The Robinson Crusoe Economy
Key ideas: Walrasian equilibrium allocation, optimal allocation, invisible hand at work
In Chapter 3 we studied equilibrium and efficiency in exchange economies. In this chapter we add firms to the economy and show how the welfare theorems generalize. In this introductory section we consider the simplest such economy – the one-person economy. To introduce trade, we assume that the single individual Robinson Crusoe is schizophrenic, making his decisions as a manager and a consumer separately. His decisions are guided by market prices. In Section 5.2 we examine a general equilibrium model with production and extend the two welfare theorems.
The power of the first theorem hinges critically on the assumption that a Walrasian equilibrium exists. This is addressed in Section 5.3. In the basic model all goods are private. In Sections 5.4 and 5.5 we show how the basic model can be extended to incorporate multiple time periods and public goods.