Monopoly andOligopoly
In a paper first published in Italian in 1897, and not translated until the collected Papers (Edgeworth 1925), Edgeworth examined several problems relating to monopoly. He began with Cournot's (1838) example of the “source minerale” in which there are “two monopolists” (i.e.
duopolists), each owning a spring of mineral water. It would be natural for Edgeworth to expect an indeterminate price in this “small numbers” context. Cournot arrived at a determinate solution for price and output, but Edgeworth showed that ‘when two or more monopolists are dealing with competitive groups, economic equilibrium is indeterminate' (Edgeworth 1925, i: 116). He argued that ‘[A]t every stage...it is competent to each monopolist to deliberate whether it will pay him better to lower his price against his rival as already described, or rather to raise it to a higher...level for that remainder of customers of which he cannot be deprived by his rival' (ibid.: 120).Edgeworth went on to define (what are now called) reaction curves and isoprofit lines, for variations in prices. However, it was not until Bowley's (1924) discussion that these matters began to be presented in a more transparent manner.
Edgeworth then considered the case of complementary demand within the context of bilateral monopoly, where the two goods are demanded in fixed proportions for use in the production of a further article. A feature is that he wrote the equations of the reaction curves and explicitly dealt with what came to be called conjectural variations, reflecting the extent to which one duopo- list is expected to change price in response to changes made by the second duopolist. In discussing this problem, Edgeworth also introduced the concept of a “saddle point”, which he called the “Hog's Back”, indicating its importance for stability.
Walras (1874: 225) had introduced the concept of the entrepreneur who neither gains nor loses.
This result applied only to the competitive equilibrium, where there are no incentives for entrepreneurs to enter any industry.This does not of course mean that there are no profits, in the accounting sense, since the returns to homogeneous units of inputs of organisation and management services are subsumed in the costs of the firm. Edgeworth’s criticisms of this concept of the no-profit entrepreneur, reproduced in his Papers (Edgeworth 1925, i), recognised that with Walras’s assumptions there is nothing illogical about the argument. The theory simply means that nothing remains, ‘after the entrepreneur has paid a normal salary to himself’ (ibid.: 26). Furthermore, ‘If [the general expenses] are taken into account, the argument becomes a fortiori. For why should not a substantial remuneration for the entrepreneur be included in the general expenses of the business’ (Edgeworth 1925, ii: 469-470). Edgeworth’s difference with Walras was to some extent “only verbal”, but he was also unhappy with the idea that entrepreneurship is homogeneous and divisible.
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