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  • Print publication year: 2012
  • Online publication date: November 2012

5 - General Equilibrium


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.

References and Selected Historical Reading
Arrow, K.Debreu, G. 1951 An Extension of the Basic Theorems of Classical Welfare EconomicsProceedings of the Second Berkeley Symposium on Mathematical Statistics and ProbabilityNayman, J.BerkeleyUniversity of California Press507
Arrow, K.Debreu, G. (1954).Existence of Equilibrium for a Competitive EconomyEconometrica 22 265
Debreu, G. 1959 Cowles FoundationMonograph. New York:John Wiley & Sons
Kirman, A.Hildenbrand, 1988 Equilibrium Analysis: Variations on Themes by Edgeworth and WalrasNorth Holland
Lindahl, E. 1919 Die Gerechtigkeit der BesteuringMusgrave, R.Peacock, T.London:Macmillan
Samuelson, P. 1948 163
Stolper, W.Samuelson, P. A. 1941 Protection and Real WagesReview of Economic Studies 9 58