1. Parallel Trade with an Endogenous Market Structure
Pei-Cyuan Shih, Hong Hwang and Cheng-Hau Peng
 2017/12/21
Department of Economics
National Chung Cheng University

2. What is parallel trade?
Parallel trade (PT) occurs when a genuine product is sold back by foreign distributers without the permission of the domestic intellectual property owner who, we call it manufacturer in the model, also sells its product directly to the domestic market.
Examples:
Electronic products
Textbooks
Automobiles
Medicine
2017/6/8
Shih, Hwang and Peng

3. Motivation
Whether PT should be permitted or banned is an open question and has received growing attention in public debates.
It is illegal in EU but legal in Japan, China and Taiwan. PT was illegal in USA according to the First Sale Doctrine of the US copyright law. Not until recently, however, the Supreme Court of the United States rules in favor of PT.
The academic literature on PT in general concludes that PT lowers the profits of the manufacturer and also worsens the SW of the PT importing country.
In this paper, we employ a free entry oligopoly model to examine the effects of PT. It is found that PT increases not only the profits of the manufacturer, but also the SW of the PT importing and exporting countries.
2017/6/8
Shih, Hwang and Peng

4. Related literature
Trade cost : Maskus and Chen (2004), Chen and Maskus (2005), Mueller-Langer (2012)
Labor union: Mukherjee and Zhao (2012)
To the best of our knowledge, there is no research examining how free entry or an endogenous market structure (EMS) affects the optimal PT policies and their welfare implications.
2017/6/8
Shih, Hwang and Peng

5. Outline of this paper
Section 2 investigates the equilibrium of PT under free entry oligopoly.
Section 3 analyzes the profits of the manufacturer and welfare implications.
Section 4 concludes the paper.
2017/6/8
Shih, Hwang and Peng

6. free-entry rivals: /v, F
Model settings
Domestic; A
manufacturer: w, T; q/c
free-entry rivals: /v, F
p(Q)
Foreign; B
foreign distributor:
/t, y*
p*(y*)
2017/6/8
Shih, Hwang and Peng

7. Model settings
Assume there are two countries, country A and country B.
A manufacturer, located in country A, sells units of its product to its own market (i.e., market A).
The manufacturer also sells its product to market B via a foreign distributor.
The foreign distributor may engage in parallel trade, selling to market B and
back to market A, if country A allows parallel trade.
2017/6/8
Shih, Hwang and Peng

8. Model settings
The manufacturer incurs a constant marginal cost, c , to produce the product.
We further assume that the manufacturer charges a two-part tariff, i.e., a fixed fee ( T ) and a wholesale price ( w ) when selling the product to the distributor.
There are potential entrants in market A, all producing the same product, , with marginal cost v and fixed cost .
2017/6/8
Shih, Hwang and Peng

9. Model settings
The inverse demand functions of markets A and B are respectively
and , where
, with the property ,
PT incurs a per-unit trade cost .
2017/6/8
Shih, Hwang and Peng

10. Game structure
In the first stage, the manufacturer determines the optimal two-part tariff (i.e., and T) for its sales to the foreign distributor.
In the second stage, domestic potential entrants determine whether to enter the market. Moreover, the entrants and the manufacturer determine their outputs for market A whereas the foreign distributor determines its sales to market A (i.e., PT) and market B as well.
2017/6/8
Shih, Hwang and Peng

11. The equilibrium
In the final stage, the profit functions for the manufacturer, the entrants and the foreign distributor can be respectively expressed as follows:
(1)
(2)
(3)
2017/6/8
Shih, Hwang and Peng

12. The second-stage game
The first-order conditions for profit maximization:
(4)
(5)
(6)
(7)
(8)
2017/6/8
Shih, Hwang and Peng

13. The second-stage game
First, by summing (4) and (6), we can derive the joint RF of the manufacturer and the foreign distributor as follows:
, where (9)
Moreover, from the zero profit condition, we have
By substituting it into the joint RF and the representative RF of the local rivals, we can depict the two RFs in Figure 1.
2017/6/8
Shih, Hwang and Peng

14. Figure 1. The reaction functions
2017/6/8
Shih, Hwang and Peng

15. Lemma 1
The joint reaction function is horizontal if the structure of the domestic market is endogenously determined.
It implies that the optimal output of the representative domestic rival is independent of the joint output of the manufacturer and the foreign distributor.
2017/6/8
Shih, Hwang and Peng

16. Comparative static effects
We can derive the comparative static effects as follows: , .
2017/6/8
Shih, Hwang and Peng

17. Proposition 1
If the market structure is endogenously determined, an increase in the wholesale price increases the number of domestic rivals but has no effect on the equilibrium output and the price of the domestic market.
Intuition: For any given n, an increase in w => p increases => incumbent local rivals make profits => n increases until p = AC, i.e., the zero profit condition is restored.
2017/6/8
Shih, Hwang and Peng

18. Lemma 2
The equilibrium domestic market price and total sales are not affected by parallel trade if the market structure is endogenously determined.
Intuition: Other things being equal, an increases in PT turns the profit of the local rivals into negative, causing some local rivals to exit from the market. This shifts the perceived demand of the representative local rival back to its tangency position.
2017/6/8
Shih, Hwang and Peng

19. The first-stage game
The profit function of the manufacturer for the first-stage game can be expressed as follows:
The FOC:
2017/6/8
Shih, Hwang and Peng

20. The optimal wholesale price
If there is no PT, we have: as
By contrast, if PT is allowed, by evaluating the first-order condition at
, we derive that
2017/6/8
Shih, Hwang and Peng

21. Proposition 2
If the market structure is endogenously determined and parallel trade is allowed, the wholesale price charged by the manufacturer is necessarily lower than its marginal cost.
The above result differs sharply from those in Maskus and Chen (2004) and Li and Maskus (2006).
Intuition: They assume the manufacturer faces no local rivals and adopts two-part tariff pricing under an exogenous market structure, they find that when the trade cost is high, the manufacturer would definitely set the wholesale price higher than the marginal cost to save on the trade cost. Contrarily, the manufacturer in our model always set the wholesale price lower than the marginal cost to increase its market share in and profit from the domestic market via PT.
2017/6/8
Shih, Hwang and Peng

22. Profits of the manufacturer under free entry
Note that the manufacturer sets if PT is banned.
Given , a marginal increase of PT necessarily increases the manufacturer’s profit as the profit from the foreign market remains the same but that from the domestic market increases.
This explains again why the manufacturer would set the wholesale price below its marginal cost and also implies that PT is profitable for the manufacturer under an EMS.
2017/6/8
Shih, Hwang and Peng

23. Proposition 3
If the market structure is endogenously determined, PT increases the profit of the manufacturer. The above result is of interest and in sharp contrast to the findings in Maskus and Chen (2004) and Li and Maskus (2006). Under an exogenously given market structure, they both conclude that PT definitely reduces the profit of the manufacturer.
2017/6/8
Shih, Hwang and Peng

24. Welfare implications
The social welfare functions of the domestic and foreign countries are expressed respectively as follows: .
PT increases SW as the profit of the manufacturer goes up and the market output is unchanged.
PT necessarily increase SW* as (i) It lowers the wholesale price and thus the p* there and (ii) The profit of the foreign distributor is unchanged by the two-part tariff assumption.
2017/6/8
Shih, Hwang and Peng

25. Proposition 4
If the market structure is endogenously determined, PT enhances the welfare of the domestic country as well as the foreign country. This result is different from those in Maskus and Chen (2004), Li and Maskus (2006) and Mueller‐Langer (2012) in which PT is welfare- reducing and should be banned by the host government. This is because they assume an exogenous market structure.
2017/6/8
Shih, Hwang and Peng

26. Conclusions
By considering EMS, this paper examines how parallel trade affects the profit of the manufacturer and the welfare of the two involved countries.
It is found that PT enhances the profit of the domestic manufacturer as well as the welfare of both the domestic and foreign countries.
It also offers an explanation as why many governments engage in parallel trade deregulation.
2017/6/8
Shih, Hwang and Peng

27. Thank you!
2017/6/8
Shih, Hwang and Peng