1 The purpose of the general equilibrium theory (GET) is to construct a system of conditions which are necessary and sufficient to determine all the variables contained in the system. As Walras was the first economist to clearly set forth the idea, he is usually acknowledged as the originator of GE analysis. But the idea of the system-theoretic analysis of the economy can evidently be traced back to Ricardo. Although he did not mathematically spell out what conditions were necessary and sufficient to determine the values of the variables with which he was concerned, we can easily excavate the conditions and reconstruct the whole system of Ricardo's Principles as we have done in Chapter 3 above. Indeed, Ricardo is the fore-runner, if not the founder, of the general equilibrium school.

The existence of a state of general equilibrium is, therefore, the most central problem of the GET. The conventional view is that the problem was first examined in a serious way by a number of German-speaking economists in the 1930s. Prior to this, however, Walras himself noted that ‘it is possible for these curves [demand and supply curves] to have no point of intersection at all’. This remark by Walras is, at first sight, in obvious contradiction to the Arrow–Debreu proposition that there always exists a GE if demand and supply curves are continuous in price variables. We find, nevertheless, no inconsistency between the two if we carefully examine Walras' and Arrow–Debreu's propositions.