of the union for graduate students, his organizing role in Occupy Wall Street, and his move to London. I read his essay "Bullshit Jobs", but have yet to read the book.

This post is totally inadequate for an appreciation of him.

Update: Benjamin Balthaser in Jacobin, Michael Hardt in Jacobin, Malcolm Harris in the Nation, Sam Roberts for the New York Times, Nathan Robinson in his Current Affairs, Rebeccca Solnit in the Guardian, and many in the New York Review of Books.

Friday, September 04, 2020

A Derivation Of Sraffa's First Equations

1.0 Introduction

Piero Sraffa wrote down his 'first equations' in 1927, for an economy without a surplus. D3/12/5 starts with these equations for an economy with three produced commodities. I always thought that they did not make dimensional sense, but Garegnani (2005) argues otherwise. This post details Garegnani's argument, albeit with my own notation.

There are arguments about how and why Sraffa started on his research project I do not address here. The question is how did he relate what he was doing at this early date to Marx. In addition to Garegnani, DeVivo, Gehrke, Gilibert, Kurz, and Salvadori are worth reading here.

2.0 Givens

I assume an economy in a self-replacing state in which n + 1 commodities are produced.

  • c0,0 is the input of the first commodity used in producing the output of the first industry.
  • (c., 0)T = [c1,0, c2,0, ..., cn,0] are the inputs of the remaining n commodities used in producing the output of first industry.
  • c0 = [c0,1, c0,2, ..., c0,n] are the inputs of the first commodity used in producing the output of the remaining industries
  • The element ci,j, i, j = 1, 2, ..., n, of the matrix C is the input of the ith commodity used in producing the output of the jth industry.
  • q0 = is the quantity produced of the first commodity.
  • (q)T = [q1, q2, ..., cn] are the outputs of the remaining n commodities used in producing the output of first industry.

All quantities are given in physical units. I abstract from fixed capital; all inputs are used up in the production of the outputs. Table 1 presents these parameters for the first example in the first chapter in Sraffa 1960.

Table 1: The Example from Sraffa (1960), Chapter 1
Ironc0, 0 = 8 tons ironc0 = [12 tons iron]
Wheatc., 0 = [120 quarters wheat]C = [280 quarters wheat]
Outputq0 = 20 tons ironq = [400 quarters wheat]

The following must hold for economy to be in a self-replacing state:

qi = ci,0 + ci,1 + ... + ci,n, i = 0, 2, ..., n

All quantities are non-negative. The economy must hang together in some sense. In Sraffa's terminology, all commodities are basic.

3.0 Coefficients of Production

I like to think of the coefficients scaled for unit output in each industry. Accordingly, define:

a0, 0 = c0, 0/q0
(a., 0)i = (c., 0)i/qj, i = 1, 2, ..., n
(a0)j = (c0)j/qj, j = 1, 2, ..., n
(A)i,j = (C)i,j/qj, i, j = 1, 2, ..., n
4.0 All Quantities Measured in Unit Outputs of the First Industry

The given inputs can be thought of as produced in the previous year. The amount of, say, iron directly used as input in producing other commodities is (a0 q). Table 2 indicates how much iron is needed as input in all previous years.

Table 2: Iron Inputs for Other Commodities
0a0 q
1a0 A q
2a0 (A)2q
na0 (A)nq

Even though my notation picks out the first commodity, there is nothing special about it. Suppose some commodity is selected. Let v0 be the quantity of this commodity needed directly and indirectly to produce a unit of the first commodity. Let v be the quantities of this commodity needed directly and indirectly to produce each of the remaining commodities. v0 and v must satisfy the following system of n + 1 linear equations:

v0 a0, 0 + v a., 0 = v0
v0 a0 + v A = v

For a non-trivial solution to exist, the determinant of the matrix in Table 3 must be zero, which it is in the case pf the Sraffa example.

Table 3: A Matrix
1 - a0, 0 = (3/5) tons-a0 = [(-3/100) tons]
-a., 0 = [-6 quarters]I - A = [(3/10) quarters]

I set v0 to unity. The amount of this commodity used directly and indirectly in the production of all other commodities is easily found:

v = a0(I - A)-1

5.0 Rescaling the Givens

I then rescale the givens.

b0, 0 = v0 c0, 0
bi, 0 = vi (c., 0)i, i = 1, 2, ..., n
b0, j = v0 (c0)j, j = 1, 2, ..., n
bi, j = vi ci, j, i, j = 1, 2, ..., n
s0 = v0 q0
si = vi qi, i = 1, 2, ..., n

Table 4 presents Sraffa's example with these calculations. Here, a unit of wheat is 10 quarters. That is, one ton iron is used directly and indirectly in producing 10 quarters of wheat.

Table 4: Sraffa's Example Again
Ironb0, 0 = 8 tons ironb0 = [12 tons iron]
Wheatb., 0 = [12 tons wheat]B = [28 tons wheat]
Outputs0 = 20 tons irons = [40 tons wheat]

I then have Sraffa's 'first equations':

b0, j + b1, j + ... + bn, j = sj, j = 0, 1, ..., n

For the economy to be in a self-replacing state, the following must hold:

bi, 0 + bi, 1 + ... + bi, n = si, i = 0, 1, ..., n

Even though I am adding together, say, quantities of iron and wheat, the dimensions are consistent.

6.0 A Re-interpretation

Suppose the first produced commodity is labor, not iron. c0, 0 becomes the amount of labor performed in households (outside the market) to reproduce the labor force. c., 0 is the commodity basket paid out in wages when the workers obtain all of the surplus product. a0 are the direct labor coefficients for each industry, and A is the Leontief input-output matrix. v is the vector of labor valus (also known as employment multipliers). Under the assumptions, prices of production are identical to labor values.

This model is descriptive. The givens do not show how required inputs might decrease with innovation or the formal and real subsumption of labor.

  • Garegnani, Pierangelo (2005) On a turning point in Sraffa's theoretic and interpretative position in the late 1920s. European Journal of the History of Economic Thouht 12 (3): 453-492.
  • Gehrke, Christian, Heinz D. Kurz, and Neri Salvadori (2019) On the 'origins' of Sraffa's production equations: A reply to de Vivo. Review of Ploitical Economy 31 (1): 100-114.