Incentives and Risk Sharing in Sharecropping

Abstract

At least from the time of Ricardo, economists have begun their investigations of how competitive markets work, how wages, rents and prices are determined, by a detailed examination of agriculture. Even today, agriculture is taken as the paradigm-and perhaps almost the only important example-of a truly competitive market (or at least this was the case until the widespread government intervention in this market). For a number of years I have been concerned with how competitive markets handle risk taking, and how risk affects real resource allocation. Risks in agriculture are clearly tremendously important, yet remarkably the traditional theoretical literature has avoided explicit treatment 3 of risk sharing in agricultural environments. The consequences of this are important. First, it makes suspect the traditional conclusions regarding sharecropping. Is it really true that sharecropping results in too low a supply of labour, because workers equate their share of output times the (value of the) marginal productivity of labour to the marginal disutility of work, whereas Pareto optimality requires the (value of the) marginal productivity of labour be equal to the marginal disutility of work? Or is it true, as Wicksell asserted, that there is no distincion between landlords hiring labour or labour renting land? Second, it leaves unanswered many of the important economic questions. How is the equilibrium share determined? Why have some economies (in the past or at present) used one distribution system, other economies used others? Our object is to formulate a simple general equilibrium model of a competitive agricultural economy. (Other general equilibrium models of competitive economies with uncertainty have been formulated by Arrow [2] and Debreu [9], Diamond [10], and Stiglitz [14]. Each of these has its serious limitations in describing the workings of the modern capitalist economy. (See Stiglitz [15]).) The model is of interest not only for extending our understanding of these simple economies but also in gaining some insight into the far more complex phenomena of shareholding in modern corporations. Our focus is on the risk sharing and incentive properties of alternative distribution systems. The analysis is divided into two parts. In the first, the amount of labour (effort) supplied by an individual is given, and the analysis focuses on the risk sharing aspects of