Endogenous Price Policies and International Wheat Prices: Comment

Abstract

In a 1983 article in this Journal Sarris and Freebairn claim to model international wheat prices as Cournot equilibrium prices resulting from interaction of national excess demand functions. National pricing policies are determined so as to maximize a domestic welfare function, specified as a weighted sum of producer and consumer surplus, government revenue, and a price variability measure. The function is maximized subject to pricing policies of all other countries. In Sarris and Freebairn model, each country assumes that any pricing policy which it implements, such as imposition of a tariff, will not affect world price. We contend that this assumption is not consistent with usual determination of a Cournot equilibrium. In Cournot oligopoly model, each firm takes account of price implications of output it sets. Therefore, we reformulate Sarris and Freebairn's model to account for impact of policies on world price and recalculate implicit welfare weights for wheat-trading countries. In traditional Cournot oligopoly model, each firm takes account of production levels set by it and other firms, although each (naively) expects no response from its rivals. The Cournot-Nash equilibrium is a point at which no trader (acting unilaterally) can do better than playing its optimal strategy, given that all other traders are playing their optimal strategies. Interaction between traders leads to convergence to an equilibrium from which none would want to move. In contrast to traditional model, Sarris and Freebairn derive their solution on simplifying assumption that every trading country takes [the world price] as given .... [This] implies that each country is concerned with domestic objectives and is not concerned with other countries' reactions to its policies. In other words, we posit a Cournot oligopoly problem (p. 215). In fact, Sarris and Freebairn posit zero conjectural variations (i.e., each trader conjectures that its rivals will not vary their policies) as in a Cournot model but assume no effect on world prices. This latter assumption is not consistent with a Cournot model. In a Cournot-Nash model, traders assume that rivals do not respond to their policies, although these (zero) conjectures are subsequently found to be incorrect. Although unanticipated, retaliation does occur, and by imposing assumption of a given world price, and that market power remains unused, Sarris and Freebairn are led to conclude that with equal weights on all components of welfare function, the optimal policy for country is a free-trade one (p. 216). This conclusion is consistent with simplifying small country assumption. However, it is unlikely that countries with market power will ignore it in setting tariffs. After dropping this assumption, our calculations (presented in table 1) show that optimal policies are nonzero even if weights are equal. The method used here for obtaining Cournot-Nash solution involves calculating firstorder conditions to maximize a weighted welfare function for each country. The reaction functions, showing how each country reacts to tariffs imposed by others, can then be derived.' The functions can be solved simultaneously to obtain CournotNash solution.2 Consider a homogenous product traded between n countries with linear demand and supply curves: