Published online by Cambridge University Press: 08 February 2010
After DKR was published in Japanese in 1950, a great theoretical development has been made in the three main areas of the general equilibrium theory, concerning existence, uniqueness and stability of general equilibrium. The existence theorem is an achievement of efforts in the first half of the 1950s, while its second half and the first half of the 1960s were devoted to uniqueness and stability, mainly to the latter. In this addendum I sketch the theoretical development after DKR in my own way and show how I see it from my present arrival point.
The existence problem has been solved by formulating Walras' economy in terms of inequalities, rather than equations. This inequality approach is not entirely foreign to Walras, who supports the scarcity theory of value asserting that the price is zero for a ‘free (or non-scarce) good’, that is a commodity for which supply exceeds demand in equilibrium. Walras is concerned with an economy in which an exchange is actually made, though some goods may be free, and distinguishes this general equilibrium (which may be called an essential equilibrium) from the more general one in which goods may all be free and, therefore, not traded.
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