I am now busy writing a paper with my colleague Paul Zimmerman, documenting a claim that I made just over four years ago that P. H. Wicksteed discovered the Coase Theorem. The paper is due to be presented at the History of Economics Society Conference next month at Duke University. At some point soon after the paper is written, I plan to post it on SSRN.
Briefly, the point of the paper is that Wicksteed’s argument that there is no such thing as a supply curve in the sense that the supply curve of a commodity in fixed supply is just the reverse of a certain section of the demand curve, the section depending on how the given stock of the commodity is initially distributed among market participants. However the initial stock is distributed, the final price and the final allocation of the commodity is determined by the preferences of the market participants reflected in their individual demands for the commodity. But this is exactly the reasoning underlying the Coase Theorem: the initial assignment of liability for damages has no effect on the final allocation of resources if transactions costs are zero (as Wicksteed implicitly assumed in his argument). Coase’s originality was not in his reasoning, but in recognizing that economic exchange is not the mere trading of physical goods but trading rights to property or rights to engage in certain types of conduct affecting property.
But Wicksteed went further than just showing that the initial distribution of a commodity in fixed supply does not affect the equilibrium price of the commodity or its equilibrium distribution. He showed that in a production economy, cost has no effect on equilibrium price or the equilibrium allocation of resources and goods and services, which seems a remarkably sweeping assertion. But I think that Wicksteed was right in that assertion, and I think that, in making that assertion, he anticipated a point that I have made numerous times on this blog (e.g., here) namely, that just as macroeconomic requires microfoundations, microeconomics requires macrofoundations. The whole of standard microeconomics, e.g., assertions about the effects of an excise tax on price and output, presumes the existence of equilibrium in all markets other than the one being subjected to micro-analysis. Without the background assumption of equilibrium, it would be impossible to derive what Paul Samuelson (incorrectly) called “meaningful theorems,” (the mistake stemming from the absurd positivist presumption that empirically testable statements are the only statements that are meaningful).
So let me quote from Wicksteed’s 1914 paper “The Scope and Method of Political Economy in the Light of the Marginal Theory of Value and Distribution.”
[S]o far we have only dealt with the market in the narrower sense. Our investigations throw sufficient light on the distribution of the hay harvest, for instance, or on the “catch” of a fishing fleet. But where the production is continuous, as in mining or in ironworks, will the same theory still suffice to guide us? Here again we encounter the attempt to establish two co-ordinate principles, diagrammatically represented by two intersecting curves; for though the “cost of production” theory of value is generally repudiated, we are still foo often taught to look for the forces that determine the stream of supply along two lines, the value of the product, regulated by the law of the market, and the cost of production. But what is cost of production? In the market of commodities I am ready to give as much as the article is worth to me, and I cannot get it unless I give as much as it is worth to others. In the same way, if I employ land or labour or tools to produce something, I shall be ready to give as much as they are worth to me, and I shall have to give as much as they are worth to others-always, of course, differentially. Their worth to me is determined by their differential effect upon my product, their worth to others by the like effect upon their products . . . Again we have an alias merely. Cost of production is merely the form in which the desiredness a thing possesses for someone else presents itself to me. When we take the collective curve of demand for any factor of production we see again that it is entirely composed of demands, and my adjustment of my own demands to the cond ditions imposed by the demands of others is of exactly the same nature whether I am buying cabbages or factors for the production of steel plates. I have to adjust my desire for a thing to the desires of others for the same thing, not to find some principle other than that of desiredness, co-ordinate with it as a second determinant of market price. The second determinant, here as everywhere, is the supply. It is not until we have perfectly grasped the truth that costs of production of one thing are nothing whatever but an alias of efficiencies in production of other things that we shall be finally emancipated from the ancient fallacy we have so often thrust out at the door, while always leaving the window open for its return.
The upshot of Wicksteed’s argument appears to be that cost, viewed as an independent determinant of price or the allocation of resources, is a redundant concept. Cost as a determinant of value is useful only in the context of a background of general equilibrium in which the prices of all but a single commodity have already been determined. The usual partial-equilibrium apparatus for determining the price of a single commodity in terms of the demand for and the supply of that single product, presumes a given technology for converting inputs into output, and given factor prices, so that the costs can be calculated based on those assumptions. In principle, that exercise is no different from finding the intersection between the demand-price curve and the supply-price curve for a commodity in fixed supply, the demand-price curve and the supply-price curve being conditional on a particular arbitrary assumption about the initial distribution of the commodity among market participants. In the analysis of a production economy, the determination of equilibrium price and output in a single market can proceed in terms of a demand curve for the product and a supply curve (reflecting the aggregate of individual firm marginal-cost curves). However, in this case the supply curve is conditional on the assumption that prices of all other outputs and all factor prices have already been determined. But from the perspective of general equilibrium, the determination of the vector of prices, including all factor prices, that is consistent with general equilibrium cannot be carried out by computing production costs for each individual output, because the factor prices required for a computation of the production costs for any product are unknown until the general equilibrium solution has itself been found.
Thus, the notion that cost can serve as an independent determinant of equilibrium price is an exercise in question begging, because cost is no less an equilibrium concept than price. Cost cannot be logically prior to price if both are determined simultaneously and are mutually interdependent. All that is logically prior to equilibrium price in a basic economic model are the preferences of market participants and the technology for converting inputs into outputs. Cost is not an explanatory variable; it is an explained variable. That is the ultimate fallacy in the doctrine of real costs defended so tenaciously by Jacob Viner in chapter eight of his classic Studies in the Theory of International Trade. That Paul Samuelson in one of his many classic papers, “International Trade and the Equalization of Factor Prices,” could have defended Viner and the real-cost doctrine, failing to realize that costs are simultaneously determined with prices in equilibrium, and are indeterminate outside of equilibrium, seems to me to be a quite remarkable lapse of reasoning on Samuelson’s part.
Uneasy Money 
Seems to me that when we draw a production possibilities curve, the slope of that curve gives the cost of production of good x. That’s before we have any concept of price or marginal rate of substitution. Then draw a budget line tangent to that production possibilities curve, and now we can see how price affects production, just by tilting the budget line while keeping it tangent to the PPC. Finally, add indifference curves to the picture, and we can see how preferences affect price.
When speaking of the Coase theorem, it’s helpful to draw a community production possibilities curve (CPPC). This is done by drawing the PPC’s of two people, A and B, turning B’s PPC upside-down (like an Edgeworth box), and placing B’s PPC tangent to an arbitrary point on A’s PPC. Then, while holding an imaginary pencil at B’s (upside-down) origin, slide B’s PPC up and down A’s PPC, keeping them tangent. Your pencil will trace out the CPPC. Finally, do Coase’s trick of transferring some x and y from A to B. This will shift A’s PPC down while shifting B’s PPC up, but the CPPC is unaffected. This yields Coase’s result that changes in the allocations of goods do not affect the CPPC.
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This is really interesting stuff.
I haven’t been able to spend much time on it yet, but is it an oversimplification to suggest that at the macroeconomic level all costs in the sense of supply become prices in the sense of demand (hence the redundancy)?
If that’s roughly correct, how would you relate the issue here to the presumably more general fallacy of composition? It always seemed to me that the fallacy of composition is a primal force driving macroeconomic thinking.
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Mike, I agree that the PPC is a very useful construct in pursuing this analysis. However, you get into trouble with indifference curves unless you assume a representative individual which, of course, is simply another form of question begging.
JKH, The fallacy of composition is always a problem. It is caused by implicitly holding some variable constant which is really not constant. And that’s the point of the discussion of costs. Costs can’t be assumed to remain constant because if prices change, costs also change.
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David:
I don’t see the problem with indifference curves, or why a representative individual enters into the picture. We just draw a PPC with a budget line tangent to it, then draw an indifference curve tangent to the budget line, and play with the budget line to see what happens to the productive and consumptive optimum points. Actually, we don’t even need indifference curves, as long as we have marginal rates of substitution. How is that question-begging?
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So where does this leave classical/neoclassical economics?
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In answering my own question above it seems reasonable to say from a Walrasian general equilibrium/tatonnement process perspective, classical/neclassical economics is still safe. In a Walrasian tatonnement process all prices are up for grabs, initially indeterminate. There is no difference between a final product price and the price of an intermediate good – an equilibrium level has to be attained for all of them. However, the unreality of the Walrasian tatonnement process brings everything back to earth. A real economy gropes towards an equilibrium, and whether it is attained in any market let alone all is almost beyond the ken of any human being to judge.
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Mike, I am probably not understanding what you are trying to show with the PPC and the indifference curve. My comment was aimed at the notion that a general equilibrium can be characterized as the tangency of a PPC with an indifference curve. An indifference curve in that situation is the indifference curve of a representative individual which is what I consider to be question begging.
Henry, Since Marshall, Pigou, Wicksteed and Coase were all within the broad stream of neoclassical economics, I don’t see that this particular controversy has any implications for neoclassical economics, which is simply a mode of reasoning about economic problems, not a specific set of doctrines.
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“which is simply a mode of reasoning about economic problems”
At least from a partial equilibrium perspective, it’s a mode of reasoning based on assumed cost prices. Wicksteed is saying these costs are indeterminate. So how can a partial equilibrium analysis proceed from that? Isn’t this Wicksteed’s point or at least a corollary of his argument?
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In a partial equilibrium setting, cost is not indeterminate, because all other prices are assumed to be at their general equilibrium levels. That is a very strong assumption, but that is the assumption underlying all of standard, i.e. neoclassical, microeconomics.
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“That is a very strong assumption”
I would say it’s an assumption strongly made.
“The whole of standard microeconomics,…… presumes the existence of equilibrium in all markets other than the one being subjected to micro-analysis. Without the background assumption of equilibrium, it would be impossible to derive what Paul Samuelson (incorrectly) called “meaningful theorems,”
Is this not saying what I am saying? Is not Wicksteed saying that without this assumption, partial equilibrium analysis is not possible? If not, then I have seriously misunderstood your post and Wicksteed and I will quietly retreat to the dunce’s corner.
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No need for extreme measures. First, you said Wicksteed was saying that partial equilibrium analysis was not possible, now you say that he said that it is possible if you assume that all other markets are in equilibrium. If they are, and the market you are analyzing is sufficiently small relative to the rest of the economy, you can do partial equilibrium analysis. I disagreed with your first statement, and I agree with your second.
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It might be easier for both of us if I proceeded to the dunce’s corner.
“Thus, the notion that cost can serve as an independent determinant of equilibrium price is an exercise in question begging, because cost is no less an equilibrium concept than price.”
Is this not saying that cost is indeterminate?
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Indeterminate in the context of a general equilibrium analysis in which all prices are determined as part of the solution. It is not indeterminate in the context of a partial equilibrium analysis in which the prices of everything but a single good are given. I should also note that the use of indeterminate may be misleading. Costs are determined in equilibrium. The point is because they are determined in equilibrium, costs cannot be used to explain why prices are what they are because costs are not determined in advance of prices they are determined simultaneously with prices.
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From a Walrasian general equilibrium/tatonnement process point of view, all prices are initially indeterminate (the point I made in my post several up). At the end of the tatonnement process all prices are determinate (i.e. set at equilibrium levels).
From the perspective of partial equilibrium, the assumption that all other prices are set at equilibrium levels then negates all questions of logical invalidity of the analysis.
Partial equilibrium is OK because of the assumption about prices.
Walrasian equilibrium is OK because of the tatonnement process.
So what is Wicksteed’s argument all about? (I can see the dunce’s corner beckoning.)
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His argument was with the Marshallians who believe that there is something called “real cost” which is what determines price.
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Is “real cost” mentioned in the main piece? Anyway.
So “real cost” is not the same as saying “all other prices are set at equilibrium levels?
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Ooops – it’s in the title. Off the optometrist before the dunce’s corner.
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David:
“My comment was aimed at the notion that a general equilibrium can be characterized as the tangency of a PPC with an indifference curve.”
I was thinking of general equilibrium as a community PPC being tangent to a community indifference curve (CIC). I’ve never seen textbooks describe it this way, so if my description below isn’t clear I can email you a drawing.
A CIC (which I first saw in Alchian’s 201A class) is drawn by turning B’s indifference curve upside down, placing it tangent to A’s indifference curve at an arbitrary point, holding an imaginary pencil at B’s origin, and sliding B’s indifference curve up and down A’s indifference curve, keeping them tangent. Your pencil will trace out the CIC.
To show general equilibrium, start with a CPPC (described in my old comment). Inscribe an Edgeworth box inside that CPPC. When we are in general equilibrium, the indifference curves of A and B will be tangent to each other, and the PPC’s of A and B will also be tangent to each other. Furthermore, the slopes of the PPC’s will equal the slopes of the indifference curves (at the point of tangency), and also equal to the slope of the CPPC.
Finally, focus in on the tangengy of the two indifference curves. Place an imaginary pencil at B’s origin, and imagine sliding B’s indifference curve up and down along A’s indifference curve, keeping them tangent. You imaginary pencil will trace out the CIC, and the CIC will be tangent to the CPPC, thus picturing general equilibrium without requiring everyone’s indifference curves to be the same.
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“But Wicksteed went further than just showing that the initial distribution of a commodity in fixed supply does not affect the equilibrium price of the commodity or its equilibrium distribution.”
I may be misunderstanding this, but I do not think Wicksteed’s argument then is correct in a general equilibrium model. With quasi-linear utility, yes, equilibrium is unaffected by initial allocation, just as with the Coase theorem version mentioned. But if quasi-linear utility cannot be assumed, then I do not think this is true in Walrasian general equilibrium.
Is the argument that this traditional general equilibrium understanding is wrong – that initial distribution does not matter?
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Ksovim, Coase and Wicksteed both recognized that the proposition that final equilibrium is independent of the initial distribution is only true when demand is unaffected by the initial distribution of goods or rights. There are some assumptions that can be made to guarantee that result, but you are correct that in general they don’t hold. But they both made the assumption for expository convenience.
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#1 on prefiguring of the so-called Coase theorem, consider also p. 396-7 of W.H. Hutt, “Co-ordination and the Size of the Firm,” South African Journal of Economics 2(4), December 1934:
“Now, under one ownership, their relations would, given competitive institutions, be exactly the same, provided that both methods were equally efficient from the social standpoint. There is no reason why the spreading of the lines of responsibility back to several sources should lead to less effective planning than subordinacy to an authority emanating from one source, given the equal availability of relevant knowledge to the managers who devise the plans…The most important significant difference between the two cases is that, in practice, in the one case there may not be the availability of relevant knowledge that there is in the other.”
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Daniel,
Nice one, but not as well-formulated as either Coase or Wicksteed. It may also provide an interesting bridge between Coase’s theory of the firm and his theory of social cost, but I will have to think about that one.
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Very good post. Some would argue that the essence of the Coase Theorem is not that the initial distribution of property rights doesn’t matter, but rather that it doesn’t matter if there are no transactions costs. I seem to recall that that was Coase’s view.
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George Stigler was very much on the money with his law about credit for all scientific discoveries. You get credit for discovering something when it stays discovered after you have written about it. Naturally, he is law of scientific epiphany repeats Merton’s law of triples.
Adam Smith may have drawn on others but he certainly made sure economics stay discovered after the Wealth of Nations. Alfred Marshall was rather poor at attributing credit to others but he certainly make sure all the ideas in his Principles of Economics stay discovered.
I happened to yesterday read in succession Earl Thomson’s 1967 discovery of the Ricardian equivalence theorem then Robert Barro’s article. Thomson’s article is as usual quite difficult to read. Barro is a straightforward article to read which is technically sophisticated and alert to all the issues he raised in the nuances and why it was important as the theorem. Why the exceptions are more important than the rule because they make everyone explain why deficits work in a very different way to the standard explanation.
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