Variation Of Prices Of Production With Time In An Example Of Intensive Rent

Figure 1: Variation of the Wage Frontier with Technical Progress

I continue to explore perturbations of an example from Antonio D'Agata. I have found a new type of fluke switch point, in models of intensive rent. Here I explore structural dynamics along a path in which technical change overwhelms the scarcity of land.

In this post, I repeat the data on technology, with a specific parameterization. Table 1 presents the available technology. Iron and steel are produced in processes with inputs of labor and circulating capital. 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

Input	Industries and Processes
	Iron	Steel	Corn
	I	II	III	IV	V
Labor	1	1	1	(11/5) e(5/4) - σt	e(1/20) - φt
Land	0	0	1	e(5/4) - σt	e(1/20) - φt
Iron	0	0	1/10	(1/10) e(5/4) - σt	(1/10) e(1/20) - φt
Steel	0	0	2/5	(1/10) e(5/4) - σt	(1/10) e(1/20) - φt
Corn	1/10	3/5	1/10	(3/10) e(5/4) - σt	(2/5) e(1/20) - φt

Requirements for use are 90 tons iron, 60 tons steel, and 19 bushels corn.

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

Technique	Process
Alpha	I, II, III
Beta	I, II, IV
Gamma	I, II, V
Delta	I, II, III, IV
Epsilon	I, II, III, V
Zea	I, II, IV, V

Suppose the coefficients or production in process IV decrease at the rate specified by setting σ to 5/4. And the coefficients of production in process V decrease, with φ set to 1/20.

Figure 1, at the top of the post, illustrates the evolution of the wage frontier with time in this scenario. Table 3 summarizes how the cost-minimizing technique varies with the rate of profits in each region. A discontinuity occurs at the pattern for requirements for use. Alpha, Delta, and Epsilon can satisfy requirements for use in Regions 1, 5, 10, and 11, while Alpha, Beta, Epsilon, and Zeta can satisfy requirements for use in Regions 12, 13, and 4. Finally, Alpha, Beta, and Gamma can satisfy requirements for use in Region 20, which is not shown in Figure 1. Region 20 is an example of a model of circulating capital. Land is in excess surprise, and rent is zero.

Table 3: Regions

Region	Range	Technique	Notes
1	0 ≤ r ≤ Rα	Alpha	No rent.
4	0 ≤ r ≤ Rβ	Beta	No rent.
5	0 ≤ r ≤ r1	Alpha	Rent per acre, when Epsilon is adopted, increases with the rate of profits and decreases with the wage.
	r1 ≤ r ≤ Rε	Epsilon
10	0 ≤ r ≤ Rε	Epsilon	Rent per acre increases with the rate of profits and decreases with the wage.
11	0 ≤ r ≤ r1	Epsilon	A range of the rate of profits exists for which no technique is cost-minimizing. The wage frontier is a non-unique function of the rate of profits. The wage curve for Delta slopes up on the frontier.
	r1 ≤ r ≤ r2	Delta and Epsilon
12	0 ≤ r ≤ r1	Epsilon	Rent per acre is a non- monotonic function of the rate of profits or of the wage. The wage curve for Zeta slopes up.
	r1 ≤ r ≤ r2	Zeta
	r2 ≤ r ≤ Rβ	Beta
13	0 ≤ r ≤ r1	Epsilon	Rent per acre is a non- monotonic function of the rate of profits or of the wage. The wage curve for Zeta slopes down.
	r1 ≤ r ≤ r2	Zeta
	r2 ≤ r ≤ Rβ	Beta
14	0 ≤ r ≤ r1	Zeta	Rent per acre, when Zeta is adopted, decreases with the rate of profits. The wage curve for Zeta slopes down.
	r1 ≤ r ≤ RΒ	Beta
20	0 ≤ r ≤ Rβ	Beta	No rent.

D'Agata's example arises when t is one. As shown in Figure 1, there is a range of the rate of profits in Region 11 in which both Delta and Epsilon are cost-minimizing. Regions 12 and 13 vary in that the wage curve for Zeta slopes up in Region 12 and down in Region 13. The cost-minimizing technique is not a unique function of the wage in Region 12.

Anyways, my approach of partitioning parameter spaces based on fluke cases applies to this example of intensive rent.

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.

The Production of Commodities by Means of Commodity and Money

Money is a medium of exchange (or means of purchase), a unit of account, and a store of wealth. I think Sraffa (1960) implicitly assumes an economy in which money is used. How would one explicitly and formally introduce money into Sraffa's scheme? I think one would want a theory of endogenous money, maybe as in a circuitist theory. How should the references below be extended? Which should I make an effort to read? I am aware that Sinha (2021) has a couple of other chapters about money and that Bellofiore and Passarella (2016) and Giuseppe and Realfonzo (2017) are introductions to special issues of ROKE and Metroeconomica, respectively. Any guidance to the literature, including these pointers, would be useful.

Reference

• Bailly, Jean-Luc, Alvaro Cencini, and Sergio Rossi (eds.) 2017. Quantum Macroeconomics: The legacy of Bernard Schmidt. Routledge.
• Bellofiore, Riccardo and Marco Veronese Passarella. 2016. Introduction: the theoretical legacy of Augusto Graziani, Review of Keynesian Economics 4(3): 243-249.
• Fontana, Giuseppe and Riccardo Realfonzo. 2017. Augusto Graziani and recent advances in the monetary theory of production, Metroeconomica 68(2): 202-204.
• Graziani, Augusto. 2003. The Monetary Theory of Production. Cambridge University Press.
• Moore, Basil. 1988. Horizontalists and Verticalists: The Macroeconomics of Credit Money. Cambridge University Press.
• Panico, Carlo. 1988. Interest and Profit in the Theories of Value and Distribution.
• Pivetti, Massimo (1991). An Essay on Money and Distribution.
• Rochon, Louis-Philippe. 1999. Credit, Money and Production: An Alternative Post-Keynesian Approach.. Edward Elgar.
• Sinha, Ajit (ed.). 2021. A Reflection on Sraffa’s Revolution in Economic Theory. Palgrave-Macmillan.
• Rochon, Louis-Philippe and Mario Seccareccia (eds.). 2013. Monetary Economics of Production: Banking and Financial Circuits and the Role of the State: Essays in Honour of Alain Parguez. Edward Elgar.
• Rogers, Colin. 1989. Money, Interest and Capital: A Study in the Foundations of Monetary Theory. Cambridge University Press.
• Venkatachalam, Ragupathy and Stefano Zambelli (2021). Sraffa, money and distribution. In Sinha (2021).

A Pattern For Non-Uniqueness

Figure 1: The Wage Frontier And Rent

I continue to explore perturbations of an example from Antonio D'Agata. I have found a new type of fluke switch point, in models of intensive rent. In this post, I repeat the data on technology, with a specific parameterization.

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

Input	Industries and Processes
	Iron	Steel	Corn
	I	II	III	IV	V
Labor	1	1	1	(11/5) e(5/4) - σt	e(1/20) - φt
Land	0	0	1	e(5/4) - σt	e(1/20) - φt
Iron	0	0	1/10	(1/10) e(5/4) - σt	(1/10) e(1/20) - φt
Steel	0	0	2/5	(1/10) e(5/4) - σt	(1/10) e(1/20) - φt
Corn	1/10	3/5	1/10	(3/10) e(5/4) - σt	(2/5) e(1/20) - φt

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

Technique	Process
Alpha	I, II, III
Beta	I, II, IV
Gamma	I, II, V
Delta	I, II, III, IV
Epsilon	I, II, III, V
Zea	I, 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.

At the specific parameter values illustrated at the top of this post, the switch point between the Alpha and Epsilon techniques occurs at the rate of profits at which the wage curve for the Delta technique intercepts the axis for the rate of profits. This fluke condition arises for a locus in the parameter space in which (φt) is a function of (σt). It reminds me of a fluke case for the order of fertility in models of extensive rent.

At a slightly lower value of (σt) or a higher value of (φt), no range of the rate of profits exists in which both the Alpha and Delta technique are cost-minimizing. A range of the rate of profits does exist in which the Epsilon technique is uniquely cost-minimizing. On the other hand, at a slightly higher value of (σt) or a lower value of (φt), a range of profits exists in which both the Alpha and Delta technique are cost-minimizing, and Epsilon is not uniquely cost-minimizing for any rate of profits. In both cases near this fluke case, a range of profits exists in which Alpha is uniquely cost-minimizing. And a range of the rate of profits exists in which both the Delta and Epsilon techniques are cost-minimizing.

So this fluke case is associated with a variation in the details of of an example in which the cost-minimizing technique is non-unique, and in which no cost-minimizing technique exists even though feasible techniques with positive prices, wages, rate of profits, and rent 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.

A Mistake In Kurz And Salvdori (1995)?

On page 299 of Kurz and Salvadori (1995), they write:

System (10.10) is identical with system (8.13).

The above statement is correct only if the steady state rate of growth is zero. The analysis presented around system 8.13 applies to any rate of growth lower than the rate of profits.

Chapter 8 is about joint production in general. Equations 8.13a through 8.13e specify a long-period position for joint production. Equation 8.13c specifies quantity relations and is:

z^T ( B - (1 + g) A) ≥ c^T

Equation 8.13d is a duality condition known as the rule of free goods. It is:

z^T ( B - (1 + g) A) y = c^T y

A full exposition would explain the notation above.

Chapter 10 is about land rent. Equations 10.10a, 10.10b 10.10c, 10.10f, and 10.10g specify a long-period position with land being cultivated. Equation 10.10a specifies quantity relationships and, more or less, is:

x^T ( B - A) ≥ d^T

Equation 10.10b is the rule of free goods for models with rent. It is:

x^T ( B - A) p = d^T p

If the rate of growth were positive in models of rent, a steady state could not be maintained. Eventually, a less efficient technique (at the given rate of profits) must be adopted, and the rate of growth must be lower.

I find I often may explain the dual quantity system for Sraffa's price equation in a confused manner. I often want to consider the trade-off between a steady state rate of growth and consumption per worker, with a given composition of the consumption basket. Given the technique, this trade-off is identical to the wage curve for the technique. On the other hand, one could present the quantity relations for a given level and composition of net output, that is, for given requirements for use. In an exposition, one must choose one of these approached.

Kurz and Salvadori (1995) is comprehensive. Of the mathematics I understand, this is as close as I found to a mathematical mistake. After publication, some argued about what I think are matters of history and judgement in the critique of neoclassical theory in Chapter 14. I think it was demonstrated about half a century ago that most of what most mainstream economists teach in North America is, at best, incorrect. From twitter, I have learned that economics is astrology for white men.

• Heinz D. Kurz and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge University Press.

Geoffrey Harcourt (1931-2021)

This overview of Geoff Harcourt's work is insufficient. He was interested in economics as a means to a better world. Consequently, he offered political advice, sometimes in the form of 'package deals', in the context of Australian politics, which I know nothing about. Also, I do not know Australian rules football, rugby, or cricket. Apparently, he was very good at mentorship and at introducing young scholars to the professional community. Capital theory is a very contentious topic, but Harcourt was on good terms with all sides.

Geoffrey C. Harcourt was born on 27 June 1931. He married Joan Bartrop in July 1955. Their children are Wendy, Robert, Timothy,and Rebecca. I had not known that the economist Claudid Sardoni married Wendy and was his son-in-law. He died on 6 January.

Harcourt attended the University of Melbourne as an undergraduate and came to Cambridge in July 1955. Nicholas Kaldor was his PhD. supervisor for a short while, but he later had Ronald Henderson as supervisor. His dissertation compared depreciation allowances at historical costs with capital consumption at replacement cost. What are the implications of these accounting conventions for the choice of technique and for taxes on profits? In Joan Robinson's golden age, historical cost, replacement cost, and the present value of the revenues expected from the use of capital equipment are all equal. Harcourt (1965) is one paper that emerged from this work.

Harcourt returned to Australia, to a lecturing post in Adelaide, in 1958. The rest of his professional life was shared between Cambridge and Adelaide. He lectured on Kaldor's growth theory and on Robinson's The Accumulation of Capital. I gather that Harcourt quite enjoyed working with some of his Australian colleagues such as W. E. G. Salter and Eric Russell.

From August 1963 to the end of 1966, he was in Cambridge, with a fellowship at Trinity. Although he reviewed Sraffa's book and co-wrote a paper on Sraffa's subsystems, he says he was mostly an observer of the controversies.

Now comes the work that Harcourt is most noted for. Mark Perlman visited Adelaide to convince Harcourt to write a survey article for the relatively new Journal of Economic Literature. I believe another author had backed out of surveying capital theory, and that author would not have focused on the Cambridge controversies. Harcourt wrote the first draft of his 1972 book while visiting Keio University in Japan. Cambridge University Press is in the process of re-issuing this classic, long out of print.

He found Noam Chomsky's 'The responsibility of intellectuals' inspiring and participated in direct action in Australia against the Vietnam war. He helped developed the Adelaide plan in the early 1970s, and was on the National Committee of Inquiry for the Australian Labor Party (ALP) in 1978-1979. Harcourt described his approach to political programs as 'horses for courses'. I think he may have also used this phrase to describe his approach to economic theory. His political programs included an incomes policy and something like the Tobin tax to curb speculation.

He took a year study leave at Clare Hall in 1972-1973, before returning to Adelaide University. Sometime in the 1970s Harcourt edited a conference volume on microfoundations, which, I gather, had quite a different flavor than the work of, say, Robert Lucas. Harcourt and Kenyon (1976) is one of a number of Post Keynesian works of the time relating markup pricing to firms' investment plans.

Harcourt left Adelaide for Cambridge in September 1982 and became a fellow at Jesus College. He retired in September 1998. I suppose I should mention somewhere his interest in intellectual history and his short biographies of economists in the Cambridge school, such as Richard Goodwin and Lorie Tarshis. The book by Harcourt and Kerr (2009) on Joan Robinson is an example. Most of his biographies are articles, though.

On 13 June 1994, Harcourt was awarded an Office in the General Division of the Order of Australia (AO). He was the president of Jesus College in Cambridge for most of 1988 to 1992. I do not know when he was in Cambridge and when he was in Adelaide for the last 20 years.

The list of references I append is very selective. I do not list the many volumes he edited or any articles in which he set out political programs or his views on politics and its relation to economics. Barkley Rosser has an obituary. Lars Syll links to an interview with Harcourt. John Hawkins and Selwyn Cornish describe Harcourt as 'the beating hear of Australian economics.' You can read testimonials here.

References

• Cohen, Avi J. and G. C. Harcourt. 2003. Whatever happened to the Cambridge capital controversies? Journal of Economic Perspectives 17: 199-214.
• Hamouda, O. F. and G. C. Harcourt. 1988. Post-Keynesianism: From criticism to coherence? Bulletin of Economic Research. 40: 1-33.
• Harcourt, G. C. 1965. The accountant in a golden age. Oxford Economic Papers. 17: 66-80.
• Harcourt, G. C. 1969. Some Cambridge controversies in the theory of capital. Journal of Economic Literature. 7: 369-405.
• Harcourt, G. C. 1972. Some Cambridge Controversies in the Theory of Capital. Cambridge University Press.
• Harcourt, G. C. 1982. The Social Science Imperialists: Selected Essays by G. C. Harcourt (ed. by Prue Kerr). Routledge and Kegan.
• Harcourt, G. C. 1986. Controversies in Political Economy: Selected Essays by G. C. Harcourt (ed. by O. F. Hamouda). New York University Press.
• Harcourt, G. C. 1995. Capitalism, Socialism, and Post-Keynesianism: Selected Essays by G. C. Harcourt. Edward Elgar.
• Harcourt, G. C. 2001. Selected Essays on Economic Policy. Palgrave-Macmillan.
• Harcourt, G. C. 2006. The Structure of Post-Keynesian Economics: The Core Contributions of the Pioneers. Cambridge University Press.
• Harcourt, G. C. and Prue Kerr. 2009. Joan Robinson. Palgrave Macmillan.
• Harcourt, G. C. and Vincent G. Massaro. 1964. Mr. Sraffa's Production of Commodities. Economic Record 40: 442-454.
• Harcourt, G. C. and Peter Kenyon. 1976. Pricing and the investment decision. Kyklos. 29: 449-477.