Optimal industrial policy in vertically related markets

Abstract

This paper examines the optimal industrial policy for an industry with a vertical market structure. A home firm and a foreign firm both import an intermediate good from a third country to produce a final good. How the home country government sets the optimal industrial policy has to take account of both profit shifting between the two final good producers and between the intermediate good producer and the home firm. We explain how the optimal industrial policy depends on the slope of the demand curve, the levels of technology spillover and product differentiation. In particular, there exists a critical level of technology spillover at which investments of the firms are neither strategic substitutes nor complements and the optimal industrial policy is always investment tax.

Keywords:

• strategic trade policy
• industrial policy
• profit shifting
• vertically related markets

JEL Classifications:

• F12
• F13

Notes

1. At the time of print publication of this article, author Yao Liu's affiliation had changed to Dongbei University of Finance and Economics, 217 Jian Shan Street, Shahekou District, Dalian, 116025, China.

2. If the home country imposes an investment subsidy, it is possible that firm M can have a higher profit by foreclosing firm F. With the possibility of foreclosure, an investment subsidy helps firm H to become a monopoly. It does not follow that such a policy is optimal because rent shifting between firms H and M calls for an investment tax. A complete analysis needs to compare the profits of firm H with and without foreclosure. The results may be very different from those in this paper. The optimal policy under Cournot competition may be dominated by an investment subsidy aimed at inducing firm M to foreclose firm F.

3. It is immaterial whether firm M commits to its price or output but we assume that firm M sets the price for convenience of presentation. However, choosing output by the intermediate good producer may have a more appealing interpretation since it usually takes a long time to change production capacity especially in raw material industries.

4. A subsidy that partially defrays the cost of investment (1−s)k ²/2 where s < 1 could be a better specification. Obviously, the subsidy never exceeds the cost of investment. We can show that our results remain intact under this specification but the derivations of the results are more tedious. The analysis will be provided upon request.

5. See the appendix for the exact form of the stability condition.

6. For each ϕ ∈ [0,1], ϕ ≠ 1/2, there are two values of b satisfying s = 0. However, only one of these solutions satisfies the stability condition and the unstable solution is not shown in the diagram.

7. The derivation of the sufficient condition of the second-order condition of welfare maximization under Cournot competition as well as the corresponding condition for Bertrand competition will be provided upon request.