Leontief Economy Equilibrium

Keywords and Synonyms

Exchange market equilibrium with the leontief utility        

Problem Definition

The Arrow–Debreu exchange market equilibrium problem was first formulated by Léon Walras in 1874 [7]. In this problem everyone in a population of m traders has an initial endowment of a divisible goods and a utility function for consuming all goods – their own and others'. Every trader sells the entire initial endowment and then uses the revenue to buy a bundle of goods such that his or her utility function is maximized. Walras asked whether prices could be set for everyone's goods such that this is possible. An answer was given by Arrow and Debreu in 1954 [1] who showed that, under mild conditions, such equilibrium would exist if the utility functions were concave. In general, it is unknown whether or not an equilibrium can be computed efficiently, see, e. g., General Equilibrium.

Consider a special class of Arrow–Debreu's problems, where each of the ntraders has exactly one unit of...