The Robinson Crusoe model in Chapter 2 describes the price system of a simple economy as a means of making efficient decentralized choices. That model focuses on the relationship of the production side of the market to the consumption side. The market in equilibrium allocates resources between competing productive uses (consumption and leisure) so as to use the available production technology to efficiently satisfy consumer demands. It is a model of the decentralized market arranging the allocation of resources in production to satisfy households. Another aspect of efficient allocation is to arrange efficient allocation of goods among consumers. Efficient allocation of resources requires both an efficient mix of outputs and an efficient allocation among consumers. In this section, we'll ignore the production decision and concentrate on the interpersonal allocation of a fixed mix of available goods. The production and consumption sides are considered together in Chapter 4.
The modeling technique we will use for this allocation decision is the brilliant and brilliantly simple device due to F. Y. Edgeworth, known as the Edgeworth box. Suppose we have fixed positive quantities of two goods, X and Y, and two households, 1 and 2. We would like to know how to allocate the fixed supplies of X and Y between the two households. Three allocation schemes will be developed: efficient allocation, a bilateral bargaining allocation, and a market equilibrium allocation.