RISK ANALYSIS FOR PROPRIETORS WITH LIMITED LIABILITY: A MEAN- VARIANCE, SAFETY- FIRST SYNTHESIS

Abstract

Since nearly the entire U.S. output of agricultural commodities is produced by proprietors with limited liability, it is important to understand how limited liability affects decision in a risky environment. This article extends the work of Robinson and Barry; Robinson and Lev; and Robinson, Barry, and Burghart. It provides a rigorous derivation of one of their objective functions, compares it to standard risk analysis tools, and suggests several methods of empirical implementation. Under some conditions, utility maximization in the limited liability environment is consistent with optimization of Roy's safety-first criterion, while in other situations Freund's mean-variance criterion is appropriate. However, it is easy to demonstrate cases where neither criterion is applicable.

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