The Choice of Numeraire in Price Uncertainty Models

By Yeung, David | Atlantic Economic Journal, June 1989 | Go to article overview

The Choice of Numeraire in Price Uncertainty Models


Yeung, David, Atlantic Economic Journal


The Choice of Numeraire in Price Uncertainty Models

In analyzing the effects of price uncertainty on a small trading country in a general equilibrium framework, Flemming, Turnovsky, and Kemp [RES, 1977] suggest that the use of the arithmetic mean of a random price as the certainty price is inappropriate. In particular, they show that specializations are dependent upon the choice of numeraire. Many researchers are puzzled by this result. The purpose of this note is to demonstrate that this dependence does not exist.

Following Flemming, et al., and their notations, a country maximizes: W = E[U(C1,C2], subject to: PX1 + X2 = Y = PC1 + C2 = L - (1 - P)L1. (1)

The possibility of a switch in specialization is obtained by example. Specifically, U(C1,C2) = C 1C 2 and given P = (P1/P2) is lognormally distributed, the first order condition becomes:

Using the expected value of P, E(P) = er+w/2, as the certainty price, they show that under certainty, the country will specialize in commodity 1 if r + w/2 > 0 and vice versa. However, a country which specializes in commodity 1 under certainty may not necessarily specialize in commodity 1 under uncertainty because it is possible for 0 < r + w/2 < w (Turnovsky's [RES 1974] Proposition 7). …

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