The Ineffectiveness of Quantitative Restrictions with Production Diversion

Abstract

Long ago Meade [21] and Samuelson [23] noted that when number of goods exceeds number of factors in a general equilibrium model production set will not be strictly convex. Later studies have focused either on shape and geometry of production possibility frontier [22; 17; 18; 15; 26; 13] or on generalizations of Stolper-Samuelson, Rybczynski and factorprice equalization theorems [22; 16; 4; 27]. Little attention, however, has been given to policy implications for quantitative restrictions (QRs) in a model with more goods than factors. Traditional results in trade theory are based on a (2 x 2 x 2) general equilibrium model. Within this context QRs have effects similar to tariffs; namely they raise domestic price of protected good, increase output and factor usage in industry, and raise returns to factors used intensively in industry [5; 2; 14]. Bhagwati [3] has shown that quotas and tariffs are equivalent when there is perfect competition in domestic market but that equivalence will break down in presence of a domestic monopoly. Further studies by Itoh and Ono [12], Benson and Hartigan [1], Hwang and Mai [11] and Dockner and Haug [7] demonstrate surprising results about when equivalence holds under various assumptions of imperfect competition [25; 12; 20]. In this paper we will show that QRs need not be equivalent to tariffs even in a perfectly competitive model as long as there are more goods than factors of production. We define production-pattern replicate equilibria as set of world production and trade configurations that can be supported by one vector of equilibrium prices.' In general replicate equilibria exist whenever there are more goods than factors because in this situation there will exist an infinite number of production configurations consistent with any equilibrium price vector in each country.2 As Melvin [22, 1263] points out, the most important conclusion to be drawn from this . . . indeterminacy (is that) . . . actual pattern of trade depends on which of possible production configurations is chosen. This corresponds to our notion of replicate equilibria. Since a QR represents a restriction only on a particular pattern of trade, it may not preclude existence of a replicate equilibrium not restricted by QR.