The simplest general economic equilibrium system we can consider consists of a single household, usually named Robinson Crusoe. This one-person economy has many of the usual problems of any economy: production and consumption choices. The simple structure of the economy allows us fully to model a single centralized family of efficient allocation decisions. We can then, somewhat artificially, decompose the one-person economy into separate production and consumption sectors interacting through a market mechanism. This is a common classroom exercise, designed to illustrate the concepts of efficient allocation, general equilibrium, and decentralization through a market mechanism. In the one-person economy it is particularly easy to present the concept of efficient allocation. Because there is only one agent, there is a unique maximand (the utility function of the lone household/person/agent). The efficiency concept is simply to maximize Robinson's utility subject to the available resources and technology. Problems of distribution among individuals (regarding both considerations of efficiency and fairness) do not arise because there is only one household.

The exercise we perform in the Robinson Crusoe model is to solve two apparently quite separate problems and then show that they are nearly identical. First, we will solve for an efficient allocation in the Robinson Crusoe economy. This is a centralized solution concept because it treats the consumption and production decision in a single unified fashion. That is, we find a production and consumption plan that maximizes Robinson's utility subject to the constraints of available resources and technology.