A Growth Theoretical Approach
Chapter 3: A Money-Metrics Version of Weitzman’s Welfare Theorem
Weitzman’s (1976) fundamental result on welfare measurement introduced in Chapter 2 was obtained in a ﬁrst best setting with one aggregate consumption good, m capital goods, and a utility function equal to aggregate consumption. Hence, by normalizing the price of the consumption good to one, the Hamiltonian will coincide with real NNP and, consequently, the money and utility metrics will coincide. However, in a more general setting this is no longer true. Since utility is not observable, a practical problem arises, at least if we want an observable measure of the static welfare equivalent. We attempted to deal with this problem in Chapter 2 by linearizing the utility function as in equation (2.17b). In a ﬁrst best setting, with no externalities and one consumption good, this would give us an approximate relation between current NNP and future wealth. However, the approximation will be poor if the utility function deviates strongly from linearity. In addition, more than one consumption good will give rise to a price index problem. To simplify as much as possible, and since Weitzman’s (1976) result constitutes a natural starting point, we carry out the analysis in a ﬁrst best framework. As such, the most important result is Proposition 3.2, which provides a money-metric analogue to the ﬁrst best welfare theorem in a utility metrics. It shows exactly what information is required for measuring welfare at a given point in time, as well as explaining why the traditional approach of linearizing the Hamiltonian might be misleading. 3.1 THE...
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