A Look at the Structure of Optimal Tariff Rates

Abstract

NUMEROUS ARTICLES HAVE APPEARED on the subject of an optimum tariff. We speak of an optimum tariff advisedly, for there has been little attempt to discuss the possibility of a tax on more than one commodity-usually within the context of a two-commodity trade model in which either the import or export is taxed. The most well known of the exceptions are those of Graaff [1] and Kemp [2]. As notable as the work of these authors may be, they did not provide satisfactory answers to the many-commodity case.' We urge the reader to note that it is a structure of optimal tariffs, rather than an optimum tariff, which is relevant to this aspect of international trade analysis. This paper was motivated by the need to demonstrate a completely general optimal tariff structure in a model which would readily lend itself both to interpretation and practical application. By employing concepts immediately familiar to economists, estimates of known parameters may be inserted directly into the model whenever desired. On the other hand, the principal intellectual interest focused on the question of whether or not the optimal tariff structure might contain some negative elements. Although Graaff, in fact, claimed that in order for the structure of tariffs to be optimal, it might be necessary to have one or more subsidies in the structure, he did not prove that the case might even exist, let alone upon what assumptions such a case would have to rest. Since it will be shown that the optimal tariff structure requires the solution of a system of homogeneous linear equations, the solution is not unique. The vector of optimal tariffs will be arbitrary to the extent of a scalar constant factor. Arbitrary designation of a commodity numeraire upon which the tariff is set at some (arbitrarily) specified level will determine a particular vector of optimal tariffs. Hence the tariff on the numeraire may be regarded as a parameter in terms of which the remaining tariffs can be linearly and uniquely expressed. At first sight the choice of numeraire may appear to be important because it enables us to select a particular solution to the optimal tariff structure from the infinity of solutions inherent in the system of homogeneous equations. It might then appear that we are left open to choose a solution involving negative tariffs. Although it would be quite ridiculous to regard this as an answer, it does at least give us a clue with respect to the question we ought to ask.