Uniform versus discriminatory tariffs in increasing marginal costs and endogenous competition

Abstract

By allowing exporters to produce under asymmetric increasing marginal costs, we investigate the impact of tariff discrimination when considering exporters' endogenous choice of competition mode. When considering endogenous competition mode, discriminatory tariffs lead to Cournot competition, whereas uniform tariffs lead to diverse modes of competition. The discriminatory (uniform) tariffs can obtain Pareto superiority from the perspective of consumers surplus, social and global welfare if product differentiation is either high or low (intermediate). Contrast to previous results, since the importing country tends to impose a lower (higher) tariff on the efficient (inefficient) exporter, the inefficient exporter always prefers the uniform tariffs while the efficient exporter's preference for tariff regime varies for any degree of product differentiation. Thus, with increasing marginal costs for any degree of product differentiation, there is a possibility that the preferences for tariff regimes change in the same direction for the exporters' profits, consumers surplus, social and global welfare.

Keywords:

• Increasing marginal cost
• uniform and discriminatory tariffs
• competition mode

JEL Classifications:

• F12
• F13
• L13

Acknowledgment

I am grateful to anonymous referees for their valuable comments on our paper. In particular, I would like to give our special thanks to Editor, Prof. Lex Zhao for many suggestions on the paper. Kangsik Choi acknowledges that this work was supported by a 2-year Research Grant of Pusan National University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Under current rules of the WTO, although non-member countries face discrimination at the hands of PTA members, they themselves are obligated to abide by MFN and treat PTA members in a non-discriminatory fashion. Recently, tariff discrimination in international trade became again a real issue with FTA in the 2000s. That is, FTA, the most commonly occurring type of PTA in today's global economy. While GATT Article XXIV requires FTA members to impose zero internal tariffs on each other, FTA members do not always abide by this restriction. An analysis of PTAs involving 85 countries and 90 percent of world trade in 2007 found that roughly two-thirds of tariff lines with MFN rates greater than 15 percent were not reduced through PTAs (Bagwell, Bown, and Staiger 2016; WTO 2011, 2013). See Tabakis (2015) for FTA.

2 The quadratic cost is popular in IO. For example, see Gori, Lambertini, and Tampieri (2014), Delbono and Lambertini (2016a, 2016b) and Chen (2022). Most natural case of diminishing-marginal-return technologies is the case where some industries are unable to replicate some inputs, i.e. due to the presence of some fixed inputs (Varian 1992, 16). Huang and Wang (2001) empirically argued that banks in Taiwan exhibit scope diseconomies. On the other hand, Hsieh (1995) investigated that although many industries show constant returns to scale, there are a number of industries that display decreasing or increasing returns to scale. However, Basu and Fernald (1997) found that a typical industry appears to have significantly decreasing returns to scale, using aggregate data to estimate production of 34 manufacturing industries in the U.S. and see references therein.

3 Flaaen, Hortacsu, and Tintelnot (2020) estimated the price effect of US import restrictions on washers. The 2012 and 2016 antidumping duties against South Korea and China were accompanied by downward or minor price movements along with production relocation to other export platform countries. With the 2018 tariffs, in nearly all source countries, the price of washers increased nearly 12%.

4 See Bagwell and Staiger (1999), Horn and Mavroidis (2001), McCalman (2002), Saggi (2004) and Bagwell and Staiger (2010) for analyzes of the various legal and economic aspects of MFN.

5 Saggi (2004) considered a model of n countries and n exporters with differential costs. He found that each country imposes higher tariffs on efficient exporters, while the adoption of the MFN clause by each country improves global welfare.

6 As Maggi (1996) pointed out, however, it is reasonable to presuppose that the mode of competition, rather than being identified with the variable chosen by firms, is determined endogenously by the importance of capacity constraints. Much like no capacity constraints models, our approach, too, is conventional and popular in the literature on industrial organization. Previous literature on the issue of Cournot and Bertrand competitions has followed two streams. One focuses on extensions and generalizations of the Singh and Vives (1984) comparison of the equilibrium outcomes (e.g. profit and welfare) under Cournot and Bertrand competitions. For example, Cheng (1985), Dastidar (1997), Amir and Jin (2001), and Tasnadi (2006), among others, have analyzed counterexamples based on the framework of Singh and Vives (1984) by allowing for a wider range of cost and demand asymmetries. The other strand explores the endogenous choice of competition mode under either a one-tier market or two-tier market. For example, in the context of a vertically related market, Correa-López and Naylor (2004), Correa-López (2007), Arya, Mittendorf, and Sappington (2008), and Manasakis and Vlassis (2014) also addressed the Cournot–Bertrand debate.

7 We observe diverse competition modes in the real economy. Tremblay, Tremblay, and Isariyawongse (2013) present examples of asymmetric competition mode, where some firms compete on output and others on price. In the US market for small cars, Scion (and Saturn) dealers behave as Bertrand-type firms, while Honda (and Subaru) dealers behave as Cournot-type firms. Another example is the aerospace connector industry in the US where leading distributors act as Bertrand-type firms while smaller distributors act as Cournot-type firms.

8 Considering the level of social and global welfares, the assumption is also widely applied in the literature of international trade even though the importing country has a monopsony power.

9 According to Saggi and Yildiz (2005, 249), ‘Owing to market segmentation, it is sufficient to consider the sum of the welfare of the importing country and the profit of home and foreign exporters in the importing country.’ The market segmentation in our setting implies that exported goods are only consumed by importing country, where the exporting countries do not consume exporting goods as we (or previous studies) assumed. Since importing goods derived by demand become tariff revenue of importing country with the level of tariffs, this market segmentation forces global welfare to define the sum of the welfare of the importing country and the profit of home and foreign exporters in the importing country.

10 In the case of asymmetric increasing marginal costs, it is important for the home country's government to know the level of production costs of exporters in either case of constant marginal costs or increasing marginal cost. In fact, readers who are outside of firm easily cannot observe the marginal cost, while the marginal cost in increasing marginal cost changes when the output changes. Without these informations, the importing country cannot set tariffs to maximize its welfare. For the incomplete information in the global trade, see Antrás (2003) and Martimort and Verdier (2012) among others. They investigated the implications of incomplete information for international trade (e.g. domestic regulation and rent-shifting trade policy). Drenski, Hallren, and Lee (2019), found the evidence of substantial underreporting of imports relative to export data on average.

11 Thus, our model reflects the fact that the tariff rate changes often in the international trade, justifying our timing of game as a reasonable assumption. If governments move first before firms' choice of strategic variable, governments induce firms to choose the strategic variable from the welfare viewpoint. That is, governments do not necessarily set the optimal tariff in some case. For instance, if the choice of contract variable is more efficient for social welfare, government sets the optimal tariff. Thus, this implies that exporters are rendered the choice of their strategic variable by governments. The case where trade tariff policy of the importing country precedes the determination of competition mode will be examined later.

12 The marginal welfare effects of import tariff under both p−p and asymmetric games, p−q and q−p take the same functional form.

13 The tax-wedge effect equals the initial difference between the domestic and import prices times the change in imports.

14 Before analyzing endogenous competition mode, we provide the case of which the policy of importing government precedes choice of competition mode (i.e. if we assume that the tariff is chosen first stage). Comparing firms' profits from Equations (4(4) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{qq}}& =\frac{(2+m)\left[3\right(1-t_{\mathrm{iD}}^{\mathrm{qq}})-d(1-t_{\mathrm{jD}}^{\mathrm{qq}}){]}^2}{2\left[3\right(2+m)-d^2{]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{qq}}& =\frac{3\left[\right(2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{qq}})-d(1-t_{\mathrm{iD}}^{\mathrm{qq}}){]}^2}{2\left[3\right(2+m)-d^2{]}^2}.\end{array}\end{array}$(4) ), (9(9) $\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{pp}}& =\frac{\left[2\right(1-d^2)-m]\left[\right(3-d^2\left)\right(1-t_{\mathrm{iD}}^{\mathrm{pp}})-d(1-t_{\mathrm{jD}}^{\mathrm{pp}}){]}^2}{2\left[d^2\right(6+m)-d^4-3(2+m){]}^2},\end{array}$(9) ), (10(10) $\begin{array}{rl}{\hat{\pi }}_{\mathrm{jD}}^{\mathrm{pp}}& =\frac{(3-2d^2)\left[\right(1-t_{\mathrm{jD}}^{\mathrm{pp}}\left)\right(2+m-d^2)-d(1-t_{\mathrm{iD}}^{\mathrm{pp}}){]}^2}{2\left[d^2\right(6+m)-d^4-3(2+m){]}^2}.\end{array}$(10) ), (15(15) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{pq}}& =\frac{(2+m)\left[\right(3-d^2\left)\right(1-t_{\mathrm{iD}}^{\mathrm{pq}})-d(1-t_{\mathrm{jD}}^{\mathrm{pq}}){]}^2}{2\left[3\right(2+m)-d^2(3+m){]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{pq}}& =\frac{(3-2d^2)\left[\right(2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{pq}})-d(1-t_{\mathrm{iD}}^{\mathrm{pq}}){]}^2}{2\left[3\right(2+m)-d^2(3+m){]}^2},\end{array}\end{array}$(15) ) and (16(16) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{qp}}& =\frac{\left[2\right(1-d^2)+m]\left[3\right(1-t_{\mathrm{iD}}^{\mathrm{qp}})-d(1-t_{\mathrm{jD}}^{\mathrm{qp}}){]}^2}{2\left[3\right(2+m)-4d^2{]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{qp}}& =\frac{3\left[\right(2-d^2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{qp}})-d(1-t_{\mathrm{iD}}^{\mathrm{qp}}){]}^2}{2\left[3\right(2+m)-4d^2{]}^2}.\end{array}\end{array}$(16) ) yields $\frac{{\pi }_{\mathrm{iD}}^{\mathrm{qp}}}{{\pi }_{\mathrm{iD}}^{\mathrm{pp}}}=\frac{\left[6\right(1-d^2)+d^4+m(3-d^2\left){]}^2\right[3(1-t_i^{\mathrm{qp}})-d(1-t_j^{\mathrm{qp}}){]}^2}{(6-4d^2+3m{)}^2[(3-d^2)(1-t_i^{\mathrm{pp}})-d(1-t_j^{\mathrm{pp}}){]}^2},\frac{{\pi }_{\mathrm{iD}}^{\mathrm{qq}}}{{\pi }_{\mathrm{iD}}^{\mathrm{pq}}}=\frac{[6-3d^2+m(3-d^2\left){]}^2\right[3(1-t_i^{\mathrm{qq}})-d(1-t_j^{\mathrm{qq}}){]}^2}{(6-d^2+3m{)}^2[(3-d^2)(1-t_i^{\mathrm{pq}})-d(1-t_j^{\mathrm{pq}}){]}^2},\frac{{\pi }_{\mathrm{jD}}^{\mathrm{pq}}}{{\pi }_{\mathrm{jD}}^{\mathrm{pp}}}=\frac{\left[6\right(1-d^2)+d^4+m(3-d^2\left){]}^2\right[(2+m)(1-t_j^{\mathrm{pq}})-d(1-t_i^{\mathrm{pq}}){]}^2}{[6-3d^2+m(3-d^2\left){]}^2\right[(2+m-d^2)(1-t_j^{\mathrm{pp}})-d(1-t_i^{\mathrm{pp}}){]}^2}$ and $\frac{{\pi }_{\mathrm{jD}}^{\mathrm{qq}}}{{\pi }_{\mathrm{jD}}^{\mathrm{qp}}}=\frac{(6-4d^2+3m{)}^2[(2+m)(1-t_j^{\mathrm{qq}})-d(1-t_i^{\mathrm{qq}}){]}^2}{(6-d^2+3m{)}^2[(2-d^2+m)(1-t_j^{\mathrm{qp}})-d(1-t_i^{\mathrm{qp}}){]}^2}$; if the tariff is chosen first stage, then since the tariff is not paid theoretically by each competition mode in SPNE system and exporters cannot know the value of discriminatory tariffs including rival's as in the equations (i.e. the payoff ratio of each competition), it would have no direct effect on the choice of competition mode under discriminatory tariff regime.

15 $\sum _{i=1}^2(q_{\mathrm{iD}}^{\mathrm{pp}}-q_{\mathrm{iD}}^{\mathrm{pq}})=\frac{2d^2(5-d+2d^2{)}^2}{{\mathrm{\Psi }}_{\mathrm{ap}}{\mathrm{\Psi }}_p}>0$; $\sum _{i=1}^2(q_{\mathrm{iD}}^{\mathrm{pq}}-q_{\mathrm{iD}}^{\mathrm{qp}})=\frac{8d^2(4-d-d^2+m)(m-1)}{{\mathrm{\Psi }}_{\mathrm{ap}}{\mathrm{\Psi }}_{\mathrm{aq}}}>0$; $\sum _{i=1}^2(q_{\mathrm{iD}}^{\mathrm{qp}}-q_{\mathrm{iD}}^{\mathrm{qq}})=\frac{2d^2(5-d{)}^2}{{\mathrm{\Psi }}_{\mathrm{aq}}{\mathrm{\Psi }}_q}>0$.

16 From simple comparisons of equilibrium outcomes, we can easily know the ranking of tariff revenue, $T{R}_D^{\mathrm{qp}}>T{R}_D^{\mathrm{pp}}>T{R}_D^{\mathrm{qq}}>T{R}_D^{\mathrm{pq}}$. More formally, given quantity (price) contract of the inefficient (efficient) exporter, choosing price (quantity) contract for the efficient (inefficient) exporter yields higher output in the home country than choosing quantity (price) contract for the efficient (inefficient) exporter. This is mainly because home country makes choosing Cournot (Bertrand) competition increase output for the profit of the inefficient (efficient) exporter with the ranking of tariff revenue.

17 In fact, when comparing the inefficient (efficient) exporter's output in the p−p and q−q with the inefficient (efficient) exporter's output in the q−p and p−q (p−q and q−p), the critical value, $d^{†}\left(d^e\right)$ is very slightly larger (smaller) than the critical value, $d^{\ast }\left(d^{\mathrm{ee}}\right)$. Thus, for simplicity, we assume $d^{†}\approx d^{\ast }$ and $d^e\approx d^{\mathrm{ee}}$.

18 Similar to the discriminatory tariff regime, if we assume that the tariff is chosen first stage, then we have comparisons using $t_i=t_j=t$ from Equations (4(4) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{qq}}& =\frac{(2+m)\left[3\right(1-t_{\mathrm{iD}}^{\mathrm{qq}})-d(1-t_{\mathrm{jD}}^{\mathrm{qq}}){]}^2}{2\left[3\right(2+m)-d^2{]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{qq}}& =\frac{3\left[\right(2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{qq}})-d(1-t_{\mathrm{iD}}^{\mathrm{qq}}){]}^2}{2\left[3\right(2+m)-d^2{]}^2}.\end{array}\end{array}$(4) ), (9(9) $\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{pp}}& =\frac{\left[2\right(1-d^2)-m]\left[\right(3-d^2\left)\right(1-t_{\mathrm{iD}}^{\mathrm{pp}})-d(1-t_{\mathrm{jD}}^{\mathrm{pp}}){]}^2}{2\left[d^2\right(6+m)-d^4-3(2+m){]}^2},\end{array}$(9) ), (10(10) $\begin{array}{rl}{\hat{\pi }}_{\mathrm{jD}}^{\mathrm{pp}}& =\frac{(3-2d^2)\left[\right(1-t_{\mathrm{jD}}^{\mathrm{pp}}\left)\right(2+m-d^2)-d(1-t_{\mathrm{iD}}^{\mathrm{pp}}){]}^2}{2\left[d^2\right(6+m)-d^4-3(2+m){]}^2}.\end{array}$(10) ), (15(15) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{pq}}& =\frac{(2+m)\left[\right(3-d^2\left)\right(1-t_{\mathrm{iD}}^{\mathrm{pq}})-d(1-t_{\mathrm{jD}}^{\mathrm{pq}}){]}^2}{2\left[3\right(2+m)-d^2(3+m){]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{pq}}& =\frac{(3-2d^2)\left[\right(2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{pq}})-d(1-t_{\mathrm{iD}}^{\mathrm{pq}}){]}^2}{2\left[3\right(2+m)-d^2(3+m){]}^2},\end{array}\end{array}$(15) ) and (16(16) $\begin{array}{r}\begin{array}{rl}{\hat{\pi }}_{\mathrm{iD}}^{\mathrm{qp}}& =\frac{\left[2\right(1-d^2)+m]\left[3\right(1-t_{\mathrm{iD}}^{\mathrm{qp}})-d(1-t_{\mathrm{jD}}^{\mathrm{qp}}){]}^2}{2\left[3\right(2+m)-4d^2{]}^2},\\ {\hat{\pi }}_{\mathrm{jD}}^{\mathrm{qp}}& =\frac{3\left[\right(2-d^2+m\left)\right(1-t_{\mathrm{jD}}^{\mathrm{qp}})-d(1-t_{\mathrm{iD}}^{\mathrm{qp}}){]}^2}{2\left[3\right(2+m)-4d^2{]}^2}.\end{array}\end{array}$(16) ): $\frac{{\pi }_{\mathrm{iU}}^{\mathrm{qp}}}{{\pi }_{\mathrm{iU}}^{\mathrm{pp}}}=\frac{\left[6\right(1-d^2)+d^4+m(3-d^2\left){]}^2\right(3-d{)}^2}{(6-4d^2+3m{)}^2(3-d-d^2{)}^2}>1,\frac{{\pi }_{\mathrm{iU}}^{\mathrm{qq}}}{{\pi }_{\mathrm{iU}}^{\mathrm{pq}}}=\frac{(6-3d^2+m(3-d^2\left){]}^2\right(3-d{)}^2}{(3-d-d^2{)}^2(6-d^2+3m^2{)}^2}>1,\frac{{\pi }_{\mathrm{jU}}^{\mathrm{pq}}}{{\pi }_{\mathrm{jU}}^{\mathrm{pp}}}=\frac{(2-d+m{)}^2[6(1-d^2)+d^4+m(3-d^2){]}^2}{(2-d-d^2+m{)}^2[6-3d^2+m(3-d^2){]}^2}>1$ and $\frac{{\pi }_{\mathrm{jU}}^{\mathrm{qq}}}{{\pi }_{\mathrm{jU}}^{\mathrm{qp}}}=\frac{(6-4d^2+3m{)}^2(2-d+m{)}^2}{(6-d^2+3m{)}^2[2-d-d^2+m{]}^2}>1$. If the tariff is chosen first stage under a uniform tariff regime, choosing Cournot competition for each exporter is a dominant strategy. This implies that the uniform tariff has no direct effect on the choice of competition mode, which provides that the result is the same from the one obtained by Singh and Vives (1984) even with uniform tariff regime.

19 $T{C}_{\mathrm{iD}}(\equiv t_{\mathrm{iD}}^{\mathrm{qq}}{q}_{\mathrm{iD}}^{\mathrm{qq}}+\frac{m}{2}(q_{\mathrm{iD}}^{\mathrm{qq}}{)}^2)-T{C}_{\mathrm{jD}}(\equiv t_{\mathrm{jD}}^{\mathrm{qq}}{q}_{\mathrm{jD}}^{\mathrm{qq}}+\frac{1}{2}\left(q_{\mathrm{jD}}^{\mathrm{qq}}{)}^2\right)=\frac{\begin{array}{l}-(m-1)\left[a\right(d)+a(d)m+a(d)m^2\\ +a\left(d\right)m^3+a\left(d\right)m^4+a\left(d\right)m^5]\end{array}}{\begin{array}{l}2\left[5\right(3+2m)-d^2{]}^2(47-26d-2d^2\\ +2d^3+2m(19-8d)+5m^2{)}^2\end{array}}<0$, where $\left[a\right(d)+a(d)m+a(d)m^2+a(d)m^3+a(d)m^4+a(d\left)m^5\right]>0$.

20 $\sum _{i=1}^j(q_{\mathrm{iU}}^{\mathrm{pp}}-q_{\mathrm{iU}}^{\mathrm{pq}})=\frac{2d^2(3-d-d^2)[80-92d-40d^2+54d^3+11d^4-9d^5-2d^6+(26-16d-16d^2+6d^3+3d^4)m+(2-d^2\left)m^2\right]}{{\mathrm{\Theta }}_{\mathrm{pU}}{\mathrm{\Theta }}_{\mathrm{AU}}}>0$; $\sum _{i=1}^j(q_{\mathrm{iU}}^{\mathrm{pq}}-q_{\mathrm{iU}}^{\mathrm{qp}})=\frac{2d^2(5-2d-d^2-m{)}^2(6-3d-d^2+m\left)\right(m-1)}{{\mathrm{\Theta }}_{\mathrm{aU}}{\mathrm{\Theta }}_{\mathrm{AU}}}>0$; $\sum _{i=1}^j(q_{\mathrm{iU}}^{\mathrm{qp}}-q_{\mathrm{iU}}^{\mathrm{qq}})=\frac{2(3-d)d^2[80-92d+21d^2+4d^3-d^4+2(13-8d)m+2m^2]}{{\mathrm{\Theta }}_{\mathrm{aU}}{\mathrm{\Theta }}_{\mathrm{qU}}}>0$.

21 From simple comparisons of equilibrium outcomes, we can easily know $T{R}_U^{\mathrm{qp}}>T{R}_U^{\mathrm{pp}}>T{R}_U^{\mathrm{qq}}>T{R}_U^{\mathrm{pq}}$. See also footnote 16 under discriminatory tariff regime.

22 $q_{\mathrm{iU}}^{\mathrm{pp}}-q_{\mathrm{iD}}^{\mathrm{qq}}=\frac{K}{\left[5\right(3+2m)-d^2]{\mathrm{\Theta }}_{\mathrm{pU}}}>0$, where $K=10-12d-154d^2+135d^3+73d^4-54d^5-12d^6+4d^7-(5-7d+26d^2-19d^3-3d^4+6d^5)m-(5-5d-2d^3)m^2$.

23 It is interesting to extend the issue of the scope of bargaining between duopolistic firms and unions in an open economy with strategic trade policy. See Fanti and Buccella (2016) for endogenous bargaining framework.