Quantitative restrictions in the presence of cost-based informational asymmetries.

• Author: Herander, Mark G.

1. Introduction

   Recognition that incomplete information is the rule rather than the exception when decisionmakers interact in an international setting has stimulated an emerging literature on the effects of trade policy in the presence of informational failures. Particularly germane to the present study are those papers that introduce an informational asymmetry into an international model of imperfect competition. The majority of this literature examines the sensitivity of optimal strategic trade policy to information failures within a Brander-Spencer (1985) model where the domestic and foreign firms compete for export sales to a third market and either the domestic or foreign government employs export subsidies (Collie and Hviid 1993; Qiu 1994; Maggi 1995; Brainard and Martimort 1997; Wright 1998). Collie and Hviid (1994), on the other hand, allow for domestic consumption, and consider optimal import policy in the presence of a foreign monopolist. Analysis that focuses on the positive effects of trade policy in the presence of informational failures is more limited. One such example is a study by Hartigan (1994), which considers the effects of antidumping duties.(1)

   To date, however, there has been no analysis of how (and whether) the

   introduction of an informational failure alters the effects of quantitative restrictions to trade. The aim of the present study is to extend the existing literature by examining the effects of a quantitative restriction to trade in the presence of a cost-based informational asymmetry within a standard two-period entry model.(2) During the initial time period, a domestic firm supplies the home market and recognizes the threat of the potential foreign rival where the latter is uninformed of the cost structure of the domestic firm and faces an import quota (or negotiated voluntarily export restraint [VER]). As is well known from the industrial organization literature, the incumbent (domestic) firm may have an incentive to change its time-period-one behavior so as to signal information on costs to the foreign firm in an effort to deter entry (see Milgrom and Roberts 1982).

   The objective of this study is to determine how and whether the effects of a quantitative restriction differ under a cost-based informational asymmetry from the standard full-information effects. To this end, the analysis focuses on the role of quantitative restrictions in altering the strategic interaction between a rival foreign and domestic firm when the former lacks complete information on the latter's cost structure. Because of the emphasis on firm behavior, we limit the strategic role of policymakers by assuming that the quota quantity is set by uninformed policymakers prior to time period one and remains fixed over the course of the game.

   A key element of the analysis is the role of policy in conveying information. Because the foreign firm cannot infer domestic costs by merely observing the quota quantity, the foreign firm must rely on signals provided by the domestic firm in time period one. Under Cournot competition, the uninformed firm observes the combination of quota quantity and the domestic firm's output choice in time period one and responds by either updating or maintaining its priors on cost structure. Thus, the quota quantity plays an indirect role in signaling firm type - certain quota quantities induce the domestic firm to play quantities that signal actual costs, whereas domestic quantities played at other quota levels convey no information.

   Two underlying assumptions of the model merit brief comment. An exogenous quota quantity implies that policymakers have no discretion in policy formation. Indeed, policy discretion is limited, or even absent, in the face of binding trade agreements such as negotiated VERs.(3) Also, a two-period entry model abstracts from the fact that quantitative restrictions are typically set in the presence of (or in response to) existing imports. The present model, employed for analytical convenience, is best thought of as a stylized representation of a quota policy that is nonbinding in time period one where the domestic firm faces potential competition from a new foreign entrant in time period two.(4)

   Our analysis begins by establishing the relation between quota policy and domestic firm signaling behavior in sections 4 and 5. In so doing, we identify a range of quota quantities for which the domestic firm selects a quantity that signals costs (a separating equilibrium) as well as a range for which the quantity chosen reveals no information and yields a sustainable pooling equilibrium.

   The possibility of a sustainable pooling equilibrium where a high-cost domestic firm successfully conceals its cost structure is a unique result in this literature.(5) Moreover, the possibility of a pooling equilibrium significantly alters the usual effects of quantitative restrictions under full information. In section 6 we demonstrate, for example, that higher levels of allowable imports may no longer promote foreign entry, since the threat of greater import competition can induce a pooling equilibrium where a high-cost domestic firm raises output to conceal information from the potential foreign entrant and so deters entry.

   Even in a separating equilibrium, where actual costs are signaled, full-information results may no longer hold. For example, at extremely high quota quantities, a low-cost domestic firm may play a quantity that is greater than the full-information optimal quantity in order to signal actual costs, deter entry, and so avoid the high level of import competition.

   In section 7, we show that the realized welfare effects of policy are also altered. Because these results are dependent on actual domestic cost structure, uninformed policymakers cannot predict beforehand the qualitative impact of quota policy, much less its quantitative effects. In section 8, we conclude by offering policy implications of our results and possible extensions of the model.

2. Information Structure

   Consider a two-period model of a world market where two firms, one located in the domestic country the other in the foreign country, supply an identical product. In time period one (TP1), no international trade takes place. In time period two (TP2), it is possible for the foreign firm to compete with the domestic firm for sales to domestic consumers. During TP1 the domestic firm recognizes that the foreign firm is a potential entrant in TP2.(6)

   The domestic firm's production costs are private information, so that although the domestic firm knows the value of the foreign firm's costs, the latter is uninformed of the value of domestic costs in TP1. Since we are interested in the relation between policy and signaling, we simplify the analysis by assuming that foreign costs are known to the domestic firm.(7) In time period one, however, the foreign firm knows that the domestic firm is one of two types, high or low cost, and holds a prior subjective probability [Alpha] (assumed to be common knowledge) that the domestic firm is the high-cost type. In TP1 the domestic firm may, by its choice of quantity, convey information on the value of its costs, causing the foreign firm to update its prior probability which, in turn, affects expected profits of the foreign firm in TP2 and possibly the foreign firm's entry decision. The domestic firm takes into account this signaling effect when making its TP1 quantity choice.

   Subsequent analysis assumes quota (or VER) licenses are issued free of charge so that the two types of quantitative restrictions are analytically equivalent. Henceforth, we use the term quota quantity to refer to the level of import restrictions under either policy.

3. Model

   We restrict our analysis to pure strategy perfect Bayesian equilibria. As is standard, the signaling game is solved via backwards induction by first obtaining second-period solutions. For analytical convenience, and without loss of qualitative results, linear inverse demand is employed:

   p = a - ([x.sub.j] + [x.sup.f]) (1)

   where a [greater than] 0, p is the price paid by domestic consumers, [x.sub.j] equals output of a domestic firm of type j (j = h for high cost, 1 for low cost), and [x.sub.f] represents output of the foreign firm.

   Consider first the case where no entry occurs so that the domestic firm remains the sole supplier to domestic consumers in TP2 ([x.sub.f] = 0). With constant marginal costs, [c.sub.j], the profit-maximizing quantity played by a type j domestic monopolist equals:

   [Mathematical Expression Omitted] (2)

   where the superscript M denotes, throughout, the value of domestic variables when the domestic firm is a monopolist.

   The foreign firm incurs a fixed cost of entry. As is typical in models of entry, we assume that foreign variable costs are such that, absent entry costs, foreign profits are positive. Should expected foreign variable profits exceed entry costs, entry occurs and Cournot duopoly characterizes competition in TP2. Postentry, the domestic firm selects the quantity to maximize:

   [Mathematical Expression Omitted] (3)

   where superscript D refers, throughout, to domestic variable values under duopoly. The foreign firm maximizes expected profits subject to the quota quantity, q:

   [Mathematical Expression Omitted] (4)

   where [c.sub.f] equals constant marginal cost of the foreign firm and superscript e denotes expected value. The Cournot reaction functions are given by:

   [Mathematical Expression Omitted] (5)

   [Mathematical Expression Omitted] (6)

   where [Mathematical Expression Omitted] represents the foreign firm's expectation of domestic output. Consider, initially, a nonbinding quota: [x.sub.f] [less than or equal to] q. Substitute the foreign firm's expectation of domestic costs, [c.sup.e], into Equation 5 for actual domestic costs ([c.sub.j]) and combine Equations 5 and 6 to obtain optimal foreign output, conditional on its expectation of domestic firm type:

   [x.sub.f]([c.sup.e]) = (a +...