Sharecropping, Production Externalities and the Theory of Contracts

A corollary of the Bebreu-Scarf theorem is that, under ideal conditions, contracts serve as perfect substitutes for markets. Applying these propositions to sharecropping provides a rigorous foundation for the competitive theory of share tenancy. In addition, it is shown that the competitive theory serves as a good approximation even for a small number of landowners. Applying the proposition to production externalities provides a precise and non-trivial version of the Coase theorem, i.e., the contracting equilibrium is equivalent to a Walrasian equilibrium with universal markets, including a market for the "externality". Thus under ideal conditions the contract solution, the market solution, and the government intervention solution (e.g. Pigouvian taxes) are identical. Their relative efficiency cannot be assessed without incorporating transactions costs into the analysis. Even without such complication, however, the abstract model developed here appears to be useful for positive purposes, such as explaining certain patterns in agricultural contracts.