Comparative Statics of Money-Goods Specifications of the Utility Function

Abstract

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem.

The Economic Record versus AER: Twenty Six Years Ahead on the Money-Goods Model

“…We also demonstrate that, when a two-stage maximization framework is adopted, there are at least six identical forms of the modified Slutsky matrix for the money-goods model, and discuss the implications of this finding for empirical testing. Finally, we relate the results obtained to the more general results of Paris and Caputo (2001). Because the work of Samuelson and Sato (1984) is integral to our results, we begin by reviewing their basic setup and central result.…”

“…Fortunately, the recent results of Paris and Caputo (2001) permit one to overcome this practical difficulty. Their main result is obtained by solving problem (8) in one step yielding the following symmetric negative semidefinite matrix…”

An Atemporal Microeconomic Theory and an Empirical Test of Price-Induced Technical Progress

“…This is therefore how we intend to formally model the price-induced TP hypothesis of Hicks (1932). Our formal specification of priced-induced TP is thus perfectly analogous to the introduction of commodity prices into the direct utility function in order to account for Patinkin's conjecture about real cash balances [see Samuelson and Sato (1984) and Paris and Caputo (2002)]. With this background in mind, we now proceed more formally.…”