On the Choice of Numeraire and Certainty Price in General Equilibrium Models of Price Uncertainty

Over the past few years a number of papers have been written analysing the effects of price uncertainty on a small trading country.' The conventional approach adopted in these studies is first to pick a numeraire commodity, thereby defining a relative price (terms of trade) which the small country takes as exogenously given. The objective is then to compare various decisions and quantities when this relative price is random with what they would be under certainty. To make this comparison one must introduce a " certainty price " and without exception this has quite naturally and unquestioningly been the arithmetic mean of this relative price. Typical of such studies is a recent article in this Review by one of the present authors, Turnovsky [12]. He considers the impact of price uncertainty on a small country's allocation of a single input to the production of two goods using a Ricardian technology.2 It turns out that by using the arithmetic mean of a relative price as the certainty price, some of his propositions are weakened in so far as they are dependent upon the choice of numeraire good. This is clearly an unsatisfactory situation since this choice is presumably an arbitrary one. The purpose of this paper is two-fold. First we wish to use one of his propositions (proposition 7) to illustrate how the use of the arithmetic mean makes the result dependent upon the choice of numeraire. We also show (Section 3) how this dependence can be avoided if some other measure of central tendency such as the geometric mean is used as the certainty price, in which case the proposition holds unambiguously. The second objective is a somewhat more general one. As already indicated, the procedure followed by Turnovsky is in fact the standard one in this literature. Much of it, particularly those papers dealing with the neoclassical technology, makes extensive use of Jensen's inequality, which enables the effects of uncertainty to be determined from the convexity-concavity properties of relevant functions.3 It turns out that in many cases the choice of numeraire influences these properties, leading to the same kind of difficulty as