Abstract
Barney [1] argues that our proofs in Appendix A and footnotes 9 and 10 contain a fundamental error and therefore, the discussion of partial insurance in Section III of our article [2] is fatally flawed. He asserts that our equation (A.2) is not correct and consequently our comparative statistics results for partial and full insurance are invalid. To help us understand our error, Barney provides a demand and supply metaphor, where quantity demanded and quantity supplied are denoted by Qd = F(P) and QS = G(P), and P is the price of goods. At the point of intersection of demand and supply, F(P) = G(P), but the derivatives of both curves, F'(P) and G'(P), are unequal. Barney's comments demonstrate lack of understanding of an important technique called implicit differentiation used in the comparative static analysis. We were not concerned with the first derivatives of the two curves. Rather, we were concerned about the comparative statistics. In other words, we were not interested in the slopes of two curves (i.e., demand and supply), but were interested in the changes in the positions of two curves as a result of changes in exogenous factors (e.g., weather). Barney agrees that at the intersection of the two marginal benefit curves (MBp and MB) for partial and full insurance the following equality holds:
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