Jevons Versus Marshal On Ricardo

I have been pointing out that much teaching in most universities and high schools in economics is propaganda. Mistakes that were exposed more than half a century ago continue to be taught. Alternatives have been available, at varying levels, in textbooks for decades.

Does an alternative, building on classical political economy and Marx, exist? Assertions on this topic go back more than a century.

A (bad) way of reading classical political economy is that its proponents were struggling towards developing the one true system, that of marginalist economists. With this incorrect view of continuity, you might say incorrectly that they overemphasized supply. Their theories were corrected by developing theories of utility and demand.

A better reading recognizes that they had their own approach. Jevons held this view, although he was wrong about which approach was better:

"When at length a true system of Economics comes to be established, it will be seen that that able but wrong-headed man, David Ricardo, shunted the car of Economic science on to a wrong line - a line, however, on which it was further urged towards confusion by his equally able and, wrong-headed admirer, John Stuart Mill." -- William Stanley Jevons, The Theory of Political Economy, Preface to the Second Edition, p. li.

Marshall, on the other hand, was an early progenitor of a supposedly generous reading that blurs the distinctiveness of the classical theory of value and distribution:

"1... [Ricardo's] book makes no pretence to be systematic. He was with difficulty induced to publish it; and if in writing it he had in view any readers at all, they were chiefly those statesmen and business men with whom he associated. So he purposely omitted many things which were necessary for the logical completeness of his argument, but which they would regard as obvious. And further, as he told Malthus in the following October, he was 'but a poor master of language.' His exposition is as confused as his thought is profound; he uses words in artificial senses which he does not explain, and to which he does not adhere; and he changes from one hypothesis to another without giving notice.

If then we seek to understand him rightly, we must interpret him generously, more generously than he himself interpreted Adam Smith. When his words are ambiguous, we must give them that interpretation which other passages in his writings indicate that he would have wished us to give them. If we do this with the desire to ascertain what he really meant, his doctrines, though very far from complete, are free from many of the errors that are commonly attributed to them...

...Again, in a profound, though very incomplete, discussion of the difference between 'Value and Riches' he seems to be feeling his way towards the distinction between marginal and total utility. For by Riches he means total utility, and he seems to be always on the point of stating that value corresponds to the increment of riches which results from that part of the commodity which it is only just worth the while of purchasers to buy; and that when the supply runs short, whether temporarily in consequence of a passing accident, or permanently in consequence of an increase in cost of production, there is a rise in that marginal increment of riches which is measured by value, at the same time that there is a diminution in the aggregate riches, the total utility, derived from the commodity. Throughout the whole discussion he is trying to say, though (being ignorant of the terse language of the differential calculus) he did not get hold of the right words in which to say it neatly, that marginal utility is raised and total utility is lessened by any check to supply.

2. But while not thinking that he had much to say that was of great importance on the subject of utility, he believed that the connection between cost of production and value was imperfectly understood; and that erroneous views on this subject were likely to lead the country astray in practical problems of taxation and finance; and so he addressed himself specially to this subject. But here also he made short cuts." -- Alfred Marshall, Principles of Economics, Appendix I

Marshall is wrong here. For example, Ricardo describes riches as a collection of commodities. They were not measured along a single scale, whatever measurement level you might think that scale obtains. Even less could his labor values be said to have been marginal utilities.

Samuel Hollander is the greatest exponent in my lifetime of the view of continuity in the development of theories of value and distribution. Even he, though, recognizes that Marx had reasons for his reading of Ricardo, but I forget where.

Supply And Demand Breaking Down Half A Century Ago: The Sonnenschein-Mantel-Debreu Theorem

"[M]ainstream economists [divide] into effective 'castes', with only a tiny but exalted subset of the profession undertaking the detailed mathematical work needed to discover the weaknesses in the theory. The vast majority of economists believe that this high caste, the mathematical economists, did their work properly, and proved that the theory is internally consistent. The caste has indeed done its work properly, but it has proved precisely the opposite: that the theory is consistent only under the most restrictive and specious of assumptions." - Steve Keen, Debunking Economics

1.0 Introduction

Economists like to tell stories about supply and demand, in which a higher price of a good signals that it is more scarce and encourages agents to substitute other goods for the more scarce good. Mainstream economists have known for more than half a century that these stories have no justification in the most rigorous versions of their theory. Their stories are ad hoc and arbitrary.

I have summarized the Cambridge Capital Controversy before. Here I concentrate on the Sonnenschein-Mantel-Debreu (SMD) theorem.

If General Equilibrium Theory (GET) were to have empirical implications, it would restrict what was possible for market behavior. It turns out that, however, supply and demand functions can have almost any shape. No reason exists, in the theory, for equilibria to be unique or stable. As Andreu Mas Colell and his co-authors put it, anything goes.

I rely more on Alan Kirman's presentations than the original papers for the SMD theorem.

2.0 General Equilibrium Theory (GET)

Leon Walras invented GET and set out its canonical problems: the existence of an equilibrium, its uniqueness, and its stability. For the latter, he invented the tatonnement process, an auction in which no transactions are allowed until prices are found in which demand and supplies are equal. The Arrow-Debreu-McKenzie model is the current canonical statement of GET. For purposes of this post, you can consider a pure exchange economy.

Supply and demand are functions. For example, the quantity demanded and supplied of butter are depicted as functions of its price. The difference between demand and supply is an excess demand function.

Expressing the supply and demand of butter as only a function of its price seems inadequate. Should the demand not also depend on the price of margarine? If the price of bread fell and consumers consumed more bread, would not their demand for butter also rise? Would not the supply of bread, and thus the demand for butter, be impacted by decisions of farmers between growing wheat and producing crops for ethanol?

GET attempts to model all these interactions. Households, in a competitive pure exchange economy, are assumed to start with given endowments, with a certain basket of goods. They also are assumed to have preferences among these goods and to face given prices. The households decide how much of each good in their endowment to sell on the market and how much more to buy. In the jargon, they maximize their utility subject to a wealth constraint.

So for any set of prices, the model describes the difference, for each household, between the quantity demanded on the market of each good and their endowment of each good. This is the household's excess demand function. Under certain general and non-restrictive assumptions, individual excess demand functions have certain supposedly intuitive properties. I think the demonstration that demand functions slope down, if substitution effects dominate income effects, applies to the analysis of a household's maximization problem.

Aggregate or market excess demand functions are found by summing over all households. (Aggregate demand, in this sense, is not the aggregate demands in macroeconomics. They are specified for each of thousands of goods, not somehow summed over all goods.) Suppose the market excess demand for some good was positive at some price vector. Then the households would be trying to buy more of that good than exists. This is a disequilibrium.

An equilibrium exists when the prices are such that utility-maximization decisions of the households are mutually consistent. No good exists in which the households want to buy more than the aggregate endowment of that good.

3,0 Characterization of Market Excess Demand Functions

Arrow & Debreu and McKenzie proved that, under fairly general conditions, an equilibrium exists. I am unsure if the first welfare theorem, from GET, is the theoretical justification for claims that an unregulated capitalism can be efficient. Debreu always denied this interpretation, as I understand it. Debreu (1959) provides no attempt to describe how an equilibrium can be achieved. This remains an unsolved problem (see Fisher 1983).

Almost any functions can be excess demand functions. The restrictions are that the functions be continuous, homogeneous of degree zero, and satisfy Walras' law. Also, we only consider the functions bounded an arbitrarily small distance away from zero. That is, the behavior of the function when all prices are zero is not considered.

Homogenity here means only relative, not absolute prices matter. It does not matter if prices are denominated in dimes or dollars, euros or yuan.

Walras law states that if the excess demand for some good is positive, at disequilibrium prices, then some other markets have excess supplies. The disequilibria cancel out, in some sense.

The conclusion is that GET has no empirical implications at the level of markets.

4.0 Failed Attempts at Workarounds

Market excess demand functions can inherit nice properties on individual excess demand functions if all individuals are identical and have homothetic preferences. The latter implies that Engel curves are linear functions. Your relative demands for different goods, for say, chicken or lobster, does not depend on your income.

These assumptions were typical of macroeconomists for a long time after the so-called rational expectations revolution. They talk a lot about micro foundations, but their models lack them. They could not accommodate individuals with different tastes or with tastes that varied in some way with income.

Kirman may have been sensitized to the importance of the SMD theorem by his attempts, with co-authors to relax these assumptions. What happens if individuals have homothetic preferences, but individuals vary among themselves in their preferences? The same class of functions can still be excess demand functions, with the above extremely limited constraints. How about if individuals have identical preferences, but they are not necessarily homothetic? This does not help. Nor does it help to include production.

5.0 Conclusion

Kirman suggests, as I understand it, that part of the problem is that individuals interact in the model only through markets. Maybe some sort of norms or fashions shape preferences to provide some sort of coordination. Or maybe economists should consider broad classes of households as having common preferences. This type of approach is like that of the classical political economists who assumed, for example, that workers consume all their income (they do not have much), capitalists save, and landlords indulge in spending on luxuries.

References

• Gerard Debreu (1959) Theory of Value: An Axiomatic Analysis of Economic Equilibrium.
• Gerard Debreu (1974) Excess demand functions. Journal of Mathematical Economics 1(1): 15-21.
• Franklin M. Fisher (1983) Disequilibrium Foundations of Equilibrium Economics.
• Alan Kirman (1989) The intrinsic limits of modern economic theory: the emperor has no clothes. Economic Journal 99(395): 126-139.
• Alan Kirman (1992). Whom or what does the representative individual represent? Journal of Economic Perspectives 6(2): 117-136.
• Alan Kirman and K. J. Koch (1986) Market excess demand in exchange economies with identical preferences and collinear endowments. Review of Economic Studies 53(3): 457-463.
• Rolf R. Mantel (1974) On the characterization of excess demand functions. Journal of Economic Theory 7(3): 348-353.
• Hugo Sonnenschein (1972) Market excess demand functions. Econometrica 40(3): 549-563.
• Leon Walras(1874/1877) Elements of Pure Economics.

The Centre Of The Solving Subsystem In A Model With Fixed Capital And Scarce Land

1.0 Introduction

This post revisits my example with fixed capital and two types of land. It presents, by means of an example, the concept of the centre of a solving subsystem. Quadrio Curzio & Pellizzari (2010) introduce the solving subsystem in models of rent so as to first solve the price equations without rent. Schefold (1989) introduces the centre of the price system for a pure fixed capital model to, following Sraffa, initially eliminate the prices of old machines from price equations. As far as I know, nobody has combined these concepts before.

The concept of a solving subsystem clarifies how a switch point can lie along a single wage curve. A system of equations for prices is associated with each technique. Each operated process contributes an equation equating revenues and costs. The revenues can include the prices of joint products, and costs include a charge for the rate of profits on advanced capital goods. A last equation specifies the value of the numeraire as unity. In models of extensive rent, a subsystem can be formed from the processes that characterize industrial processes, with no inputs from land, and processes run on land that are not scarce. The resulting subsystem, with the equation for the numeraire concatenated, can be solved, given the rate of profits, for the wage and the prices of produced commodities. In models of intensive rent, the solving subsystem includes the equations for industrial processes and a linear combination of the equations for the processes that operate on one type of land to the limits of its endowment. As Sraffa (1960) explains, a variable for rent is eliminated by this linear combination. In the case of extensive rent, with no joint production otherwise, the solving subsystem also applies to a model of single production. In any case, the solution to the solving subsystem can then be used to find rents. The example in this post, extends the concept of a solving subsystem to a case with extensive rent and fixed capital. I do not know if the concept of a solving subsystem can usefully apply to joint production more generally

The centre of a pure fixed capital system (Schefold 1989) helps solve the price system of a pure fixed capital system. Joint utilization of machines does not exist in any process in a model of pure fixed capital. Old machines are not consumer goods. In the example, a single commodity is a consumption good and acts as numeraire. Old machines may be freely disposed of; no cost arises in junking a machine, including before its technical life is complete. Nice properties of single production systems generalize to such cases of fixed capital. In particular, the "determination of the cost-minimising technique is independent of the structure of requirements for use" (Huang, 2019). The cost-minimizing technique can be determined by the construction of the wage frontier. These properties are not retained in the combination of pure fixed capital with scarce land. The centre still helps solve the price system.

2.0 Technology, Endowments, Final Demand

Tables 1 and 2 specify the technology. This technology extends an example of fixed capital from Baldone (1974). Labor uses circulating capital to manufacture a machine in process I. The machine has a physical life of three years. Labor uses circulating capital and the machine to produce corn on type 1 land in processes II, III, and IV. The machine is operated on type 2 land in processes V, VI, and VII. A process that produces corn jointly produces a machine one year older than the machine used as input, up to its physical life. One hundred acres of each type of land are assumed to exist. Final demand is for 87 bushels corn, a level that ensures one or the other type of land is scarce. The numeraire is a bushel of corn.

Table 1: Inputs for Processes Comprising the Technology

Input	Processes
	I	II	III	IV	V	VI	VII
Labor	a0,1 = 0.4	a0,2 = 0.2	a0,3 = 0.6	a0,4 = 0.4	a0,5 = 0.23	a0,6 = 0.59	a0,7 = 0.39
Type 1 Land	0	c1,2 = 1	c1,3 = 1	c1,4 = 1	0	0	0
Type 2 Land	0	0	0	0	c2,5 = 1	c2,6 = 1	c2,7 = 1
Corn	a1,1 = 0.1	a1,2 = 0.4	a1,3 = 0.578	a1,4 = 0.6	a1,5 = 0.39	a1,6 = 0.59	a1,7 = 0.61
New Machines	0	1	0	0	1	0	0
Type 1 1-Yr. Old Machines	0	0	1	0	0	0	0
Type 1 2-Yr. Old Machines	0	0	0	1	0	0	0
Type 2 1-Yr. Old Machines	0	0	0	0	0	1	0
Type 1 2-Yr. Old Machines	0	0	0	0	0	0	1

Table 2: Outputs for Processes Comprising the Technology

Input	Processes
	I	II	III	IV	V	VI	VII
Corn	0	b1,2 = 1	b1,3 = 1	b1,4 = 1	b1,5 = 1	b1,6 = 1	b1,7 = 1
New Machines	1	0	0	0	0	0	0
Type 1 1-Yr. Old Machines	0	1	0	0	0	0	0
Type 1 2-Yr. Old Machines	0	0	1	0	0	0	0
Type 2 1-Yr. Old Machines	0	0	0	0	1	0	0
Type 1 2-Yr. Old Machines	0	0	0	0	0	1	0

3.0 Techniques

Tables 3, 4, and 5 specify the techniques that may be chosen with this technology. Alpha, Beta, and Gamma differ in the economic life of the machine on non-scarce, type 1 land. No processes are operated on type 2 land. Under Delta, Epsilon, and Zeta, on the other hand, type 1 land is not farmed at all, and the economic life of the machine varies among the techniques in the processes operated on type 2 land. The remaining techniques fully cultivate one or the other type of land and require rent to be paid to landlords

Table 3: Techniques of Production with Non-Scarce Land

Technique	Processes	Type 1 Land	Type 2 Land
Alpha	I, II	Partially farmed	Fallow
Beta	I, II, III	Partially farmed	Fallow
Gamma	I, II, III, IV	Partially farmed	Fallow
Delta	I, V	Fallow	Partially farmed
Epsilon	I, V, VI	Fallow	Partially farmed
Zeta	I, V, VI, VII	Fallow	Partially farmed

Table 4: Techniques of Production with Type 1 Land Scarce

Technique	Processes	Type 1 Land	Type 2 Land
Eta	I, II, V	Fully farmed	Partially farmed
Theta	I, II, III, V	Fully farmed	Partially farmed
Iota	I, II, III, IV, V	Fully farmed	Partially farmed
Kappa	I, II, V, VI	Fully farmed	Partially farmed
Lambda	I, II, III, V, VI	Fully farmed	Partially farmed
Mu	I, II, III, IV, V, VI	Fully farmed	Partially farmed
Nu	I, II, V, VI, VII	Fully farmed	Partially farmed
Xi	I, II, III, V, VI, VII	Fully farmed	Partially farmed
Omicron	I, II, III, IV, V, VI, VII	Fully farmed	Partially farmed

Table 5: Techniques of Production with Type 2 Land Scarce

Technique	Processes	Type 1 Land	Type 2 Land
Pi	I, II, V	Partially farmed	Fully farmed
Rho	I, II, III, V	Partially farmed	Fully farmed
Sigma	I, II, III, IV, V	Partially farmed	Fully farmed
Tau	I, II, V, VI	Partially farmed	Fully farmed
Upsilon	I, II, III, V, VI	Partially farmed	Fully farmed
Phi	I, II, III, IV, V, VI	Partially farmed	Fully farmed
Chi	I, II, V, VI, VII	Partially farmed	Fully farmed
Psi	I, II, III, V, VI, VII	Partially farmed	Fully farmed
Omega	I, II, III, IV, V, VI, VII	Partially farmed	Fully farmed

Under techniques Eta through Omicron, type 1 land is fully farmed and pays rent. Under Eta, Theta, and Iota, the machine is operated for only one year on type 2 land and then discarded. The techniques differ on the economic life of the machine on type 1 land. Under Kappa, Lambda, and Mu, the machine is operated for two years on type 2 land, while it is operated for its full physical life of three years under Nu, Xi, and Omicron. Under Pi through Omega, type 2 land is scarce and pays rent. Each technique between Eta and Omicron corresponds to a technique between Pi and Omega in which the same processes are operated. The economic life of the two types of machines are the same in these corresponding techniques. The scale at which the processes are run varies so as to vary which type of land is fully farmed.

4.0 The Price System for Omicron

I consider the price equations for Omicron to illustrate the concepts of the solving subsystem and of the centre. All seven processes are operated under Omicron, and type 1 land is scarce. The following seven displays, in obvious notation, specify the price system for Omicron:

a_1,1(1 + r) + w a_0,1 = p₀

(a_1,2 + p₀)(1 + r) + rho₁ c_1,2 + w a_0,2 = b_1,2 + p_1,1

(a_1,3 + p_1,1)(1 + r) + rho₁ c_1,3 + w a_0,3 = b_1,3 + p_1,2

(a_1,4 + p_1,2)(1 + r) + rho₁ c_1,4 + w a_0,4 = b_1,4

(a_1,5 + p₀)(1 + r) + w a_0,5 = b_1,5 + p_2,1

(a_1,6 + p_2,1)(1 + r) + w a_0,6 = b_1,6 + p_2,2

(a_1,7 + p_2,2)(1 + r) + w a_0,7 = b_1,7

Revenues for operating each process at a unit level are shown on the right-hand side of these equations. Revenues for the first process are obtained by selling new machines. Revenues for the second process result from products of both corn and a type 1 one-year old machine. That type 1 machine, in turn, enters into the advanced costs of the third process, and so on. Type 1 land obtains a rent, and type 2 land is free.

The first equation and the last three of the seven constitute the solving subsystem for Omicron. Given the rate of profits, the solving subsystem specifies the wage, the price of a new machine, and the prices of one-year old and two-year old machines when operated on free type 2 land. The remaining three equations can then be used to find the rent on type 1 land and the prices of one-year old and two-year old machines when operated on type 1 land. The solving subsystem for Omicron is also the solving subsystem for Zeta, Nu, and Xi. In all these techniques, the machine is run for its full physical life of three years on free type 2 land.

The prices of old type 2 machines can be eliminated from the solving subsystem for Omicron. Multiply both sides of the second equation of the solving subsystem by (1 + r)²:

(a_1,5 + p₀)(1 + r)³ + w a_0,5(1 + r)² = b(1 + r)²_1,5 + p_2,1(1 + r)²

Multiply both sides of the third equation of the solving subsystem by (1 + r):

(a_1,6 + p_2,1)(1 + r)² + w a_0,6(1 + r) = b_1,6(1 + r) + p_2,2(1 + r)

Add these two equations and the last equation of the solving subsystem:

where the row vector and matrix in this system of equations is as follows:

The ordered pair consisting of this row vector and matrix is the centre (Schefold 1989) for the solving subsystem for Omicron. Given the rate of profits, this system of matrix equations can be solved for the wage and the price of a new machine. This price system has the form of a price system for a circulating capital model, with the exception of the dependence of the Leontief input matrix and the vector of direct labor coefficients on the rate of profits. Unlike in the model of circulating capital, the wage curve derived from the centre of a pure fixed capital system can slope up for part of its range. The wage frontier of a pure fixed capital system, however, decreases throughout its length (Baldone 1974, Varri 1974).

The prices of old type 1 machines can be similarly eliminated from the full price system for Omicron.

5.0 Conclusion and Questions

The above illustrates the centre of a solving subsystem. In the example, the solving subsystem shows that a system of seven equations for a price system can be decomposed such that a system of four equations is solved first. And the centre of the solving subsystem shows that that system of four equations can be further decomposed so that a system of two equations is solved first.

Perhaps the centre of a solving subsystem can be used to address a theoretical question. Is the wage frontier always decreasing in a model combining fixed capital and rent? Can the wage frontier sometimes slope up?

In a model of extensive rent, the wage frontier is not the outer envelope of the wage curves for the technique. But it is always decreasing. Each wage curve is found from a solving subsystem. And the solving subsystem is from a related circulating capital model. So the wage curves inherit the properties of circulating capital models. The wage frontier is formed from the wage curves of the cost-minimizing techniques and always is decreasing.

In a pure fixed capital model, the wage frontier is the outer envelope of the wage curves for the techniques and is always decreasing. Individual wage curves can be increasing, but the ranges of the rate of profits at which they are increasing is never on the frontier.

I suspect the wage frontier for a model combining extensive rent and fixed capital can be increasing over some range of the rate of profits. This suspicion should be validated by constructing a numerical example. On the other had, if the wage frontier is alwys decreasing in such a model, that should be capable of a proof. And such a proof, if it exists, will probably use the concept of the centre of a solving subsystem.

References

• Baldone, S. (1974), Il capitale fisso nello schema teorico di Piero Sraffa, Studi Economici, XXIV(1): 45-106. Trans. in Pasinetti (1980).
• Huang, B. 2019. Revisiting fixed capital models in the Sraffa framework. Economia Politica 36: 351-371.
• Pasinetti, L.L. 1980. (ed.), Essays on the Theory of Joint Production, New York, Columbia University Press.
• Quadrio Curzio, Alberto. 1980. Rent, income distribution, and orders of efficiency and rentability (in Pasinetti 1980).
• Quadrio Curzio, Alberto and Fausta Pellizzari. 2010. Rent, Resources, Technologies. Berlin: Springer.
• Schefold, Bertram. 1989. Mr. Sraffa on Joint Production and other Essays, London, Unwin-Hyman.
• Sraffa, Piero. 1960. The Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory. Cambridge: Cambridge University Press.
• Varri, P. 1974. Prezzi, saggio del profitto e durata del capitale fisso nello schema teorico di Piero Sraffa, Studi Economici, XXIX(1): 5-44. Trans. in Pasinetti (1980).

Old Papers On Rent And One New One

This post annotates some papers that I want to remind myself of.

Montani (1975) references Quadrio Curzio (in Italian), defines the order of fertility and rentability, notes that they are different, and has something like the reswitching of the order of fertility. He does not have the reswitching of the order of rentability. He treats both extensive and intensive rent, but does not combine them. He notes the wage frontier can slope up under intensive rent. I have to read more closely to see if he already has multiple cost-minimizing techniques. I am under the impression that D'Agata first notice this possibility.

Montet (1979) criticizes Metcalfe and Steedman in that their perversities are more general than they know. Land provides another degree of freedom. They have a wage, rent, rate of profits frontier. I generally do not set equations for natural resources out this way. I once set out an example with heterogeneous labor, relabeling 'land' as 'skilled labor'.

Gibson & McLeod (1983) look at extensive, intensive, and external intensive rent. They go into difficulties of defining basics in joint production. One definition is about the decomposability of matrices and the other is about the rank of some sort of block matrix. They define quasi-basics for the latter. D’Agata has some sort of objection to this. They have interchanges in both the CJE and the RRPE.

Erreygers (1995) considers joint production. Toward the end of his paper, he shows how extensive rent fits into this framework. He wants to avoid setting out another equation in the quantity system to constrain levels of operations of processes from requiring more land to be farmed than exist. And rents should be part of the price vector in the price system, not seperate variables. Kurz & Salvadori (1995) show how to define certain block structured matrices to achieve this end. I think Erreygers may have created this approach.

Ianni (2026) is about international trade, not rent. The theory of intensive and extensive rent can show why most lands are specialized, so the theory may have implications for the theory of international trade. Also, my way of analyzing the choice of technique with long-lasting and given ratios of the rate of profits among industries may have implications for trade. Different countries may be modeled as having different rates of profits.

References

• Erreygers, Guido. 1995. On the uniqueness of cost-minimizing techniques. The Manchester School 63: 145-166
• Gibson, Bill and Darryl McLeod. 1983. Non-produced means of production in Sraffa's system: basics, non-basics and quasi-basics. Cambridge Journal of Economics 7: 141-150.
• Ianni, Guido. 2026. Class struggle and the international division of surplus: The distributive surface in the open economy. Metroeconomica
• Montani, Guido. 1975. Scarce natural resources and income distribution. Metroeconomica 27(1): 68=101.
• Montet, C. 1979. Reswitching and primary input use: a comment. Economic Journal 89 (355): 642-647.

Factor Demand Curves For An Example With Fixed Capital And Rent

Figure 1: Demand Curve for Labor

I have created and worked through an example in which a machine with a physical life of three years can be used in producing an agricultural commodity on one of two types of land.

My example is one of capital-reversing. It occurs to me that I have not plotted the demand for so-called factors of production in this example. Accordingly, Figure 1 plots the wage against the employment firms want to offer, given final demand. Switch points are horizontal line segments in this graph. Around the 'perverse' switch point, a higher wage is associated with firms wanting to employ more workers.

Given final demand and the rate of profits, a price system is defined for each technique. I can add up the value of the capital goods that must exist at the start of the year to produce the given final demand. Prices of production are used to aggregate heterogeneous goods. Figure 2 shows the demand for capital, in some sense. Here, too, the 'perverse' switch point is indicated for a step function approximation for an increasing demand curve. The value of capital varies between switch points because of price Wicksell effects.

Figure 2: Demand Curve for Capital

A model with both fixed capital and the rent of natural resources is a step towards realism if you want. It is also a step beyond what can be found from empirical Leontief matrices, as I understand it. Still, wages and employment, for example, cannot be explained in the long run by the interactions of well-behaved supply and demand functions in the labor market.

Some Phenomena In Price Theory

I occasionally list theoretical possibilities that I think interesting. Outside of a working paper at Centro Sraffa, I have not managed to publish papers detailing the possibilities listed in this post. Some I have not even written up outside of blog posts. I now know that:

• The recurrence of truncation can occur without the reswitching of techniques. This possibility arises in an example of pure fixed capital, with long-lived machines used in both industries that exist in the example.
• A switch point can lie along a single wage curve, with no other wage curve intersecting at the switch point. This possibility occurs in an example with both fixed capital and rent.
• The order of rentability can be completely opposite the order of efficiency. This possibility can arise in a model that combines extensive and intensive rent.
• The partitioning of parameter spaces by fluke switch points is useful in the analysis of structural economic dynamics with a choice of technique.
• Capital-theoretic paradoxes are transient, in many instances, in secular time (also known as the very long run).

I have some difficulties in writing these up. First, my status as an independent researcher creating examples as a hobby should make reviewers be a bit skeptical. Second, many may not be interested in these refinements. Does not Kurz and Salvadori (1995) provide a definitive statement of post Sraffian price theory? You need to have mastered quite a bit of that to understand the point of any of these. Third, I try to put each in a somewhat more general framework I cast the first, the recurrence of truncation, as an example of the last. I suggest that the second, a switch point along a single wage curve, is an anomalous switch point, a concept I am introducing. I want to say that the third is an example of a special case of a model of intensive and extensive rent in which 'nice' properties of models of extensive rent obtain; wage curves slope down and no issues of the non-existence or multiplicity of cost-minimiing techniques away from switch points arise. Last, when I make such generalizations, I have trouble casting my results into the abstract theorem-proof form needed to be precise.

Is the analysis of structural economic dynamics with a choice of technique an interesting problem? Maybe a book of bookprints never exists at a point of time. Capitalists do not have option of costlessly choosing another page. When a new technique is introduced, it typically dominates the existing technique. On the other hand, I have trouble with part II of Sraffa's book preceding part III. Part II treats joint production, including rent and fixed capital. Part III treats the choice of technique. Which lands to cultivate and what economic lives of machines to adopt are part of the choice of technique. So maybe I should limit my program to aspects of joint production. But I also have some consideration of Harrod-neutral technical progress.

It seems I still have years of work.

Murray Rothbard Muddled And Confused

1.0 Introduction

I try to read Rothbard's 'Toward a reconstruction of utility and welfare economics' (in On Freedom and Free Enterprise: The Economics of Free Enterprise (ed. Mary Sennholz), 1956). It does not go far toward its declared goal.

Some Austrian fanboys point to this paper to show Rothbard with a good understanding of the technical details of economics. And it fails.

2.0 Demonstrated Preference and Indifference

Rothbard proposes a concept, 'demonstrated preference', but never explains it clearly. He cites Ludwig Von Mises, among others, as a forerunner. He says that "Actual choice reveals, or demonstrates, a man’s preferences."

Rothbard asserts, like Von Mises, that marginal utilities can be ranked. You will find it difficult to identify anybody outside the Austrian school who agree today. I do not see that confining oneself to discrete increments of a single good helps Rothbard make his case.

I find strange Rothbard's rejection of an indifference relation. He writes:

"Indifference can never be demonstrated by action. Quite the contrary. Every action necessarily signifies a choice, and every choice signifies a definite preference. Action specifically implies the contrary of indifference."

And his arguments are quite curious. I do not find this persuasive:

"It is immaterial to economics whether a man chooses alternative A to alternative B because he strongly prefers A or because he tossed a coin. The fact of ranking is what matters for economics, not the reasons for the individuals arriving at that rank."

I would think that if I use a coin flip to decide, I am demonstrating that I do not care which way the decision comes out.

"The other attempt to demonstrate indifference classes rests on the consistency - constancy fallacy, which we have analyzed above. Thus, Kennedy and Walsh claim that a man can reveal indifference if when asked to repeat his choices between A and B over time, he chooses each alternative 50 percent of the time.

The above is silly. Would you say that the agent is indifferent if his preferences were constant over the observed time? Refusing to accept the hypothesis does not answer the question.

Does getting rid of the indifference relation hinder the use of 'demonstrated preference' to derive individual demand functions, whether defined on a discrete space or not? Maybe a primitive relation of 'not preferred to' is all that is needed. But Rothbard does not say.

3.0 Praxeology and Logic

I understand logic to be about the form of an argument or deduction. The content or meaning of propositions that appear in an argument are not supposed to matter for its validity.

Rothbard attempts to clarify a different conception:

"...a fundamental epistemological error ... pervades modern thought: the inability of modern methodologists to understand how economic science can yield substantive truths by means of logical deduction (that is, the method of 'praxeology')."

Rothbard asserts that his starting axioms must be true:

"...economics, or praxeology, has full and complete knowledge of its original and basic axioms. These are the axioms implicit in the very existence of human action, and they are absolutely valid so long as human beings exist. But if the axioms of praxeology are absolutely valid for human exisence, then so are the consequents which can logically be deduced from them. Hence, economics, in contrast to physics, can derive absolutely valid substantive truths about the real world by deductive logic."

We now know that Rothbard is incorrect on the his axioms. But never mind that.

"...mathematical logic is uniquely appropriate to physics, where the various logical steps along the way are not in themselves meaningful; for the axioms and therefore the deductions of physics are in themselves meaningless, and only take on meaning 'operationally,' insofar as they can explain and predict given facts. In praxeology, on the contrary, the axioms themselves are known as true and are therefore meaningful. As a result, each step-by-step deduction is meaningful and true. Meanings are far better expressed verbally than in meaningless formal symbols."

I have no idea what formal logic has to do with physics. As far as I know, the conception that logic is about the form of an argument goes back to Plato and Aristotle. Hegel may have had a different idea. Frege was writing about the foundations of arithmetic, not about physics.

4.0 Von Neumann-Morgenstern Cardinal Utility

Rothbard has a few remarks on the Von Neumann-Morgenstern definition of utility. Their exposition goes along with the development of a theory of measurement. A measurement scale is such that statements about things measured along that scale are only meaningful up to a set of transformations.

But according to Rothbard, "Measurement, on any sensible definition, implies the possibility of a unique assignment of numbers which can be meaningfully subjected to all the operations of arithmetic." "No arithmetical operations whatever can be performed on ordinal numbers." But non-parametric statistics was already being developed then. I think of the Mann-Whitney-Wilcoxon statistic, for example. In fact, the first edition of Sidney Siegel's textbook, Non-Parametric Statistics for the Behavioral Sciences, dates from 1956.

Rothbard tells us that those who follow Von Neumann and Morgenstern only apply probability to repeatable events: "... unique events are not repeatable. Therefore, there is no sense in applying numerical probability theory to such events. It is no coincidence that, invariably, the application of the neo-cardinalists has always been to lotteries and gambling. It is precisely and only in lotteries that probability theory can be applied." And Rothbard also asserts that "The leading adherents of the Neumann-Morgenstern approach are Marschak, Friedman, Savage, and Samuelson". But Leonard Savage, in his 1954 book, starts the development of his personalistic approach to probability with unique events. His application of personalistic probability to small worlds is supposed to apply numeric probabilities to unique events there. So, again, Rothbard is mistaken. (I take no position on whether unique events can meaningfully be assigned probabilities, either in a small world or not.)

5.0 Conclusion

Rothbard makes a lot of other dubious or incorrect statements. I concede that his references are wide ranging.

Rothbard's undergraduate degree was in mathematics. I pity the fool.