Cobb-Douglas Utility - Eventually!

Abstract

Consider the following two opinions, both of which can be found in the literature of consumer demand systems: (a) As the real income of a consumer becomes indefinitely large, re-mixing the consumption bundle becomes irrelevant: having chosen the ultimately satisfying budget shares at any given set of relative prices, the superlatively wealthy continue to allocate additional income in the same proportions. With very large and increasing per capita income, ultimately the utility function becomes indistinguishable from Cobb-Douglas. (b) Consumer demand systems in which the income elasticities monotonically approach one (from above, in the case of luxuries; from below, in the case of necessities) are unsatisfactory both theoretically and empirically. For instance, a necessity with a low (consumer demand system; applied general equilibrium; separability; implicitly directly additive preferences; effectively global regularity; Cobb-Douglas, calibration; AIDADS.