We show that, in the exogenous market structure where the extensive margin is fixed and only the intensive margin responds to trade policy, when the Home optimal tariff is higher, the thicker the Home final-good market (relative to the Foreign intermediate-good market) . In the endogenous market structure where both extensive and intensive margins respond to trade policy, this relationship is reversed and the higher the Home optimal rate, the thinner the Home final-good market. Furthermore, the price and quantity of final goods (resp. intermediate goods) are determined at the market clearing levels in the House (resp.
In this setting, we derive the relationship between the optimal tariff and market thickness (i.e., the number of firms in domestic and foreign markets) in exogenous and endogenous market structures. In an exogenous market structure, where the extensive margin is fixed and only the intensive margin responds to trade policy, we find that the domestic optimal tariff is higher, the thicker the domestic market (relative to the foreign market). This has a policy implication that the domestic government should impose higher tariffs on foreign intermediate goods in fixed-entry markets if the domestic final goods market is more competitive.
In an endogenous market structure, where both extensive and intensive margins respond to trade policy, we find that this relationship is reversed and that the higher the domestic optimal tariff, the thinner the domestic final goods market. Although the optimal tariff is dictated by intensive margin reduction and terms-of-trade gains (as in an exogenous market structure), these two forces do not always appear for all logconcave demand functions in an endogenous market structure, since, in addition to directly raising prices, the tariff also indirectly raises prices by by reducing the number of companies (extensive margin). First, we analyze third-stage Cournot competition between domestic firms in the final good market.
Now consider second-stage Cournot competition among Foreign firms in the intermediate-good market.
Tariffs
Equation (3.7) indicates that the number of firms plays a key role in determining the sign of the optimal rate. An import subsidy increases the welfare of the home country by increasing production and the optimal tariff is indeed negative. Because the pass-through from tariff to domestic prices is incomplete for all logconcave demand functions, 1−∂ˆ∂tr >0, which implies that the optimal tariff is strictly positive.
The above intuition suggests that the optimal rate in the home country is positive if the number of foreign firms (n) is relatively smaller than the number of home firms (m), and negative if n is relatively larger than m. Furthermore, with an occupation on the standard continuity argument, a range of values such that the optimal rate is strictly decreasing. Note that the optimal rate property in Proposition 3.1 holds for this specific demand function.
Since the optimal tariff is increasing (decreasing) inm(n), our model predicts that the optimal tariff should be decreasing in mn. Note that the optimal tariff is higher (i.e. higher) the more competitive the domestic market for the final good is relative to the foreign intermediate product market (i.e. lower mn).
Profits
4 Endogenous Market Structure
Cournot Competition
In the long run, where entry is unlimited, entry continues until domestic firms' post-entry profits are equal to entry costs. Let πH(m)≡(P(mq)−r)q denote the profit after domestic firms enter SPNE of level 3. Assume that KH ≤πH(1)≡K¯H, which guarantees that at least one Domestic firm enters equilibrium.
Since πH is a continuous inm and strictly decreasing inm for allm >1, Assumption 3 also ensures that mˆ uniquely exists in the SPNE of the phase 3 subgame. 13We define≡g(X)in the short run (see (3.2)), since the main focus is on comparative statics with respect to tons. Here we explicitly define a function that is both long-term and endogenous. where Xˆ satisfies the following for each datum:.
LetπF(n) ≡ (g(nx)− c−t)x denotes the post-entry profits of foreign firms in the SPNE of stage 2. We assume that KF ≤ πF(1) ≡ K¯F, which guarantees that at least one foreign company enters the equilibrium. Applying the similar claim also ensures that nˆ exists uniquely in the SPNE of the phase 2 subgame.14.
To summarize, in the Cournot competition given KH, KF and t we have an output vector (ˆq,Q,ˆ x,ˆ These two conditions together determine the number of firms and the output of these firms in the long-run equilibrium. Similarly, an equilibrium in the SPNE of the Phase 2 subgame is a vector (ˆX,n), which solves (4.3) and (4.4) in the intermediate input market in Foreign.
In the long-run configuration with fixed input costs, they show that the higher tariff increases the number of firms in the importing country and decreases the number of firms in the exporting country. In general, our model suggests that the decrease in aggregate output is mainly accounted for by the decrease in the number of firms,ˆ n, while the net changes in average outputsˆ q,ˆ xˆ are unclear.18 The effect of a change in input cost: We recall in a short-term period that we examine comparative statics with respect to the number of foreign firms n (other than the total). However, in the long run, since the number of firms is an endogenous variable, we cannot make these comparative statistics.
The difference is that we analyze homogeneous goods in the Cournot model of oligopolistic competition. As is often the case, the fact that zˆ increases with KH implies that, although both mˆ and nˆ decrease with an increase in KH, mˆ decreases relatively more sen.ˆ. The following lemma summarizes the comparative static results regarding KH.19 Lemma 4.2. i).
Tariffs
As in the short run, the first term captures the welfare loss due to the reduction in output caused by the tariffs (∂∂tQˆ < 0), and the second term captures the welfare gain resulting from the improvement in the terms of trade (∂ r∂ t∗ <0). However, unlike in the short run, the third term captures the welfare loss due to domestic firms' tariff reduction (∂∂tmˆ <0), which arises only in the long run due to the firm's co-location effect. Noting that ∂∂tXˆ < 0in (4.9), the optimal fee is strictly positive (negative) if and only if. 4.10) Contrary to section 3, the sign of the optimal tariff cannot be argued with the numbers of domestic and foreign firms,ˆnˆ since these numbers are not parameters in the long run.
This implies that the sign of the optimal fee does not depend on whether profits are positive or zero. Together with (4.11), it follows that the sign of the optimal rate also depends on². In particular, the optimal tariff is positive for concave demand functions (²≥²∗) since we have that ∂∂tqˆ>0and1−∂ˆ∂tr ≥0.
On the other hand, the optimal tariff is negative for convex demand functions (²≤0) since ∂∂tqˆ≤0and1−∂ˆ∂tr <0. This suggests that there is a discontinuˆ lt; ²∗) in which the sign of the optimal tariff is determined: the optimal tariff is positive for² > ²∗∗, while the optimal tariff is negative for² <²∗∗. In contrast to the short run, we cannot use firm numbers to examine the impact of market thickness on the optimal rate in the long run.
Therefore, the lower the domestic entry cost, the thicker the domestic market relative to the foreign market and the lower the optimal tariff (in absolute terms). Proposition 4.1 Denote the optimal tariff. where Qˆ is total output estimated at att= ˆt. ii) tˆ increases (decreases) monotonically in KH if² >(<)²∗∗. In long-run equilibrium, however, this relationship reverses and our model predicts that there is a positive relationship between mn and t.
As noted above, in the long run, the thickness of the market, where firms can enter and exit freely, is limited by the limits of entry costsKH. Note that the higher the optimal rate (i.e., higher), the less competitive the domestic market for final goods is relative to the foreign market for intermediate inputs (i.e., higher mn). For example, the classic result that the sign of the optimal tariff in the presence of a foreign monopoly depends on whether there is incomplete pass-through, which in turn depends on whether the demand curve is flatter than the marginal revenue curve (Brander and Spencer). , 1984a,b; Helpman and Krugman, 1989, chapter 4).
5 Conclusion
Appendix
- Equivalence between Assumptions 1 and 1’
- Proof of Lemma 3.1
- Proof of Proposition 3.2
- Proof of Lemma 4.1
- Proof of Lemma 4.2
Although we have focused on comparative statics related to tons, it is easy to examine comparative statics related to tons. Regarding prices, we especially note that the input price r depends on both m and X (see (3.2)). Although we apply the abbreviated definition r ≡ g(X) for the short-term analysis (since we mainly focus on comparative statics involving tons), we must explicitly define ≡ g(X, m).
While we focus on the sign of ∂∂n∂t2WH, it is possible to show for future reference that dndˆt <0 also holds by directly differentiating the optimal rate in (3.9) with respect to tonandm. We first show that the impact of n on ΠˆF is decomposed into the competition effect and tariff reduction effect. Although we have focused on comparative statics with respect to KH, it is straightforward to investigate comparative statics with respect to KF.
