Arrow-Debreu Model of General Equilibrium

It is not easy to separate the significance and influence of the Arrow–Debreu model of general equilibrium from that of mathematical economics itself. In an extraordinary series of papers (Arrow, 1951 ; Debreu, 1951; Arrow–Debreu, 1954), two of the oldest and most important questions of neoclassical economics, the viability and efficiency of the market system, were shown to be susceptible to analysis in a model completely faithful to the neoclassical methodological premises of individual rationality, market clearing, and rational expectations, through arguments at least as elegant as any in economic theory, using the two techniques (convexity and fixed point theory) that are still, after thirty years, the most important mathematical devices in mathematical economics. Fifteen years after its birth (e.g. Arrow, 1969), the model was still being reinterpreted to yield fresh economic insights, and twenty years later the same model was still capable of yielding new and fundamental mathematical properties (e.g. Debreu, 1970, 1974). When we consider that the same two men who derived the most fundamental properties of the model (along with McKenzie, 1954) also provided the most significant economic interpretations, it is no wonder that its invention has helped earn for each of its creators, in different years, the Nobel Prize for economics.