Elsewhere

• Ramon Llul was a medieval scholar who invented social choice theory (specifically, the Borda count), as seen in a manuscript discovered in 2001(?). (Other discoveries.)
• A review of Steve Paxton's Unlearning Marx: Why Soviet Failure was a Triumph for Marx. Maybe I want to read this.
• Pierangelo Garegnani's Capital Theory, the Surplus Approach, and Effective Demand.

Welcome

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.

Variations In Switch Points With Markups In The 'Corn' Industry

Figure 1: Variation of Switch Points with the Markup in the Corn Industry

1.0 Introduction

I have been re-creating some of my past analyses. The graphs in this post look a bit different because I impose a requirement that the relative markups sum to unity.

2.0 Technology

Consider an economy which produces three commodities, iron, steel, and corn, with the technology specified in Table 1. Two processes are available for producing each commodity. The coefficients of production in a column specify the person-years of labor, tons of iron, tons of steel, and bushels of corn required to produce a unit of output of the given industry.

Table 1: The Technology

Input	Iron Industry		Steel Industry		Corn Industry
	a	b	c	d	e	f
Labor	1/3	1/10	5/2	7/20	1	3/2
Iron	1/6	2/5	1/200	1/100	1	0
Steel	1/200	1/400	1/4	3/10	0	1/4
Corn	1/300	1/300	1/300	0	0	0

Eight techniques (Table 2) are defined for this technology. Each technique is defined by the operation of one process in each of the three industries. All three commodities are Sraffian basics in all techniques. That is, each commodity is a direct or indirect input in the production of all commodities. For example, iron is used directly as an input in the first corn-producing process, and steel is used indirectly in producing corn with this process since steel is an input in either iron-producing process

Table 2: Techniques

Technique	Processes
Alpha	a, c, e
Beta	a, c, f
Gamma	a, d, e
Delta	a, d, f
Epsilon	b, c, e
Zeta	b, c, f
Eta	b, d, e
Theta	b, d, f

3.0 Prices of Production

Prices of production are defined here for given ratios of markups among industries. The ratios of rates of profits among industries are assumed stable, but rates of profits are not necessarily uniform. Lack of uniformity in rates of profits can result from variations in evaluations of profits among industries due to idiosyncratic properties of investment; from barriers to entry arising from, for example, secrets in manufacture; and from legal monopolies (D’Agata 2018). Let s₁ r, s₃ r, and s₃ r be the rate of profits in the iron, steel, and corn industries respectively. I call r the scale factor for the rate of profits. The usual system of equations, with labor advanced, must be satisfied for prices of production for a given technique.

As a matter of scaling, suppose the markups lie on a simplex:

s₁ + s₂ + s₃ = 1

Suppose that a bushel of corn is the numeraire. In drawing various graphs, I consider only variations in the markup in the corn industry, with markups in producing iron and steel assumed identical:

s₁ = s₂

The solution to this system, for each technique, has a single degree of freedom, which can be expressed with the wage as a function of the scale factor for the rate of profits

4.0 The Choice of Technique with Competitive Markets

Figure 1 graphs the wage curves for four techniques, given competitive markets. The same relative markups are obtained in all industries. The cost-minimizing technique at a given wage maximizes the scale factor for the rate of profits. The cost-minimizing technique at a given scale factor maximizes the wage. The outer frontier of all wage curves shows the variation of the cost-minimizing technique with distribution. Wage curves are graphed in Figure 1 only for the techniques on the outer frontier. This type of figure, usually for competitive markets, is the most well-known graph in post-Sraffian price theory

Figure 2: Capital-Reversing with Competitive Markets

Around the so-called perverse switch point, the firms in the corn industry switch from the second corn-producing process to the first at a lower wage. That is, they adopt a process that requires less labor to be hired per bushel of corn produced gross. This is known as the reverse substitution of labor (Han and Schefold 2006). For the economy as a whole, the technique adopted at a lower wage requires less labor per unit of net output. This is a consequence of capital-reversing as manifested in a comparison of stationary states (Harris 1973).

5.0 Fluke Cases

Five fluke cases can be found by perturbing the relative markup in the corn industry (Table 3). Figure 3 depicts the wage frontier for the first fluke case. This markup occurs when reswitching is just emerging.

Table 3: Fluke Switch Points

Markup for Corn	Fluke Case
s3 ≈ 0.211996	Reswitching pattern for Gamma vs. Delta.
s3 ≈ 0.249246	Four technique pattern for Gamma, Delta, Eta, and Theta.
s3 ≈ 0.8232415	Alpha vs Beta switch point at wage of zero.
s3 ≈ 0.8696757	Four technique pattern for Alpha, Beta, Gamma, and Delta.
s3 ≈ 0.9307414	Beta vs Delta pattern over r axis

Figure 3: Wage Curves for Gamma and Delta Tangent at Switch Point

6.0 The Choice of Technique with the Full Range of the Markup in the Corn Industry

Figure 1, at the top of this post, is my new type of diagram illustrated for depicting the analysis of the choice of technique. The abscissa is the markup in the corn industry, with given markups of unity in the iron and steel industry. The maximum wage and the wage at switch points along the frontier are plotted. The number and sequence of switch points along the wage frontier are invariant in each numbered region. Fluke switch points partition the numbered regions. Figure 4 enlarges Figure 1 on the right for low wages

Figure 4: Variation of Switch Points with the Markup (Detail)

The qualitative properties of the wage frontier are invariant in each numbered region in Figures 1 and 4. Table 4 describes each numbered region. The cost-minimizing technique along the wage frontier is listed, from a wage of zero to the maximum wage. Some salient properties of switch points and the cost-minimizing technique are summarized in Table 5. Figure 2 depicts the wage frontier for a markup in the corn-industry in region 3, while Figure 3 depicts the wage frontier on the boundary between regions 1 and 2.

Table 4: Variations in the Cost-Minimizing Technique

Region	Range	Technique
1	0 ≤ w ≤ w1	Alpha
	w1 ≤ w ≤ w2	Gamma
	w2 ≤ w ≤ wmax,η	Eta
2	0 ≤ w ≤ w1	Alpha
	w1 ≤ w ≤ w2	Gamma
	w2 ≤ w ≤ w3	Delta
	w3 ≤ w ≤ w4	Gamma
	w4 ≤ w ≤ wmax,η	Eta
3	0 ≤ w ≤ w1	Alpha
	w1 ≤ w ≤ w2	Gamma
	w2 ≤ w ≤ w3	Delta
	w3 ≤ w ≤ w4	Theta
	w4 ≤ w ≤ wmax,η	Eta
4	0 ≤ w ≤ w1	Beta
	w1 ≤ w ≤ w2	Alpha
	w2 ≤ w ≤ w3	Gamma
	w3 ≤ w ≤ w4	Delta
	w4 ≤ w ≤ w5	Theta
	w5 ≤ w ≤ wmax,η	Eta
5	0 ≤ w ≤ w1	Beta
	w1 ≤ w ≤ w2	Delta
	w2 ≤ w ≤ w3	Theta
	w3 ≤ w ≤ wmax,η	Eta
6	0 ≤ w ≤ w1	Delta
	w1 ≤ w ≤ w2	Theta
	w2 ≤ w ≤ wmax,η	Eta

Table 5: Notes on Regions

Region	Summary
1	No reswitching, no capital-reversing, no reverse substitution of labor, no process recurrence.
2	Reswitching of techniques between Gamma and Delta. Capital-reversing and the reverse substitution of labor at the switch point between Gamma and Delta at the lower wage. Process recurrence of the first process in the corn industry.
3	No reswitching. Capital-reversing and the reverse substitution of labor at the switch point between Gamma and Delta. Process recurrence of the first process in the corn industry.
4	No reswitching. Capital-reversing and the reverse substitution of labor at the switch point between Gamma and Delta. Process recurrence of both processes in the corn industry.
5	No reswitching, no capital-reversing, no reverse substitution of labor, no process recurrence.
6	No reswitching, no capital-reversing, no reverse substitution of labor, no process recurrence.

This example allows for a graphical display showing that reswitching arises with an increased markup in corn-production, starting from a markup much less than in other industries. The ‘perverse’ switch point between Gamma and Delta remains on the wage frontier after the other switch point between these techniques falls off the frontier at a higher markup. Eventually, the ‘perverse’ switch point is no longer on the frontier when corn-production has a much higher markup than other industries.

7.0 Conclusion

The properties of the wage frontier might be thought to have some impact on the struggle between capitalists and workers. These properties can be altered both by technical change and by variations in relative market power among capitalists.

Intensive Rent With Two Types Of Land

Figure 1: Wages Curves for Example of Intensive Rent

1.0 Introduction

This post modifies an example from Antonio D'Agata. Two types of land exist, each specialized for producing a specific commodity.

In the example, some wage curves slope upwards, which is not possible in a model with circulating capital alone. The cost-minimizing technique is not found from the outer frontier of the wage curves. For one range of the rate of profits, no cost-minizing technique exists, even though a feasible technique exists in that range with a positive wage and positive prices. If the wage is taken as given, more than one cost-minimizing technique exists in the range of wages where a cost-minimizing technique exists.

This example does not illustrate variation in the order of rentability with the wage or rate of profits. Hence it also does not illustrate the reswitching of the order of rentability.

2.0 Technology, Endowments, Requirements for Use

Table 1 provides the technology for such an example. Each column specifies the quantities of labor, iron, wheat, and rye needed to produce a unit output of the commodity produced by the corresponding industry. The table also specifies the quantity of land that must be rented to operate that process. Constant returns to scale are assumed, with the limitation that the endowments of each type of land are givens.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Wheat		Rye
	I	II	III	IV	V
Labor	a0,1 = 1	a0,2 = 1	a0,3 = 2	a0,4 = 1	a0,5 = 1
Type 1 Land	0	c1,2 = 1	c1,3 = 1	0	0
Type 2 Land	0	0	0	c2,4 = 1	c2,5 = 1
Iron	a1,1 = 0	a1,2 = 0	a1,3 = 1/100	a1,4 = 1/10	a1,5 = 1/10
Wheat	a2,1 = 0	a2,2 = 0	a2,3 = 0	a2,4 = 2/5	a2,5 = 1/10
Rye	a3,1 = 1/10	a3,2 = 3/5	a3,3 = 11/20	a3,4 = 1/10	a3,5 = 2/5

I show each type of land as specialized to produce a different kind of agricultural commodity. The givens include the amount of each type of land available. Let t₁ be the acres of type 1 land available and t₂ be the acres of type 2 land available:

• t₁: 97 acres.
• t₂: 100 acres.

The column vector d representing the requirements for use has components:

• d₁: 90 tons iron.
• d₂: 60 quarters wheat.
• d₃: 19 bushels rye.

This vector d of net ouput is also the numeraire.

Table 2 specifies the techniques. All three commodities are Sraffa basics in all techniques. Only the Gamma, Zeta, Eta, and Iota techniques are feasible. For a technique to be feasible, the processes comprising the technique can be operated at a level to produce the required net output.

Table 2: Is Process Operated By Technique?

Input	Industry
	I	II	III	IV	V
Alpha	Yes	Yes	No	Yes	No
Beta	Yes	Yes	No	No	Yes
Gamma	Yes	No	Yes	Yes	No
Delta	Yes	No	Yes	No	Yes
Epsilon	Yes	Yes	No	Yes	Yes
Zeta	Yes	No	Yes	Yes	Yes
Eta	Yes	Yes	Yes	Yes	No
Theta	Yes	Yes	Yes	No	Yes
Iota	Yes	Yes	Yes	Yes	Yes

3.0 Prices of Production

The equations for prices of production vary among the techniques. Both lands are in excess supply and pay no rent for Gamma. Type 2 land is fully farmed under Zeta, and it pays a rent. Type 1 land pays a rent under Eta. Both lands pay a rent under Iota.

In the usual notation, the equations for prices of production for Iota are:

(p₁ a_1,1 + p₂ a_2,1 + p₃ a_3,1)(1 + r) + w a_0,1 = p₁

(p₁ a_1,2 + p₂ a_2,2 + p₃ a_3,2)(1 + r) + rho₁ c_1,2 + w a_0,2 = p₂

(p₁ a_1,3 + p₂ a_2,3 + p₃ a_3,3)(1 + r) + rho₁ c_1,3 + w a_0,3 = p₂

(p₁ a_1,4 + p₂ a_2,4 + p₃ a_3,4)(1 + r) + rho₂ c_2,4 + w a_0,4 = p₃

(p₁ a_1,5 + p₂ a_2,5 + p₃ a_3,5)(1 + r) + rho₂ c_2,5 + w a_0,5 = p₃

The price of the numeraire is unity:

p₁ d₁ + p₂ d₂ + p₃ d₃ = 1

These equations can be solved, given either the wage or the rate of profits. Figure 1, at the top of this post, shows the resulting wage curves for the feasible techniques. Figure 2 shows the rent curves.

Figure 2: Rent Curves for the Example

4.0 The Choice of Technique

For a low rate of profits, Iota is the cost-minimizing technique. For a rate of profits greater than that at the switch point for the Iota and Zeta wage curves, the Zeta technique is cost-minimizing, up to the maximum rate for Zeta. No technique is cost-minimizing for a larger rate of profits. Type 2 land has a larger rent per acre than type 1 land in the full range of the rate of profits in which a cost-minimizing technique exists. Type 1 land obtains a rent in the range in which Iota is cost-minimizing. It is free when Zeta is cost-minimizing.

These conclusions are justified by looking at which processes can obtain extra profits when prices of production for a given technique rule. Figure 3 graphs extra profits as a function of the rate of profits with prices of production for the Gamma technique. Either both the third and fifth process can obtain extra profits or the fifth process alone, depending on the level of the rate of profits. Thus, the Gamma technique is never cost-minimizing.

Figure 3: Extra Profits at Gamma Prices

Suppose the rate of profits is given and is in the range from the maximum rate of profits for the Zeta technique to the maximum rate of profits for the Gamma technique. Gamma is feasible, but not cost-minimizing. At prices of production for Gamma, managers of firms would want to operate the fifth process, which produces rye. Firms would adopt either the Delta or the Zeta technique, depending on whether they continue to operate the fourth process at some level. But Delta is infeasible, and prices of production for Zeta are such that the wage is negative in this range. Thus, no cost-minizing technique exists here.

Figure 4 shows extra profits for prices of production for Zeta. At a rate of profits less than the rate at the the switch point for Zeta and Iota, operating the second process obtains extra profits. Iota can be adopted in this range. Zeta is cost-minimizing for a higher rate of profits, up to the maximum rate of profits for Zeta.

Figure 4: Extra Profits at Zeta Prices

Figure 5 graphs extra profits for prices of production for the Eta process. Eta is never cost-minimizing. Operating the fifth process at Eta prices obtains extra profits.

Figure 5: Extra Profits at Eta Prices

Prices of production for Iota are such that extra profits are not obtained in operating any of the five processes in the technology. As long as the wage and rent on both types of land are non-negative, at a given rate of profits, Iota is cost-minimizing.

5.0 Conclusion

Type 2 land obtains a rent for the cost-minizing technique in the full range of the rate of profits where a cost-minimizing technique exists. Type 1 land only obtains a rent for a low range of the rate of profits.

Certain properties of models of circulating capital do not generalize, annoyingly, to the theory of joint production. Are there any such properties that are violated in models of pure joint production that are not also violated in models of intensive rent?

Givens For Two Approaches To The Theory Of Value And Distribution

1.0 Introduction

Broadly speaking, the history of political economy contains two approaches to value and distribution. For purposes of this post, I do not distinguish between classical and Marx's political economy. Institutionalists and those who know about German historical schools, for example, might have a complaint about being ignored.

This post is quite unoriginal. I thought I would just record these properties of two approaches.

2.0 Marginalism

Marginalist economics is about the allocation of given resources among alternatives. In marginalism, the theory of value and distribution is almost co-extensive with economic theory. The givens, for the theory of value and distribution, are:

• Endowments, including distribution of endowments among households.
• Tastes or preferences of each agent.
• Technology.

How to take capital as a given endowment is a difficulty with this approach. It can hardly be taken as a given quantity of value. The theory is supposed to explain prices, including the prices of capital goods. This problem is not just with aggregate theory. It is also a problem with microeconomic theory.

Another approach is to take initial quantities of individual capital goods as given. The neo-walrasian approach abandons the long run and the equalization of the rate of profits among industries. Conceptually, some expectations and plans must have been mistaken before the initial point in time. Yet the theory does not seem to accomodate such mistakes at the given time or into the future. Furthermore, debts and entitlements to future income streams do not seem possible to include among the givens. Disequilibrium processes that change the initial endowments and their distribution do not seem possible to include in the theory either.

3.0 Classical Political Economy

Classical political economics analyzes the conditions needed to ensure the reproduction of society. For the theory of value and distribution, the givens are:

• Technology.
• Requirements for use, which I take as net output.
• Wage or the rate of profits.

The theory of value can be combined with other elements of political economy. The classicals had various theories of wages, combined with demographics. Marx rejected Malthus and developed his theory of the reserve army of labor for similar purposes. The theory is compatible with a rejection of Say's law and enduring unemployment. Many have argued for combining this theory with a long-period interpretation of Keynes' general theory. A theory of growth and the dynamics of technical change can be built upon this theory of value and distribution.

Intensive Rent And The Order Of Rentability

I have thought about what would be the minimal structure of an example that combines extensive and intensive rent. I want to include a commodity produced without land, as well as an agricultural commodity.

This post considers a simpler example. An analysis of extensive rent includes the identification of the order of efficiency and the order of rentability, given the wage or the rate of profits. I take the concept of these orders from Alberto Quadrio Curzio. Can these orders be defined in a model of intensive rent? What would the minimum structure of an example be in which to explore this question? I continue to insist on including an industrial commodity with negligible inputs of land.

I suggest Table 1 provides the technology for such an example. Each column specifies the quantities of labor, iron, wheat, and rye needed to produce a unit output of the commodity produced by the corresponding industry. The table also specifies the quantity of land that must be rented to operate that process. Constant returns to scale are assumed, with the limitation that the endowments of each type of land are givens.

Table 1: The Coefficients of Production

Input	Industry
	Iron	Wheat		Rye
	I	II	III	IV	V
Labor	a0,1	a0,2	a0,3	a0,4	a0,5
Type 1 Land	0	c1,2	c1,3	0	0
Type 2 Land	0	0	0	c2,4	c2,5
Iron	a1,1	a1,2	a1,3	a1,4	a1,5
Wheat	a2,1	a2,2	a2,3	a2,4	a2,5
Rye	a3,1	a3,2	a3,3	a3,4	a3,5

I show each type of land as specialized to produce a different kind of agricultural commodity. I am unsure if that specialization is needed for my point. If not, the table defining the techniques below would contain four more techniques. In each, only one of the processes producing the agricultural commodity would be operated.

As noted, the givens include the amount of each type of land available. Let t₁ be the acres of type 1 land available and t₂ be the acres of type 2 land available

The vector d representing the numeraire has components:

• d₁: The quantity of iron in the numeraire.
• d₂: The quantity of wheat in the numeraire.
• d₃: The quantity of rye in the numeraire.

Let net output y consist of a multiple of the numeraire:

y = c d

Net output is among the givens.

Table 2 specifies the techniques. Non-zero coefficients of production in Table 1 should be such that all three commodities are Sraffa basics in all techniques. Not all techniques are feasible for any level of net output.

Table 2: Is Process Operated By Technique?

Input	Industry
	I	II	III	IV	V
Alpha	Yes	Yes	No	Yes	No
Beta	Yes	Yes	No	No	Yes
Gamma	Yes	No	Yes	Yes	No
Delta	Yes	No	Yes	No	Yes
Epsilon	Yes	Yes	No	Yes	Yes
Zeta	Yes	No	Yes	Yes	Yes
Eta	Yes	Yes	Yes	Yes	No
Theta	Yes	Yes	Yes	No	Yes
Iota	Yes	Yes	Yes	Yes	Yes

One can examine which processes are introduced in the cost-minimizing technques as the level of net output expands. That is, is process II adopted before process III or vice versa? Is process IV or process V operated first? Presumably, the answer to these questions depends on the wage or the rate of profits, whichever variable is taken as given in solving the system of equations for prices of production. This model is a model of intensive rent in that, for example, Epsilon or Zeta is cost minimizing, Type 2 land will be fully farmed and obtain a rent. The scarcity of land is shown by having two processes operating side-by-side on a single type of land. Anyways, the analysis outlined here corresponds to determining the order of efficiency in a model of extensive rent.

Suppose the Iota technique is feasible and cost-minimizing. The solution of the equations for prices of production yields the rent per acre for each type of land. Which type of land obtains the larger rent per acre? Does this order vary with the given wage or rate of profits? Is reswitching of this order possible? Does postulating a stable ratio of the rate of profits among industries change the answers, at least in detail? I suggest that this analysis corresponds to determining the order of rentability in a model of extensive rent.

I assume that the order of rentability varies with distribution and that reswitching of this order is indeed possible. As far as I know, nobody has answered these questions or presented a numerical example. I always think that nothing I say would surprise Betram Schefold, Heinz Kurz, or Neri Salvadori, for example. What I try to do is present concrete examples of their more abstract analyses. My identification of fluke cases, of extending the analysis to markup pricing, and presentation of graphs to aid visualization of the results are my own tweaks, I guess.

Elsewhere

• John Cassidy on Donald Harris in the Mew Yorker.
• Dean Dettloff on The Catholic case for communism in America.
• Enrico Bellino and Gabriel Brondino, Circular vs. one-way production processes: two different views on production and income distribution, in Review of Political Economy. I want to recall this for my work on Hayekian triangles.
• Bob Murphy and David Glasner on the Sraffa-Hayek debate. (They spend to much time on monetary policy before getting to the debate.)
• Leland Yeager and Steve Hanke. 2024. Capital, Interest, and Waiting: Controversies, Puzzles, and New Additions to Capital Theory. I probably will not order this.
• Pierangelo Garegnani. 2024. Capital Theory, the Surplus Approach, and Effective Demand. Appears to now be available.