Quasilinear Approximations
Quasilinear approximations Marek Weretka ∗ August 2, 2018 Abstract This paper demonstrates that the canonical stochastic infinite horizon framework from both the macro and finance literature, with sufficiently patient consumers, is in- distinguishable in ordinal terms from a simple quasilinear economy. In particular, with a discount factor approaching one, the framework converges to a quasilinear limit in its preferences, allocation, prices, and ordinal welfare. Consequently, income effects associated with economic policies vanish, and equivalent and compensating variations coincide and become approximately additive for a set of temporary policies. This ordi- nal convergence holds for a large class of potentially heterogenous preferences that are in Gorman polar form. The paper thus formalizes the Marshallian conjecture, whereby quasilinear approximation is justified in those settings in which agents consume many commodities (here, referring to consumption in many periods), and unifies the general and partial equilibrium schools of thought that were previously seen as distinct. We also provide a consumption-based foundation for normative analysis based on social surplus. Key words: JEL classification numbers: D43, D53, G11, G12, L13 1 Introduction One of the most prevalent premises in economics is the ongoing notion that consumers be- have rationally. The types of rational preferences studied in the literature, however, vary considerably across many fields. The macro, financial and labor literature typically adopt consumption-based preferences within a general equilibrium framework, while in Industrial Organization, Auction Theory, Public Finance and other fields, the partial equilibrium ap- proach using quasilinear preferences is much more popular. ∗University of Wisconsin-Madison, Department of Economics, 1180 Observatory Drive, Madison, WI 53706.
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