A model of the economy that incorporates consistent decision-making by individual consumers and firms. The Arrow–Debreu model was the culmination of a research programme to demonstrate the existence of equilibrium in a competitive economy. Adam Smith (1723–1790) identified how the ‘invisible hand’ of competition implied the efficiency of economic activity. It was soon realized that this observation had limited value without a corresponding formal model of the competitive economy. A formal model needed to derive market demand from the utility maximization of consumers and market supply from the profit maximization of firms. An equilibrium would then consist of a set of prices that ensured demand was equal to supply for all goods simultaneously. Léon Walras (1834–1910) developed such a model to the point of demonstrating that the number of relative prices was equal to the number of independent demand–supply equations but could not prove the existence of a simultaneous solution to his equations. The contribution of Kenneth Arrow (1921–2017) and Gerard Debreu (1921–2004) was to specify a competitive model for which they could prove the existence of an equilibrium. Their analysis provided final settlement of the existence question. It also introduced many new tools to economists (specifically, the role of convexity arguments, the use of correspondences, and the value of fixed point theorems in equilibrium arguments). In addition, Arrow and Debreu also formalized Adam Smith’s efficiency argument in the two Fundamental Theorems of Welfare Economics. The Arrow–Debreu economy has been generalized to include dated commodities (goods available at different times) and contingent commodities (goods available in different states of the world). This allowed the model to address economic issues concerned with time and uncertainty. These extensions provided, among many uses, the basis for the formal development of the theory of finance. Arrow–Debreu state prices are now a basic tool for the valuation of financial instruments. The analysis of Arrow and Debreu set new standards of rigour in economics, and the Arrow–Debreu economy remains the foundation of much formal modelling in economics and finance. See also Edgeworth box; existence of equilibrium; general equilibrium.