Trade policy in a “super size me” world

Abstract

When a foreign monopolist sets a single market clearing price for its product, the sign of the optimal tariff is determined by the extent of pass through (also known as the terms of trade effect). However, when a foreign monopolist employs a second degree price discrimination mechanism in the domestic market the calculus of welfare maximization is very different. While there are still terms of trade effects from the imposition of a tariff, the existence of such effects are neither necessary nor sufficient to determine the sign of the optimal tariff. Instead the distribution of valuations within the population is the key determinant of the nature of policy intervention. This result differs significantly from the uniform price case and is driven by the incentive compatibility constraint which places the distribution of types at the center of the analysis. If there is a relatively large fraction of high valuation types in the population, then domestic information rents may be increased by subsidizing imports thereby increasing the consumption of the low valuation types and moving the incentive constraint in favor of the high valuation types. However, if the share of high types in the population is relatively small then the increase in information rents will also be small but the fiscal implications of a subsidy will be large. Consequently, the optimal policy will be to impose a trade tax.

Introduction

Firms use a wide variety of techniques to sell their products. The diversity of methods extends far beyond the simple notion that a lower price will attract more consumers. Indeed the whole idea that firms rely on linear prices is challenged by the contracts offered for not only telecommunication services but also by the discounts for volume available in almost all retail outlets (e.g. 500 ml of soft drink is more than half the price of 1000 ml). Colloquially, the option to buy a bigger size at a lower average price, or a higher quality at a lower quality adjusted price, is an invitation to “super size” the purchase. The literature analyzing these techniques is vast but all studies have one feature in common, they all focus exclusively on a closed economy setting. The focus on closed economy models seems natural, especially since the working assumption regarding international trade is that it is motivated, at least in part, by differences in price. Such a motivation naturally lends itself to a relatively competitive view of international markets. However, recent empirical work challenges the idea that international trade is predominantly conducted in competitive markets characterized by relatively anonymous exchange. Indeed, Rauch (1999) finds that between 60 and 70% of international trade occurs outside of organized exchanges or institutions that disseminate price information. This implies that the majority of international trade occurs in settings where information about the identity of buyers and sellers is important and that one or potentially both sides of an exchange have market power.¹ At the very least this suggests there is scope for some of the vast array of selling techniques observed in the closed economy to also be applied to international transactions.

This paper considers one such technique; 2nd degree price discrimination (also known as indirect discrimination).² Specifically a foreign monopolist is assumed to serve a heterogeneous group of domestic consumers. Unfortunately for the monopolist there is no obvious way of distinguishing between the various types of customers. Instead the foreign monopolist offers the domestic consumers a menu to pick from, each option differing in terms of the quantity and total payment required. By choosing among the different options the consumers are implicitly generating a distribution of prices for the product sold by the monopolist. How is a domestic government's view of the world altered by such behavior? More specifically, is the operation of trade policy likely to be affected by the non-linear pricing structure of the foreign monopolist?³

This question is interesting since an important consideration in assessing the implications of trade policy is the terms of trade effect. This effect is central to arguments about optimal trade policy since it provides a motivation for intervention by the domestic government. However, if there is not a single market clearing price it is not immediately obvious whether or how a domestic government should intervene in international trade.

This paper demonstrates that the optimal trade policy in the presence of non-linear pricing has a very different motivation than when the foreign monopolist charges a uniform price (see Brander and Spencer, 1984).⁴ In particular a terms of trade effect is neither necessary nor sufficient for intervention to occur by a national welfare maximizing government.⁵ This stands in direct contrast to a uniform price monopolist where the terms of trade effect not only serves as the basis for intervention but also determines whether the trade tax is positive or negative. For the uniform price case, if pass through is less than complete (i.e. a $1 trade tax raises the domestic price by less than a dollar), then it is optimal to impose a positive trade tax since the foreign firm pays part of the tax. However, if pass through is more than complete then the optimal policy is a subsidy to imports. In this instance a $1 subsidy will lower the domestic price by more than a dollar, with the terms of trade benefit once again the mechanism that motivates intervention. Finally, if pass through is complete then the optimal tariff is zero. Such logic is no longer reliable when the foreign firm uses non-linear prices.

To see that the terms of trade effect can be misleading consider the extreme case of a foreign monopolist that is able to implement 1st degree price discrimination. In such a situation the foreign monopolist captures all the surplus under free trade. Since tariff revenue is the only source of domestic surplus, the optimal trade policy response is to impose the revenue maximizing tariff. Note in particular that this policy is completely independent of the degree of pass through on to domestic prices. While 1st degree price discrimination is an extreme case, it does provide insight into the related mechanism of 2nd degree price discrimination. The main difference between the two mechanisms is that the foreign monopolist must induce the domestic consumers to reveal their type rather than being able to observe it directly. This enables some domestic consumers to capture information rents under 2nd degree price discrimination. These rents are derived from the ability of high valuation types to claim to be low valuation types and the need for the monopolist to set an incentive compatible price schedule to avoid this outcome. As a result the information rents that a high type earns are a function of the bundle designed for the low types, which creates an incentive for the monopolist to reduce the low types bundle below the efficient level.

By offering an import subsidy the domestic government moves production closer to the first best for the low valuation types. In turn, the increased consumption of the low valuation types translates into greater information rents for the high valuation types due to a change in the incentive compatibility constraint. Will a government choose a subsidy? Clearly, more than complete pass through lowers the fiscal cost of the subsidy. However, the degree of heterogeneity among consumers is more important. If the fraction of high types is relatively large, then the optimal policy is more likely to be a subsidy since the gain in information rents can be more than sufficient to offset the fiscal cost of the subsidy. This effect can be so strong that a subsidy is optimal even when pass through is less than complete. Conversely, when pass through is more than complete, the optimal trade tax can still be positive under non-linear pricing, with this more likely the higher the fraction of low types in the population. Hence, the incentive compatibility constraint introduces a role for consumer heterogeneity into the welfare calculus that implies the optimal policy is now determined by the interaction of the change in the terms of trade and the distribution of valuations. It is this interaction that generates the results that stand in stark contrast to those derived under the assumption of a uniform price monopolist. Moreover, the welfare implications tend to be more pronounced under non-linear pricing since the relevant welfare comparisons are no longer a dead weight loss triangle versus a slice of the tariff revenue rectangle paid by foreigners; rather it is an information rent trapezoid versus the full tariff revenue rectangle. In other words, both gains and losses from trade policy are of a first order of magnitude under non-linear pricing.

To demonstrate these results the paper is structured as follows. To provide some evidence for the operation of non-linear pricing of international transactions, the next section contains examples where there exists an option to “super size me” in an international context and argues that this is likely to be a relatively pervasive business strategy. This section also layouts the framework for analysis. Section 3 provides two benchmarks, the familiar single price monopoly and 1st degree price discrimination, and derives the optimal trade policy for each case. The contrast in the optimal policies associated with these two extremes then sets the scene for the analysis of 2nd degree price discrimination. In this context the optimal trade tax is derived and characterized in Section 4. Section 5 considers a number of extensions such as the implications of more than two types, the presence of a domestic retailer as well as quality choice and ad valorem tariffs. Finally, Section 6 concludes and discusses avenues of potential research.