ABSTRACT
A feasible allocation is an equal-treatment feasible allocation if xAi = xAj and xBi = xBj all i, j. The willingness of an agent to trade is represented by her offer price, or marginal rate of substitution between the two commodities, pi[{x i1, x i2}] ≡ (ui1 [{xi1, x i2}]/ u i2 [{x i1, x i2}]), where uij [{x i1, x i2}] is the partial derivative of ui[.] with respect to commodity j at the commodity bundle {x i1, x i2}. (In this chapter, commodity 2, plotted on the vertical axis, will always be the numeraire, so that the negative of the slope of a price line will be the price of commodity 1 in terms of commodity 2.) When two agents have an opportunity to exchange goods, they will be able to find a mutually advantageous exchange if and only if their offer prices differ. Thus a natural definition of an equilibrium of an exchange economy is a feasible allocation where all agents’ offer prices are identical. At an equilibrium there is a well-defined equilibrium price system, p (without superscripts) since all the agents’ offer prices are equal. At voluntary exchange equilibria which can be reached by voluntary exchanges of agents starting from their endowment point the agents’ commodity bundles must be above the indifference curves through the endowment point. Walrasian equilibria are the subset of equilibria at which the value of each agent’s commodity bundle is equal to the value of her endowment at the equilibrium prices.1
