Wednesday, January 01, 2025

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.

Saturday, November 27, 2021

Three Patterns Across The Axis For The Rate Of Profits In A Model Of Intensive Rent

Figure 1: Three Patterns Across the r Axis and One Three-Technique Pattern

This post begins a perturbation analysis of an example of intensive rent from D'Agata. I have previously claimed that certain structures in parameter space are universal in some sense.

Table 1 presents the available technology. Corn is grown on homogeneous land, and three processes are available for producing corn. One hundred acres of land are available, leading to the possibility of two processes being operated side-by-side with positive rent. Processes III and IV undergo technical progress through time. Table 2 shows the processes operated in each of the six techniques available.

Table 1: The Coefficients of Production
InputIndustries and Processes
IronSteelCorn
IIIIIIIVV
Labor111(11/5) e(5/4) - σte(1/20) - φt
Land001e(5/4) - σte(1/20) - φt
Iron001/10(1/10) e(5/4) - σt(1/10) e(1/20) - φt
Steel002/5(1/10) e(5/4) - σt(1/10) e(1/20) - φt
Corn1/103/51/10(3/10) e(5/4) - σt(2/5) e(1/20) - φt

Table 2: Techniques
TechniqueProcess
AlphaI, II, III
BetaI, II, IV
GammaI, II, V
DeltaI, II, III, IV
EpsilonI, II, III, V
ZeaI, II, IV, V

Requirements for use are 90 tons iron, 60 tons steel, and 19 bushels corn. In this parameter range, Alpha, Delta, and Epsilon can meet requirements for use. That is, one can find levels of operation of the processes comprising these techniques such that the net output of the economy is the previously specified vector and no more than 100 acres of land are farmed. Beta, Gamma, and Zeta are infeasible.

Figure 1, at the top of this post, illustrates a part of the parameter space formed by (σ t) and (φ t). Patterns of fluke switch points partition the parameter space into regions in which the wage frontier does not qualitatively vary within each region. (From the numbering, you may correctly guess other patterns of fluke switch points form other partitions off the edges of the graph.)

Table 3: Regions
RegionRangeTechniqueNotes
10 ≤ rRαAlphaNo rent.
20 ≤ rr1AlphaNon-unique cost-minimizing technique. Wage curve for Delta slopes up on frontier.
r1rr2Alpha, Delta
50 ≤ rr1AlphaPositive rent for some range of the rate of profits.
r1rRεEpsilon
60 ≤ rr1AlphaNon-unique cost-minimizing technique. Wage curve for Delta slopes up on frontier.
r1rr2Epsilon
r2rr3Delta, Epsilon

Figure 2: Wage Frontier and Rent in Region 2

Figure 3: Wage Frontier and Rent in Region 5

Figure 4: Wage Frontier and Rent in Region 6

One can summarize, as in Table 3, which switch points and wage curves appear on the frontier in each region. In region 1, the Alpha technique is cost-minimizing for all rates of profits. Land is in excess supply, and no rent is formed. Technical progress is modeled by a movement to the east, north, or northeast in Figure 1. Technical progress here eventually results in land being scarce, at least for some range of the rate of profits, and landlords receiving a rent. Figures 2, 3, and 4 show the wage frontiers and rent per acre, as a correspondence with the rate of profits, for regions 2, 5, and 6.

Some phenomena arise in regions 2 and 6 that are not possible in models with circulating capital alone. As I understand it, these phenomena are also not possible in pure fixed capital models and in models of extensive rent. I am referring specifically to upward-sloping wage curves on the frontier and a non-unique cost-minimizing technique for some rates of profits.

I like that despite these oddities, the illustrated partition of the selected part of the parameter space is qualitatively similar to partitions for parts of parameter spaces for circulating capital models. Maybe I am exploring something fundamental underlying the analysis of the choice of technique.

Monday, November 22, 2021

Elsewhere

  • Many articles from the Thames Papers in Political Economy to 1989 are now available open access.
  • The articles in Political Economy: Studies in the Surplus Approach, from 1985 to 1990, are also available open access.
  • There is now a Post Keynesian Discord server, whatever that is.
  • Here is a Post Keynesian blog, on this newish substack thingy.

Saturday, November 13, 2021

A Disconcerting Example of Intensive Rent From D'Agata

Figure 1: The Wage Frontier And Rent
1.0 Introduction

This post is another worked homework example, problem 7.8 in Chapter 10 of Kurz and Salvadori (1995). The example illustrates the possible non-existence of a cost-minimizing technique with intensive rent. I once looked at an example from J. E. Woods of joint production. I claim that that example does not make the desired point, given the possibility of a price of zero for some produced good. I do not think this example of rent can be resolved like that.

Kurz and Salvadori suggest to me how I might apply my perturbation techniques: "...calculate what will happen if either only process (4) or only process (5) were missing."

2.0 Technology, Techniques, and Requirements for Use

Anyways, Table 1 presents the available technology. Corn is grown on homogeneous land, and three processes are available for producing corn. One hundred acres of land are available, leading to the possibility of two processes being operated side-by-side with positive rent.

Table 1: The Coefficients of Production
InputIndustries and Processes
IronSteelCorn
IIIIIIIVV
Labor11111/51
Land00111
Iron001/101/101/10
Steel002/51/101/10
Corn1/103/51/103/102/5

Table 2 shows the processes operated in each of the six techniques available. (All three corn-producing processes are operated only at a switch point where the Delta, Epsilon, and Zeta techniques are simultaneously cost-minimizing. Iron, steel, and corn are basic commodities in all techniques. Land is never a basic commodity.

Table 2: Techniques
TechniqueProcess
AlphaI, II, III
BetaI, II, IV
GammaI, II, V
DeltaI, II, III, IV
EpsilonI, II, III, V
ZeaI, II, IV, V

Requirements for use are 90 tons iron, 60 tons steel, and 19 bushels corn. Alpha, Delta, and Epsilon can meet requirements for use. That is, one can find levels of operation of the processes comprising these techniques such that the net output of the economy is the previously specified vector and no more than 100 acres of land are farmed. Beta, Gamma, and Zeta are infeasible.

3.0 Cost-Minimizing Techniques and the Wage Frontier

When Alpha is used, not all land is farmed. Rent would be zero. But Alpha is never cost-minimizing.

Figure 2: Extra Profits At Delta and Epsilon Prices

To see if a technique is cost-minimizing at a given rate of profits, find prices of production, the wage, and rent for the technique. Then one can calculate extra profits for every process. Costs include the going rate of profits on advances for purchasing capital goods, wages, and rents. Figure 2 plots extra profits for processes for Delta and Epsilon prices.

The left panel illustrates Delta. No extra profits are made or extra costs are incurred in processes I, II, III, and IV. Delta only has a non-negative wage and a non-negative rent between a rate of profits of 1/9 (that is, approximately 11.1 percent) and approximately 52.3 percent. From a rate of profits of approximate 11 percent to 46 percent, extra profits cannot be made in operating process V. Delta is cost-minimizing.

For a higher rate of profits, in a range in which rent is non-negative under Delta prices, process V makes extra profits. Delta is not cost-minimizing. Which technique would be adopted under these conditions? Process V could be be the only corn-producing process, in the Gamma technique. But that technique is not feasible. Suppose process V replaces process III, in the Zeta process. That technique results in more being produced than are needed for requirements for use. Epsilon is the only feasible technique in which land is fully farmed and two corn-producing processes are operated, with a positive rent.

The right panel in Figure 2 illustrates extra profits for all processes under Epsilon prices. Epsilon has a non-negative wage and a positive rent up to a rate of profits of 2/3 (that is, approximately 66.7 percent) In the range of the rate profits from zero to approximately 46 percent, Epsilon is cost-minimizing. For a higher rate of profit, where the wage is still non-negative under Epsilon, process IV makes extra profits. I highlight in this range when Delta is feasible and consistent with a positive wage and positive rent.

The above analysis shows how the wage frontier is constructed in this example. The wage frontier is illustrated in the left panel in Figure 1 at the top of this post. The corresponding rent is shown in the right panel. A range of rate of profits exists in which Delta and Epsilon are both cost-minimizing. The switch point between Delta and Epsilon is at 19/41, (that is, approximately 46.3 percent). Above this rate of profits, no technique is cost-minimizing.

4.0 Conclusion

Between rates of profits of 19/41 and approximately 52.3 percent, Epsilon makes extra profits at Delta prices, and Delta makes extra profits at Epsilon prices. Even though feasible techniques exist that are consistent with positive wages, rates of profits, rent, and prices of production, no cost-minimizing technique need exist.

References
  • D'Agata, Antonio. 1983a. The existence and unicity of cost-minimizing systems in intensive rent theory. Metroeconomica 35: 147-158.
  • Kurz, Heinz D. and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge: Cambridge University Press.

Wednesday, November 03, 2021

An Example Of External Intensive Rent From D'Agata

Figure 1: The Wage Frontier And Rent

This post is merely a worked homework example, problem 7.10 in Kurz and Salvadori (1995). I have not considered yet which parameters I want to explore perturbing.

As a matter of history, Anderson, West, Malthus, and Ricardo took extensive rent as the paradigm case, and confined it to land. They imposed no limit on the production of industrial commodities. Ricardo, at least, also discussed the case of intensive rent. The marginalists, on the other hand, took the case of intensive rent as the paradigm case and extended it to all commodities and, sloppily, extended the explanation of rent to payments to capital and labor. I still do not get well-behaved supply and demand relationships in models of intensive rent. Marginalism remains mistaken and lacks a coherent price theory.

Table 1 presents coefficients of production for the technology. One process is known for producing iron, three processes are known for producing steel, and one process is known for producing corn. Iron and steel are industrial commodities, while corn is the single agricultural commodity. One hundred acres of land are available. All processes exhibit constant returns to scale, in corn production up to the limit imposed by the scarcity of land. The scarity of land can result in a combination of two processes being used to produce steel, with land receiving a positive rent. Requirements for use are 10 tons iron, 10 tons steel, and 78 bushels corn. I take requirements for use, that is, net output, as the numeraire.

Table 1: The Coefficients of Production
InputIndustries and Processes
IronSteelCorn
IIIIII
Labor111/1011/21
Land00001
Iron03/102/51/101/10
Steel1/103/102/51/101/10
Corn02/53/101/51/10

Six techniques are available for a sustainable economy. In each technique, the iron-producing and corn-producing processes are operated. The techniques are distinguishable by the steel-producing or combination of steel-producing processes that are operated (Table 2).

Table 2: Techniques
TechniqueSteel Process(es)
AlphaI
BetaII
GammaIII
DeltaI, II
EpsilonI, III
ZeaII, III

The Alpha technique is not feasible; requirements for use cannot be satisified by operating the specified combination of processes while respecting the constraint imposed by land. The Beta, Gamma, Delta, and Epsilon techniques are feasible. When the Beta or Gamma techniques are operated to produce the requirements for use, some land is left farrow and rent is zero. The Delta and Epsilon techniques each require all land to be farmed. Zeta produces more commodities than are required for use. It would only be adopted at a switch point between Beta and Gamma, with a rent of zero.

Prices of production for the Beta and Gamma techniques can be analyzed as in models of circulating capital. For the Beta technique, for example, each of the iron-producing, steel-producing, and corn-producing processes provides a price equation. With the specification of the numeraire, one has four equations in five unknowns: the price of iron, the price of steel, the price of corn, the wage, and the rate of profits. Rent is zero, since land is in excess supply. One can solve for each variable as a function of the rate of profits. As shown in Figure 1 at the top of this post, the wage curves for the Beta and Gamma techniques slope down.

When are the Beta and Gamma techniques cost-minimizing? For a given rate of profits, one can calculate, for each process, the difference between revenues and costs, where costs include a charge for profits on the iron, steel, and corn advanced. The Beta technique, for example, is cost-minimizing only when extra profits cannot be made in operating any process. Figure 2 shows the ranges of the rates of profits at which the Beta and Gamma techniques are cost-minimizing.

Figure 2: Extra Profits At Beta Or Gamma Prices

Prices of production can also be found for the Delta and Epsilon techniques. For the Delta technique, for example, the iron-producing, the first and second steel-producing, and the corn-producing processes provide a price equation. Given the rate of profits and the specification of the numeraire, the wage and the prices of iron, steel, and corn, can be solved for from the iron-producing and steel-producing processes. The corn-producing process then yields the rent per acre of land. I confine my attention to non-negative rents and prices. For the Delta technique, rent is negative at a rate of profits of zero, but not for a certain range of postive rates of profits.

Figure 3: Extra Profits At Delta Or Epsilon Prices

To find when the Delta technique is cost-minimizing, one performs the usual analysis. When can extra profits, at Delta prices, be made by operating a process not in the technique? The left-hand panel in Figure 3 shows that extra profits are available from the third steel-producing processes for start of the range of the rate of profits at which the Delta technique yields positive rents. At the end of this range, the Delta technique is cost-minimizing. One can repeat this analysis for the Epsilon technique. The Epsilon technique is cost-minimizing at towards the end of the range for the rate of profits at which it yields a positive rent, as shown in the right-hand panel in Figure 3.

Even though the choice of technique is not analyzed above by construction of an envelope of wage curves, one can still highlight wage curves for each technique when they are cost-minimizing. The left-hand panel in Figure 1, at the top of this post, shows the resulting wage frontier. The right-hand panel shows rent as a function of the rate of profits.

The wage curve for the Delta technique slopes up, even when it is on the frontier. You can see that there is a certain range of the rate of profits where the Beta, Delta, and Epsilon techniques are each cost-minimizing. The wage could just as well be taken as the independent variable. And there is a range of the wage where the Delta, Epsilon, and Gamma techniques are cost-minimizing. Sraffa was wrong or, at least, misleading in certain comments on intensive rent in his book on intensive rent. Some, but not all, of the analytical tools he built can be used to demonstrate these mistakes.

This post illustrates that in a model of external intensive rent, prices of production, rent, and the wage are not necessarily uniquely determined by the rate of profits. Nor are prices of production, rent, and the rate of profits necessarily uniquely determined by the wage. This non-uniqueness cannot arise in circulating capital models or pure fixed capital systems. It can only arise in a model of extensive rent in a fluke case that I have been calling a pattern for the requirements for use.

Friday, October 29, 2021

Post-Sraffian Terminology

Terms that include the word 'pattern' are my own creation, as inspired by my research program. The remainder are, as far as I am concerned, standard terminology, some of which you would be introduced to if you were taught price theory properly. (Most of what is in mainstream microeconomic textbooks is, at best, wrong.) The definitions are my own, although obviously inspired by my reading.

  • Absolute rent: A price paid for a year's services for land under cultivation due to barriers to entry to agriculture that would be otherwise manifested in persistent higher rates of profits in farming.
  • Basic commodity: A commodity that is productively consumed, either directly or indirectly, in the production of each commodity produced in an economy.
  • Capital reversing: The association of a higher rate of profits around a switch point with a cost-minimizing technique with a more capital-intensive technique. Also known as a positive real Wicksell effect.
  • Circulating capital: Produced commodities that are completely consumed in producing other commodities. Contrast fixed capital.
  • Coefficient of production: The amount of a specified commodity that is required as an input to operate a given process at a unit level or the amount of a specified commodity that is produced in operating the given process at a unit level.
  • Differential rent of the first kind: See extensive rent.
  • Differential rent of the second kind: See intensive rent.
  • Extensive rent: A price paid for a year's services for land under cultivation due to the need to cultivate more than one type of land to satisfy requirements for use while prices of production prevail.
  • External intensive rent: A price paid for a year's services for land under cultivation due to the need to more than one process, in an industry that uses negligible inputs land, so as to satisfy requirements for use while prices of production prevail. See intensive rent.
  • Factor price frontier: See wage frontier.
  • Finished good: A produced commodity that is either a consumption good, circulating capital, or a newly produced machine.
  • Fixed capital: Produced commodities that are used in producing other commodities and last over more than one production period. A good used as fixed capital is often referred to simply as a 'machine'. Contrast circulating capital.
  • Forward substitution of labor: The association of a higher rate of profits, or lower wage, around a switch point with a cost-minimizing technique in which, in one industry, the labor per unit of gross output produced is larger. Contrast with reverse substitution of labor.
  • Four-technique pattern of switch points: Occurs when there is a switch point at which four wage curves intersect.
  • Intensive rent: A price paid for a year's services for land under cultivation due to the need to operate more than one process on that land to satisfy requirements for use while prices of production prevail.
  • Intermediate good: An old machine.
  • Joint production: The phenomenon in which some production process produces more than one commodity, such as wool and mutton. Fixed capital, in which a production process produces a finished good and a machine one year older than it was when used as an input is an example. Land, which is both an input to a production process and is an unchanged output, along with a finished good, provides another example.
  • Leontief input-output matrix: A matrix of coefficients of production in models of circulating capital, where each coefficient is the amount of a specified commodity needed in the production of a unit amount of another specified commodity. Leontief matrices are often supplemented by vectors of labor coefficients, matrices for land inputs, and so on.
  • Market prices: Prices existing in markets at a particular moment in time. Market prices are consistent with inequalities in the quantities supplied and demanded and with momentary variations in the rates of profits among industries. Contrast with prices of production.
  • Natural prices: See prices of production.
  • Normal prices: See prices of production.
  • Order of efficiency: See order of fertility.
  • Order of fertility: In models with extensive rent, the order in which lands of different types are taken into cultivation, at a given rate of profits or a given wage, as the quantities in requirements for use expand. Also known as the order of efficiency.
  • Order of rentability: In models with extensive rent, the order of lands of different types from high rent per acre to zero rent, at a given rate of profits or a given wage.
  • Pattern (of switch points) for the requirements for use: Occurs with an indeterminancy in prices and levels at which processes are operated in the cost-minimizing techniques at a given rate of profits. This indeterminancy arises in models of joint reproduction due to the need to satisfy requirements for use.
  • Pattern (of switch points) in the r-order of fertility: Occurs when a switch point associated with a change in the order of fertility of land not on the margin is at the same rate of profits as a switch point on the axis for the rate of profits.
  • Pattern (of switch points) in the w-order of rentability: Occurs when a switch point associated with a change in the order of fertility of land not on the margin is at the same wage as a switch point on the axis for the wage.
  • Pattern (of switch points) over the axis for the rate of profits: Occurs when there is a switch point at a wage of zero.
  • Pattern (of switch points) over the wage axis: Occurs when there is a switch point at a rate of profits of zero.
  • Prices of production: Given technology, the rate of profits or the wage, and requirements for use, prices of commodities consistent with the smooth reproduction of a capitalist economy. Contrast with market prices.
  • Process: A process of production is specified by the quantities of labor, of a specified type of land, and of specified commodities needed to produce a specified output. Under joint production, the output can consist of more than one commodity. A technique consists of a set of processes.
  • Rate of profits: The quotient of the difference between revenue and costs in a process and the costs paid in advances at the start of the production period. The rate of profits is the same for all operated processes when prices of production prevail if there are no barriers to entry or other causes of persistent differences among industries.
  • Recurrence of processes: Occurs when a process is in the cost-minimizing techniques, at two disjoint ranges of the rate of profits, while that process is not in the techniques cost-minimizing at the rates of profits between these two ranges. The recurrence of processes always arises when techniques recur, but the recurrence of processes can occur without the recurrence of techniques.
  • Recurrence of techniques: Occurs when one technique is cost-minimizing at two disjoint ranges of the rate of profits, while one or more other techniques are cost-minimizing at the rates of profits between these two ranges. The recurrence of techniques always arises when techniques reswitch, but the recurrence of techniques can occur without the reswitching of techniques.
  • Requirements for use: The level and composition of net output or of a consumption basket, specified as given in models of production.
  • Reswitching of techniques: Occurs when one technique is cost-minimizing at two disjoint ranges of the rate of profits, while another technique is cost-minimizing at the rates of profits between these two ranges.
  • Reswitching pattern (of switch points): Occurs when two wage curves are tangent at a switch point.
  • Reverse substitution of labor: The association of a higher rate of profits, or lower wage, around a switch point with a cost-minimizing technique in which, in one industry, the labor per unit of gross output produced is smaller. Contrast with forward substitution of labor.
  • Scale factor for the rates of profits: When markups among industries hold persistent and stable ratios among themselves, a scale factor that determines the rate of profits from relative markups. See the rate of profits.
  • Single production: See circulating capital and contrast with joint production.
  • Sraffa effect: The reswitching of techniques, capital reversing, the reverse substitution of labor, the recurrence of techniques, the recurrence of processes, and other effects discovered through the analysis of prices of production that are inconsistent with obsolete marginalist dogmas.
  • Sraffa matrix: A Leontief matrix for a viable technique when at least one commodity is basic and the maximum rate of profits for the submatrix of non-basic commodities exceeds the maximum rate of profits for the submatrix for basic commodities. See pp. 123-124 in Kurz and Salvadori (1995).
  • Structural economic dynamics: The variation in the relative sizes of industries and in prices of production as the result of technical progress, variation in market structure, variations in the rate of growth, and variation in the relative quantities of commodities in consumption baskets.
  • Switch point: A point at which two wage curves intersect. Often defined to apply only to switch points on the wage frontier.
  • Technique: A set of processes. In models of circulating capital, a technique contains one process for producing each commodity in the gross output of an economy.
  • Three-technique pattern of switch points: Occurs when there is a switch point at which three wage curves intersect.
  • Wage curve: For a given technique, the wage as a function of the rate of profits in a system of prices of production. Also known as a wage-rate of profits curve.
  • Wage frontier: In models of circulating capital, the outer envelope of wage curves. Also known as the wage-rate of profits frontier or, misleadingly, the factor-price frontier.
  • Wicksell effect, price: The variation in the numeraire value of capital goods with the rate of profits for a given technique.
  • Wicksell effect, real: The variation in the numeraire value of capital goods with the technique at a given rate of profits. Around a switch point with a negative real Wicksell effect, a higher wage or lower rate of profits is associated with a larger value of capital per person-year employed in a stationary state.

Friday, October 22, 2021

Elsewhere

Why Rationality is Wrong

  • Above is a video by "Dr. Skeleman", first in a series.
  • Nick Romeo, in The New Yorker, on The CORE textbook.
  • Steve Keen's obituary of Janos Kornai.
  • J. Barkley Rosser's comments on Kornai's passing. I feel I should have more to say. I recommend autobiography, By Force of Thought: Irregular Memoirs of an Intellectual Journey, although it is somewhat dry.
  • J. Barkley Rosser's obituary of Peter Flaschel