The Case of the Three Numeraires

This paper is concerned, at a theoretical level, with that wide class of general-equilibrium models with which the word numeraire is associated: models whose ‘reduced forms’ expressing real endogenous variables as functions of real and nominal exogenous variables are homogeneous of degree zero with respect to the latter set, and whose ‘reduced forms’ expressing nominal endogenous variables as functions of real and nominal exogenous variables are homogeneous of degree one with respect to the latter set. Traditionally, in models of this type there has been only one exogenous variable expressed in nominal terms (usually the quantity of money) and movements in this variable therefore determined movements in the general level of prices. The case in which money is the nominal exogenous variable is not the only one represented in the literature, however; there is also the traditional Gold Standard case in which the exchange rate is assumed to be exogenously fixed while the money supply is endogenous, and the Keynesian case in which (at least in the original variant and in some models subsequently constructed) the wage level is taken as exogenous.