Government Intervention Brings About Free-Trade Outcomes in the Long Run

Abstract

We examine the long-run effect of government intervention on economic outcomes in an importing country in a three-country framework with free entry of the importing country’s firms. We establish the following. [1] The long-run equilibrium total output (or price) level under government intervention regime is the same as that under the free-trade regime. Without the imposition of a tariff, the importing country’s welfare is unaffected by any level of export subsidy. [2] In the long-run equilibrium, each exporting country’s government sets a positive subsidy level such that each exporter can attain the equilibrium outcome when it adopts marginal cost pricing.

Appendix

1.1 A. Derivation of (7.7)

From (7.2), we have p − c′ = −p′q _j − s _j . Substituting this into (7.6) yields

$$ \displaystyle\begin{array}{rcl} p'q_{j} \frac{\partial Q} {\partial s_{j}} - (\,p'q_{j} + s_{j})\frac{\partial q_{j}} {\partial s_{j}} = 0.& & {}\\ \end{array} $$

The above equation can be translated into

$$ \displaystyle\begin{array}{rcl} p'q_{j}& & \left [n_{j}\frac{\partial q_{j}} {\partial s_{j}} + n_{k}\frac{\partial q_{k}} {\partial s_{j}} + n_{3}\frac{\partial q_{3}} {\partial s_{j}}\right ] - (\,p'q_{j} + s_{j})\frac{\partial q_{j}} {\partial s_{j}} = 0 \\ p'q_{j}& & \left [n_{k}\frac{\tfrac{\partial q_{k}} {\partial s_{j}} } {\tfrac{\partial q_{j}} {\partial s_{j}}} + n_{3}\frac{\tfrac{\partial q_{3}} {\partial s_{j}}} {\tfrac{\partial q_{j}} {\partial s_{j}}}\right ] - s_{j} + n_{j}p'q_{j}\left (1 - \frac{1} {n_{j}}\right ). {}\end{array}$$

(A7.1)

From (A7.1), we easily derive (7.7).