Expenditure Constraints and Profit Maximization in U.S. Agriculture: Comment

Abstract

In a recent paper, Lee and Chambers (hereafter LC) developed a theory of expenditure constrained profit maximization. Because some inputs are held fixed in the model, we prefer the terminology short-run expenditure-constrained-profit maximization (SREC). The theory yields two testable hypotheses: (1) if the expenditure constraint is not binding the SREC profit function is linearly homogenous in all prices, and (2) if the expenditure constraint is binding then the sum of the expenditure level and the SREC profit function is linearly homogenous in output prices. These hypotheses are not mutually consistent and thus provide a means of testing for binding expenditure constraints. LC applied their test to U.S. farms and found that farmers do not face a perfectly elastic supply of funds or credit upon which they can effortlessly draw to finance their production decisions. (LC, p. 865). In the development of the theory, LC assume that the technology is a cone, i.e., there is constant return to scale. However, empirical studies suggest that this frequently is not the case (see Madden or Madden and Partenheimer). In this comment we show that the assumption that the technology is a cone is not necessary for (a) local version of either hypothesis, (b) a global version of the second hypothesis, or (c) if the technology is convex, a global version of the first hypothesis.