of the Arrow–Debreu model The Arrow–Debreu model models an economy as a combination of three kinds of agents: the households, the producers, and the market. The households and producers transact with the market, but not with each other directly. The households possess endowments (bundles of commodities they begin with), which one may think of as "inheritance". For the sake of mathematical clarity, all households are required to sell all their endowment to the market at the beginning. If they wish to retain some of the endowment, they would have to repurchase from the market later. The endowments may be working hours, use of land, tons of corn, etc. The households possess proportional ownerships of producers, which can be thought of as joint-stock companies. The profit made by producer is divided among the households in proportion to how much stock each household holds for the producer . Ownership is imposed at the beginning, and the households may not sell, buy, create, or discard them. The households receive a budget, as the sum of income from selling endowments and dividend from producer profits. The households possess preferences over bundles of commodities, which under the assumptions given, makes them utility maximizers. The households choose the consumption plan with the highest utility that they can afford using their budget. The producers are capable of transforming bundles of commodities into other bundles of commodities. The producers have no separate utility functions. Instead, they are all purely profit maximizers. The market is only capable of "choosing" a market price vector, which is a list of prices for each commodity, which every producer and household takes (there is no bargaining behavior—every producer and household is a price taker). The market has no utility or profit. Instead, the market aims to choose a market price vector such that, even though each household and producer is maximizing their own utility and profit, their consumption plans and production plans "harmonize". That is, "the market clears". In other words, the market is playing the role of a "Walrasian auctioneer". Notation setup In general, we write indices of agents as superscripts, and vector coordinate indices as subscripts. useful notations for real vectors iff is the set of such that is the set of such that is the N-simplex. We often call it the price simplex since we will sometimes scale the price vector to lie on it. market The commodities are indexed