Gains from Trade under Uncertainty: Further Comment - Akiba, Hiroya (American Economic Review, 1980)
In an article appearing in this Review, Raveendra Batra and William Russell (hereafter B-R) analyze the effect of uncertainty in the international terms of trade on social welfare within the framework of a small country with two goods. They conclude that the expected social welfare decreases under both firstand second-degree stochastic dominance. Also in a recent issue of this Review, Richard Hartman, commenting on B-R's article, contends that (i) B-R do not allow for the change in the optimal consumption of one good, cl, as the probability distribution of the international terms of trade p undergoes a mean-preserving spread, and (ii) they do not take into account the change in cl when comparing the expected utility for different distributions of p. Based on these criticisms, Hartman presents an alternative proof to show a decrease in the expected social welfare when the distribution of p undergoes a mean-preserving spread. Batra and Russell are interested in the change of the expected social welfare when the distribution of p changes. In their model, cl is chosen before the uncertainty in p is resolved. To analyze the effect of uncertainty in p on social welfare, B-R do not allow for the change in the optimal cl under different distributions of p on the ground that cl is chosen optimally before p is known. However, as pointed out by Hartman, the optimal value of cl will be different for different distributions of p. To discuss the change in the relationship between the expected social welfare and the optimal cl, Hartman uses a diagram similar to my Figure 1. From his diagram Hartman argues that B-R's conclusion of the decrease in the expected social welfare under greater uncertainty is correct even if the optimal cl is different for different distribution of p.' In my view, B-R, as well as Hartman, only consider a special case where the expected utility curve under a probability distribution always lies above those under different probability distributions of p. If we accept Hartman's comments, I can think of another case where the expected utility curves under different probability distributions may cross. The purpose of this note is first to examine this case that could occur within the framework of the B-R analysis, but which has not been examined by B-R or Hartman. By failing to examine this case, the B-R and Hartman analyses seem incomplete. Also, by considering this case, I modify the B-R proof to show a decrease in the expected social welfare as the distribution of p undergoes a mean-preserving spread. First, Hartman's analysis of the B-R conclusion is presented. This is followed by an exami ation of the other possible situation. Finally, the modification of the proof is presented. The discussion in this note is confined to the B-R framework and their notation is used. The B-R proof simply provides a stronger sufficient condition for the decrease in the expected social welfare and does not rely on the usual comparative statics approach. In Figure 1, I denote the original equilibrium position by point 1 on the expected utility (EU) curve, I. Batra-Russell prove that for every cl, EU decreases when the exogenous changes in distribution of the international terms of *Takushoku University. I acknowledge Vincent Munley and Kambiz Kiani for their comments on an earlier version of this note. I am also indebted to an anonymous referee and Harry Ramcharran for their comments and suggestions. Any remaining errors are my own. 'In his alternative proof summarized in his equation (4) on page 927, Hartman treats cl as constant as B-R do. This contradicts his criticism of their article.