Abstract
We examine the vertical strategies of home and foreign manufacturers that produce quality-differentiated products. In contrast to previous results that showed vertical separation as the dominant strategy, we find that the home manufacturer opts for vertical separation, while the foreign manufacturer chooses vertical integration under Bertrand competition. This is because the government of the importing country aims to increase consumer surplus by imposing tariffs, which allows the foreign manufacturer to export high-quality products at lower prices. Under Cournot competition, both manufacturers maintain a vertical separation strategy. However, if the quality levels of products are low, both manufacturers obtain higher profits when they choose vertical integration. This leads to a prisoner’s dilemma situation for both manufacturers. In the case of a free trade policy, manufacturers always choose the separation strategy. Under Bertrand competition, integration leads to higher output levels and increases social welfare for the importing country due to the high level of importation of high-quality products, suggesting the tariff policy drive the foreign manufacturer towards integration.
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There are risks of knowledge transfer when integrating, and difficulties arise in writing contracts when separating. However, our model does not cover the risks associated with integration or separation. In our model, when a manufacturer manages everything from manufacturing to sales, it is considered vertical integration. If a manufacturer delegates the sales of the final products to consumers through a retailer, this is considered vertical separation. In this case, we exclude any risks related to difficulties in writing contracts since all retailers’ profits are passed on to the manufacturer through two-part pricing contract. Therefore, a manufacturer compare the profits of each organizational structure and choose the vertical organization structure that can achieve higher profits.
In our model, even if we allow firm f also to supply its products to the foreign country’s market, it does not affect the results. With segmented markets and constant marginal costs, Bertrand competition in the home market can be analyzed independently of the foreign market, so the analysis will focus on the home market.
The opposite case also conceivable: competition in the home market between the home manufacturer producing high-quality products and the foreign manufacturer producing low-quality products. The analysis of this opposite case yields the same results as presented in this paper. Therefore, this paper focuses only on the assumption where the home manufacturer produces low-quality products and the foreign manufacturer produces high-quality products. (The data is available upon request from the authors.)
As demonstrated by Buehler and Schmutzler (2008), a firm’s vertical integration reduces competitive investments aimed at cost reduction. The same concept applies to our model.
In our model, we assume that the foreign manufacturer and the foreign retailer are located in the foreign country. The foreign manufacturer decides whether or not to separate its function such as sales to the foreign retailer. Therefore, the profits of both the foreign manufacturer and the foreign retailer are not included in the social welfare of the importing country.
We consider the case where vertically integrated firms make decision about their organizational structure (i.e., vertical integration or separation) prior to the government policy. A critical aspect of this game is that manufacturers possess superior commitment ability compared to the government. The strategic trade policy literature often assumes that the firms can choose a strategic variable before the government commits to trade policy. Examples include (Brander and Spencer 1987; Blonigen and Ohno 1998; Konishi et al. 1999), among others, who adopt the game stages where firms make their moves before the government’s decision on the strategic trade policy.
If the tariff policies of the importing country precede the decision-making of firms, there is a significant likelihood that firms may disregard the level of tariffs imposed. Furthermore, diverse perspectives acknowledge the possibility of changes in tariff rates even after firms’ decision. Given the ongoing trend of governments globally entering trade agreements like Free Trade Agreements(FTAs), resulting in fluctuating tariff rates, this paper suumes the occurrence of changes in tariff rates in the realm of international trade.
If both manufacturers decide on the vertical integration at stage 1, then this stage will be omitted. Therefore, the case will be reduced to a three-stage game.
\(t^{SI}-t^{II}=\frac{(s-1) [c(1 - s)+ s(4 s-3)]}{(2 s-1) (3 s-2) ( 12 s-7)}>0, t^{SS}-t^{IS}=\frac{ (s-1) [5 + 4 c(1 -s)+4s(4s-5)]}{(6 s-5) (23 - 68 s + 48 s^2)}>0,\)
\(q^{SI}_f-q^{II}_f=-\frac{2 (3 - 4 s)^2 [5 - 4 c ( s-1) - 20 s + 16 s^2]}{(6 s-5) (1 - 12 s + 16 s^2) (23 - 68 s + 48 s^2)}<0,q^{SS}_f-q^{IS}_f=-\frac{2 ( 2 s-1) [c - c s + s ( 4 s-3)]}{s ( 12 s-7) (2 - 11 s + 12 s^2)}<0 . \)
\(q^{SS}_h-q^{SI}_h=\frac{8 (2 - 5 s + 3 s^2) [ c (6 s-1)-4s]}{( 6 s-5) (12 s-7) (1 - 12 s + 16 s^2)}<0,q^{IS}_h-q^{II}_h=\frac{6 (3 c-2) (1 - 2 s)^2 ( s-1)}{( 3 s-2) ( 4 s-1) (23 - 68 s + 48 s^2)}<0\).
Backward induction in dominant strategy involves considering each player’s optimal response sequentially in reverse order of moves. Thus, at the final stage, the optimal quantity for each home and foreign manufacturer is optimized to zero through differentiation, given the demand function, tariffs, and the vertical structure of each firm. At the preceding stage, anticipating the optimal quantity from the final stage, the importing country optimizes the tariff level. In the first stage, by anticipating the optimal quantity and the tariff level from the previous stage, each manufacturer determines its optimal vertical structure. Consequently, in the first stage, there exists a dominant strategy of integration for the foreign manufacturer. Recognizing this, the home manufacturer utilizes the foreign manufacturer’s dominant strategy and chooses a separation strategy that maximizes its own profit.
The data is available upon request from the authors.
However, if the government policy precedes the firms’ decision on a vertical structure, then both firms choose vertical separation, as in Ziss (1997).
\(SW^{II}-SW^{IS}=\frac{(2 - 3 c)^2 (s-1)^2 (8 s-5)}{2 ( 3 s-2) (4 s-1) (23 - 68 s + 48 s^2)}>0, SW^{IS}-SW^{SI}=\frac{( s-1) (23 c^2 - 70 s + 72 c s - 145 c^2 s + 264 s^2 - 200 c s^2 + 266 c^2 s^2 - 320 s^3 + 128 c s^3 - 144 c^2 s^3 + 128 s^4)}{2 s ( 2 s-1) (12 s-7) (23 - 68 s + 48 s^2)}>0, SW^{SI}-SW^{SS}=\frac{( s-1)^2 ( 8 s-5) (c + 4 s - 6 c s)^2}{2 s ( 2 s-1) (6 s-5) (12 s-7) (1 - 12 s + 16 s^2)}>0\).
\(\hat{t}^{II}-\hat{t}^{SI}=\frac{4s-3 - c }{6 (12 s-7)}>0\), \(\hat{t}^{IS}-\hat{t}^{SS}=\frac{5 s -c+ 4 c s - 20 s^2 - 4 c s^2 + 16 s^3}{2 ( 3 s-1) (7 - 36 s + 48 s^2)}>0\).
\(\hat{SW}^{SS}-\hat{SW}^{II}=\frac{s (52 s - 96 s^2 + 64 s^3-9) - 2 c (28 s - 78 s^2 + 64 s^3-3) + c^2 (39 s - 95 s^2 + 72 s^3-5)}{6 ( 3 s-1) ( 4 s-1) (1 - 12 s + 16 s^2)}>0.\)
\(\hat{\pi }_{h}^{II}-\hat{\pi }_{h}^{SS}=\frac{2 [c^2 (2 - 36 s + 280 s^2 - 1167 s^3 + 2672 s^4 - 3120 s^5 + 1440 s^6) - \phi _1] }{9 (1 - 4 s)^2 (1 - 3 s)^2 (1 - 12 s + 16 s^2)^2}>0\),
\(\hat{\pi }_{f}^{II}-\hat{\pi }_{f}^{SS}=\frac{c^2 ( 160 s - 1164 s^2 + 4382 s^3 - 8928 s^4 + 9280 s^5 - 3840 s^6-9) +\phi _2}{18 (1 - 4 s)^2 (1 - 3 s)^2 (1 - 12 s + 16 s^2)^2}>0, if s<s^*\), \(s^*=\sqrt{[\phi _3-9 c^2]} \),
where \(\phi _1=2 c s (14 - 255 s + 1816 s^2 - 6528 s^3 + 12512 s^4 - 12096 s^5 + 4608 s^6) + s (9 - 190 s + 1596 s^2 - 6656 s^3 + 14400 s^4 - 15232 s^5 + 6144 s^6)\),
\(\phi _2=2 c s (39 - 622 s + 3870 s^2 - 12128 s^3 + 20352 s^4 - 17536 s^5 + 6144 s^6) + s ( 363 s - 3344 s^2 + 16320 s^3 - 43648 s^4 + 62976 s^5 - 45056 s^6 + 12288 s^7-18)\),
\( \phi _3=[( 78 c + 160 c^2-18) \sharp 1 + (363 - 1244 c - 1164 c^2) \sharp 1^2 + (7740 c + 4382 c^2-3344) \sharp 1^3 + (16320 - 24256 c - 8928 c^2) \sharp 1^4 + ( 40704 c + 9280 c^2-4364) \sharp 1^5 + (62976 - 35072 c - 3840 c^2) \sharp 1^6 + (12288 c-45056) \sharp 1^7 + 12288 \sharp 1^8 \& , 4] \).
The data is available upon request from the authors
See Appendix 2.
\(SW^{FSS}-SW^{FII}=-\frac{(s-1) (2 c - c^2 + s - 16 c s + 8 c^2 s + 8 s^2)}{2 (4 s-1) (1 - 12 s + 16 s^2)}<0\),
\(\hat{SW}^{FSS}-\hat{SW}^{FII}=\frac{ c^2-2c + 3 s + 14 c s - 7 c^2 s - 9 s^2 - 16 c s^2 + 8 c^2 s^2 + 8 s^3}{2 (4 s-1) (1 - 12 s + 16 s^2)}>0\).
\(q_f^{FII}-q_f^{FSS}=\frac{1 + c - 8 s + 8 s^2}{(4 s-1) (1 - 12 s + 16 s^2)}>0\),\(\hat{q}_f^{FII} - \hat{q}_f^{FSS}=\frac{c + 4 s - 8 s^2}{(4 s-1) (1 - 12 s + 16 s^2)}<0\).
\(SW^{FSS}-SW^{SI}=\frac{( s-1) (5 + 8 c - 6 c^2 - 34 s - 12 c s + 32 c^2 s + 62 s^2 - 48 c s^2 - 32 c^2 s^2 - 8 s^3 + 64 c s^3 - 32 s^4)}{(1 - 12 s + 16 s^2) (23 - 68 s + 48 s^2)}<0\),
\(\hat{SW}^{FSS}-\hat{SW}^{SS}=-\frac{( s-c)^2 (2 s-1)^2}{2 (3 s-1) (1 - 12 s + 16 s^2)}<0\).
See Appendix 2 for proof.
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We thank the editor, Prof. Justus Haucap, and anonymous referees for their helpful comments. The Corresponding Author, Seonyoung Lim, acknowledges that this Research was supported by Research Funds of Mokpo National University in 2022.
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Appendices
Appendix 1
Appendix 2
Proof of Proposition 5
Using the market equilibrium in Tables 2 and 3 of the Appendix 1, we can obtain the following results:
where \(\Theta _1=36 - 683 s + 6488 s^2 - 36032 s^3 + 120384 s^4 - 242688 s^5 + 287744 s^6 - 184320 s^7 + 49152 s^8 + c^2 (81 - 611 s + 131 s^2 + 11568 s^3 - 44752 s^4 + 74368 s^5 - 59136 s^6 + 18432 s^7) - 2 c (54 - 760 s + 5523 s^2 - 26528 s^3 + 84640 s^4 - 170880 s^5 + 206336 s^6 - 135168 s^7 + 36864 s^8)\),
\(\Theta _2=2 - 62 s + 189 s^2 + 216 s^3 - 1488 s^4 + 1920 s^5 - 768 s^6 + c^2 (7362 s - 45768 s^2 + 154800 s^3 - 309296 s^4 + 370816 s^5 - 257280 s^6 + 92160 s^7 - 12288 s^8-497) + 2 c (40 + 1205 s - 21242 s^2 + 133988 s^3 - 449872 s^4 + 896256 s^5 - 1088768 s^6 + 786432 s^7 - 307200 s^8 + 49152 s^9)\).
Proof of profit comparison under free trade regime
Proof of profit comparison between free trade and tariff policy
where \(\Theta _3=8 c^2 (3736 s^2 - 11568 s^3 + 17792 s^4 - 13568 s^5 + 4096 s^6-2-477s) - 8 c (5 + 384 s - 4786 s^2 + 22632 s^3 - 54944 s^4 + 73088 s^5 - 50688 s^6 + 14336 s^7)\).
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Choi, K., Lim, S. Vertical Strategy with Quality Differentiation in an Import-competing Market. J Ind Compet Trade 24, 16 (2024). https://doi.org/10.1007/s10842-024-00427-4
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DOI: https://doi.org/10.1007/s10842-024-00427-4