The geometry of protectionism in the imperfect substitutes model: a reminder.

1. Introduction

   This note aims to clarify the estimation of the cost of restricting imports of a good which substitutes imperfectly for goods produced and consumed at home. It reviews the estimation technique pioneered and used by the U.S. Federal and International Trade Commissions[6; 8]. This ingenious technique is valid, provided the relevant demand and supply functions are linear in prices and provided the relevant goods display zero income elasticities of demand. The base case assumes a small country. We review this method because several recent texts[1; 4] and studies[2; 3] use invalid techniques(1) to estimate the costs of protectionism in the imperfect substitutes model.

2. ITC Method

   Figure 1 illustrates the ITC method. A small country restricts imports of good 0, raising the internal price(2) from [P.sub.0b] to [P.sub.0a] and reducing consumption from [Q.sub.0b] to [Q.sub.0a]. The demand curve [D.sub.0b] takes as given the before-protection, equilibrium prices of the other goods consumed domestically. The demand curve [D.sub.0a] takes as given the after-protection, equilibrium prices of these goods. The ITC technique estimates the consumer loss as [P.sub.0b][P.sub.0a]cd and the social loss of a tariff or equivalent quota as cde.

   This technique appears peculiar and incomplete. The estimated consumer loss is an area beside neither [D.sub.0b] nor [D.sub.0a]; instead, the consumer loss is estimated as an average of the losses derived from these curves (provided the demand function is linear). Also, the technique appears to disregard the consumer and producer gains or losses in the markets for non-tradables(3) which substitute for or complement the import. However, these potential criticisms are invalid: precisely because we measure the consumer loss as an average, the disregard of gains or losses in other markets is legitimate.

3. A Basic Result

   Here we demonstrate the above assertion. Let PS and CV denote the increase in the national producer surplus and the compensating income variation for national consumers associated with the change in prices induced by the import restriction. Then, the assertion is confirmed by the result:

   Result: PS = CV - ([P.sub.0b][P.sub.0a]cf + [P.sub.0b][P.sub.0a]gd)/2.

   That is, the consumer loss which remains after accounting for the ITC average ([P.sub.0b][P.sub.0a]cd) equals the producer gain in the non-tradables markets.

   Our proof uses the following notation. Suppose there are N non-tradables, whose...