International trade and domestic distortions

Abstract

When full competition prevails in product, labor, and capital markets, positive or negative external trade shocks may be accommodated by the migration of jobs between sectors; the negative impact on some households’ income of lower nominal wages will be more than offset by lower prices of imported final goods. Unemployment, if any, will be temporary, unless labor market rigidities prevent the necessary adjustment. By contrast, we argue that trade shocks trigger a process of creative destruction that necessarily causes distortions in the structure of productive capacity and, hence, market disequilibria. Therefore, the structural change that follows trade shocks can no longer be analyzed within an equilibrium framework. The transition following a shock may be characterized by increasing imbalances, and create scope for policy intervention. The model presented in this paper, which focuses on the time dimension of production and market imbalances, allows us to clarify the debate.

Appendix: Proof of propositions

Proof of Proposition 1   $\frac{d\alpha}{dW_{a}}>0$ and $\frac{d\alpha}{dW_{b}}<0.$

Proof

$\frac{d\alpha}{dW_{a}}>0:$

$$ \begin{array}{c} \left( \dfrac{\sqrt{\xi_{b}}}{\sqrt{\xi_{a}}}\left( 1-\gamma+\gamma \delta\right) -\dfrac{\sqrt{\xi_{a}}}{\sqrt{\xi_{b}}}\gamma(1-\delta)\right) >0\\ \iff\\ \xi_{b}\left( 1-\gamma+\gamma\delta\right) -\xi_{a}\gamma(1-\delta)>0 \end{array} $$

Substituting:

$$ \begin{array}{rll} &&\left( \left( 1-\gamma\delta\right) W_{b}+\gamma\left( 1-\delta\right) W_{a}\right) \left( 1-\gamma+\gamma\delta\right) \\ &&\quad -(\gamma-\gamma\delta)\left( \gamma\delta W_{b}+\left( 1-\gamma\left( 1-\delta\right) \right) W_{a}\right) \\ &&\quad=\allowbreak W_{b}(1-\gamma)>0 \end{array} $$

$\frac{d\alpha}{dW_{b}}<0:$

$$ \begin{array}{c} \left( \dfrac{\sqrt{\xi_{b}}}{\sqrt{\xi_{a}}}\gamma\delta-\dfrac{\sqrt{\xi_{a} }}{\sqrt{\xi_{b}}}(1-\gamma\delta)\right) <0\\ \iff\\ \left( \xi_{b}\gamma\delta-\xi_{a}(1-\gamma\delta)\right) <0 \end{array} $$

Substituting:

$$ \begin{array}{rll} && \left( \left( 1-\gamma\delta\right) W_{b}+\gamma\left( 1-\delta\right) W_{a}\right) \gamma\delta\\ & &\quad-(1-\gamma\delta)\left( \gamma\delta W_{b}+\left( 1-\gamma\left( 1-\delta\right) \right) W_{a}\right) \\ & &\quad =(\gamma-1)W_{a}<0 \end{array} $$

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Proof of Proposition 2   $\frac{d\pi_{a}}{dW_{a}}>0$ and $\frac{d\pi_{a}}{dW_{b}}>0.$

Proof

Equilibrium profit can be defined, from Eqs. 7 and 8a:

$$ \pi_{a}(=\pi_{b})=\frac{\xi_{a}}{\alpha^{2}}=\frac{\left( \sqrt{\xi_{b} }+\sqrt{\xi_{a}}\right) ^{2}}{N^{2}} $$

As ξ _a and ξ _b are positively affected by both W _a and W _b , we conclude that any increase in external demand increases equilibrium profits. □