Willingness To Pay and Willingness To Accept: How Much Can They Differ? Reply
回应Amiran和Hagen关于公共物品的支付意愿与接受意愿可能无限差异的观点，指出其渐近有界条件推广了作者1991年论文中零替代弹性的局部结果，并解释了该条件如何导致无限接受意愿。
I agree with the point made by Edoh Y. Amiran and Daniel A. Hagen (2003) that there can be a substantial, or even infinite, divergence between the WTA and WTP for a public good even where there is a nonzero elasticity of substitution between market goods and the public good, provided that the indifference curves are asymptotically bounded with respect to market goods in the manner they describe. This is an important point. They are also correct to point out that the elasticity of substitution is a local concept, whereas their asymptotic boundedness condition applies also for discrete changes. My 1991 paper used a local analysis because it was following the structure of the analysis in Robert D. Willig (1976) and Alan Randall and John R. Stoll (1980); I wanted to show that, while Randall and Stoll appeared to extend Willig’s local result on WTA versus WTP from price changes to changes in the quantity of a public good, the relevant elasticity was in fact different and involved the substitution elasticity as well as the income elasticity. I view these points by Amiran and Hagen as not two separate results but essentially the same result: their asymptotic boundedness condition generalizes my zero elasticity of substitution condition to discrete changes. The asymptotic boundedness condition can be expressed as follows: assuming a bivariate utility function u( x, q), and given a reference point ( x*, q*) associated with a reference utility level u* u( x*, q*), there exists some q q* such that, for all q q , there exists no x such that u( x , q) u*. In other words, no amount of x can substitute for the reduction in public good from q* to q q . In the case of a zero elasticity of substitution, q q* but, as Amiran and Hagen show in their Theorem 1, this is unnecessarily restrictive when dealing with a discrete reduction in q. Furthermore, their Theorem 2 can be viewed as a special case of their Theorem 1 in which q 0, which makes q an essential commodity. It is well known in consumer theory that the WTA to avoid the loss of an essential market good is infinite; their Theorem 2 extends this result to the case of an essential nonmarket good. But, as their Theorem 1 shows, essentialness is not necessary for an infinite WTA. The boundedness condition is the key, and this implies a fundamental lack of substitutability between money (market goods) and the public good.