Demand andExchange
In the Principles of Economics (1890: Appendix F) Marshall included a brief discussion of Edgeworth's analysis of barter, and produced a figure showing the contract curve. During the following year, in the course of a review written in Italian, Edgeworth criticised Marshall for not having dealt sufficiently with the problem of indeterminacy.
The basic problem was that Marshall, using a model in which a series of trades are allowed to take place at disequilibrium prices, believed he had shown that prices eventually settle at the pricetaking equilibrium. However, the argument was not transparent. The adjustment process involves moving from the initial endowment point in a series of trades, where trading at “false” prices is allowed at each step. The process must conclude with both individuals at a point on the contract curve. A feature of the process is the assumption that each stage or iteration of the sequence involves Pareto improvements: individuals trade only if it makes them better off. Furthermore, it involves trading at the “short end” of the market, that is, the minimum of supply and demand. This arises from the impossibility of forcing any individual either to buy or sell more than desired at any price. Starting from a disequilibrium price, trade takes place at the short end of the market, and endowments change. At the next trading stage, the price of the good with an excess supply must be lowered. At each trade, there is a Pareto improvement. The combination of Pareto-efficient moves at each stage, combined with an adjustment process such that an excess supply leads to a price reduction, and vice versa, produces a stable process that converges to an equilibrium somewhere on the contract curve. Interestingly, this type of sequence of disequilibrium trades was later used by Launhardt in examining total utility and price-taking (see Creedy 1994b).Marshall believed that his assumption of an additive utility function, combined with the assumption that the marginal utility of one good is constant for both individuals, guaranteed a determinate price, if the good having constant marginal utility is money. This case was mentioned by Edgeworth (1925, ii: 317, fn. 1). The contract curve is a straight line parallel to the axis for the good with constant marginal utility, along which the rate of exchange is constant. So the equilibrium price does not depend on the sequence of trades. However, Edgeworth’s point was that the total amount spent on the good remains indeterminate.
There was a later disagreement between Marshall and Edgeworth over the so-called Giffen good. In a book review, Edgeworth argued that ‘Even the milder statement that the elasticity of demand for wheat may be positive, though I know it is countenanced by high authority, appears to me so contrary to a priori probability as to require very strong evidence’ (Edgeworth 1909: 105; italics in original). The authority was of course Marshall (1890: 132), who replied directly to Edgeworth that I don’t want to ‘argue... But... the matter has not been taken quite at random’ (Marshall quoted in Pigou 1925: 438). Marshall gave a numerical example involving a journey travelled by two methods, where the distance travelled by the cheaper and slower method must increase when its price increases; for details, see Creedy (1990).
It was mentioned above that Edgeworth introduced the generalised utility function. An implication is that it allows for complementarity, although he did not explicitly consider this in 1881. It was used by Edgeworth in his paper on the pure theory of monopoly. The concept amounts to what is now called gross complementarity, defined in terms of cross-price elasticities. The first major criticism came from Johnson (1913), who pointed out that the criterion is not invariant with respect to monotonic transformations of the utility function. His treatment was extended by Hicks and Allen (1934), so that the modern definition involves net complements in terms of compensated price changes. There is no symmetry between gross substitutes and complements as only the matrix of (compensated) substitution elasticities is assumed to be symmetric.
8.2