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.

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

Some Kinds Of Rent

Special Cases in the Analysis of Rent

Type	Land	Agricultural Processes	Industrial Processes
Extensive rent	Multiple types of land, each of a given quality	For a given type of land, one process producing corn is available	For a given commodity other than corn, one process for producing it is available
Intensive rent proper	One type of homogeneous land	For the given type of land, multiple processes are available for producing corn	For a given commodity other than corn, one process for producing it is available
External intensive rent	One type of homogeneous land	For the given type of land, one process for producing corn is available	For a given commodity other than corn, multiple processes for producing it are available

Economists have explored several kinds of rent in post-Sraffian price theory (Kurz and Salvadori 1995: 279). Suppose, as a simplifying assumption, that one commodity, 'corn', can be produced on land. Land is a non-produced commodity that emerges from a production process unchanged. Furthermore, assume that no pure joint production occurs otherwise. Let requirements for use be specified as a vector of net outputs.

The table at the head of this post lists three kinds of rent. They are characterized by the appending of three additional assumptions. One assumption deals with whether all land is homogeneous, or whether multiple types of land exist. Another assumption states whether one or more than one process is known for operating on any of the given types of land. A final assumption concerns whether different processes are available to produce commodities that do not require direct inputs of land in their production.

As far as I know, a general model of rent, short of the general theory of joint production, has yet to be developed that considers the relaxation and mixing of these assumptions. Those building on the work of Alberto Quadrio Curzio, I guess, have a ways to go. (I have just started reading the reference below.) Absolute rent may be introduced by postulating persisting, non-uniform ratios of rates of profits across sectors. An obvious generalization would consider the possibility of producing more than one agricultural commodity. In a mixed model of extensive and intensive rent, more than one type of land would exist, and more than one production process would be available for at least some types of land. Furthermore, one might introduce fixed capital, thereby raising the question of the cost-minimizing choice of the economic life of machines.

My impression is that results of the circulating capital model generalize to simple models of extensive rent. The dependence of the price system on requirements for use in models of extensive rent, however, is an important difference in the models. Once one considers other types of rent or any of the above complications, issues that arise in general models of joint production also arise in models of rent. These issues include upward-sloping wage curves on the frontier and the non-uniqueness or the non-existence of a cost-minimizing technique at a given rate of profits.

Reference

• Baranzini, Mauro L., Claudia Rotondo, and Roberto Scazzieri. 2015. Resources, Production and Structural Dynamics. Cambridge: Cambridge University Press.

On David Card's Nobel

The Sveriges Riksbank prize in economic sciences in memory of Alfred Nobel this year goes to David Card, Joshua Angrist, and Guido Imbens. I cannot say much about instrumental variables, Angrist, or Imbens. Since I have been pointing to Card's work with Alan Krueger on minimum wages for decades, I thought I might say somthing about his half of the prize.

I do not have much new to say. I find both natural experiments and meta-analysis intriguing.

Both Card and Krueger's natural experiments with minimum wages and their meta-analysis have been superceded. Maybe 'transcended' or 'replicated' would be better terminology. That is why, in my 2019 paper in Strucutral Change and Economic Dynamics, I reference Andrajit Dube and his colleagues, not Card and Krueger. Also, David Neumark's quibbles with Card are currently uninteresting. (Any reporter talking to Neumark should note he started out with funding from a consortium of fast food joints.)

I object to attempts to explain the lack of impact of minimum wages on employment by the theory of monopsony. Economists have known, for over half a century, that wages and employment cannot, even under ideal conditions, be explained by the interaction of well-behaved supply and demand curves in the labor market. In marginalist theory, the supply of labor is derived from utility-maximizing households trading off leisure and commodities to consume. The demand for labor is supposed to be derived from profit-maximizing firms. But no such valid derivation goes through if firms produce some commodities with the use of previously produced commodities, that is, capital goods. This well-established result is widely ignored, with no pretence at justification.

A Structure in Parameter Space with Three Patterns Across The Wage Axis

Figure 1: Three Patterns Across The Wage Axis And One Three-Technique Pattern

This post continues the approach in this post and in this post. As previously stated, I consider the same two examples. In both examples, three processes are known for producing the numeraire, called "corn". In the example for the left panel, corn is a non-basic commodity, and a different basic commodity is used in each of the three techniques. In the example for the right panel, all three corn-producing processes require inputs of labor power, corn, and iron (in different proportions), and managers firms know of a single process for producing iron. Both commodities are basic in this second example. The examples are also parametrized differently.

In both panels, loci for three patterns of switch points on the frontier and over the wage axis terminate at a point that is also the terminus for a locus for a three-technique pattern of switch points. For the example illustrated by the right panel, a second switch point exists on the wage frontier for a larger rate of profits than the one concerned in the patterns of switch points. This structure in parameter space is also depicted as Figure 2 in my paper, 'Fluke switch points in pure fixed capital systems', for a quite different example.

This generic structure in these parameter spaces is obscured by the dotted line in the panel on the right. Along it, the wage curves for the switch point between the Beta and Gamma techniques intersect at a rate of profits of zero. But this switch point is not on the wage frontier. Below and to the right of the dotted line, the switch point between Beta and Gamma on the frontier exhibits capital-reversing, while above it that switch point has a negative real Wicksell effect. Thus, the dotted line is not associated with a change in the number of sequence of switch points along the wage frontier. But it is associated with the change of the direction of real Wicksell effects around one of these switch points.

So here is another perhaps universal structure, in some sense, in parameter spaces associated with the analysis of the choice of technique in models of prices of production.

A Structure in Parameter Space With Three Patterns Across The Axis For The Rate Of Profits

Figure 1: Three Patterns Across The r Axis And One Three-Technique Pattern

This post continues the approach in this post. I consider the same two examples. In both examples, three processes are known for producing the numeraire, called "corn". In the example for the left panel, corn is a non-basic commodity, and a different basic commodity is used in all three techniques. In the example for the right panel, all three corn-producing processes require inputs of labor power, corn, and labor (in different proportions), and managers firms know of a single process for producing iron. Both commodities are basic in this second example. The examples are also parametrized differently.

These examples are all part of my investigation of how reswitching, capital-reversing, a reverse substitution of labor, process recurrence, and so on can emerge and disappear with perturbations of parameters in post Sraffian models of prices of production.

I call a case when a switch point exists on the wage frontier at a wage of zero a "pattern of switch points over the axis for the rate of profits". When three wage curves intersect on the frontier at a single switch point, I say this is a "three-technique pattern" of switch points.

I claim that the two panels in the figure at the top of this post are the same, at some level of abstaction. Suppose that in the left panel, replace every instance of "Alpha, Gamma" is replaced by S₁. Suppose every instance of "Beta" is replaced with "Gamma" and every remaining instance of "Alpha" with "Beta". Let every instance of S₁ be replaced with "Alpha". Rotate clockwise somewhat and stretch and otherwise distort the regions.

In both panels, one will then have a region labeled with "Alpha", alone. And it will be bounded by two loci, each designating parameters for a pattern of switch points over the axis for the rate of profits. The region diagonally opposite is then bounded by a locus for a third pattern of switch points over the axis for the rate of profits and a locus for a three-technique pattern.

In other words, loci for three patterns of switch points terminate at a point that is also the terminus for a locus for a three-technique pattern of switch points. For the example illustrated by the left panel, a second switch point exists on the wage frontier for a smaller rate of profits than the one concerned in the patterns of switch points.

So here is another generic structure in the parameter spaces relating to the analysis of the choice of technique.

Elsewhere

• Alex Thomas on Krishna Bharadwaj as an ideal economist.
• Her daughter, Sudha Bharadwaj is a political prisoner.
• The first page of this Jeremy Rudd paper is getting noticed. A lot of mainstream economics is "arrant nonsense."
• National Public Radio has a rememberance of Charles Mills.
• Liam Bright has a tribute, too.