Abstract
We investigate the welfare effect of an export subsidy/tax in the “third market” trade model. The conventional wisdom is that an export subsidy increases home welfare in a Cournot setting (Brander and Spencer 1985) and an export tax increases home welfare in a Bertrand setting (Eaton and Grossman 1985). By allowing firms to compete in a Cournot-Bertrand duopoly model where one firm competes in output and the other competes in price, we are able to show that the conventional wisdom is incomplete. Optimal trade policy does not depend simply on whether firms compete in a Cournot or Bertrand type game. It only depends on whether the foreign firm competes in output or price.
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Notes
This reflects the Kreps and Scheinkman (1983) contribution that when price (capacity) can adjust more quickly than capacity (price), then the Cournot (Bertrand) outcome will be reached. Maggi’s main contribution is to show that when capacity can serve as a commitment device, a subsidy on the home firm’s capacity is optimal whether firms compete in a Cournot or a Bertrand setting.
W is indirectly a function of s, because a i is a function of s. Collie (2002) allows for a tax distortion by adding parameter \( \lambda \ge 1 \) to the welfare function. In his specification, \( W\left({a}_h,\;{a}_f\right)={\pi}_h\left({a}_h,\;{a}_f,\;{s}_i\right)-\lambda s{q}_h\left({a}_h,\;{a}_f\right) \). When \( \lambda =1 \), there is no tax distortion. When \( \lambda >1 \), there is an added deadweight loss due to tax distortions and the optimal s approaches zero as \( \lambda \) increases.
The details of this derivation are as follows. Given firm h’s first-order condition (\( \partial {\varPi}_h/\partial {a}_h=0 \)) and given that welfare is a direct function of \( {a}_h \) and \( {a}_f \), the total differential of W is: \( dW=\frac{\partial {\pi}_h}{\partial {a}_h}d{a}_h+\frac{\partial {\pi}_h}{\partial {a}_f}d{a}_f= \) \( \left(\frac{\partial {\varPi}_h}{\partial {a}_h}-s\frac{\partial {q}_h}{\partial {a}_h}\right)d{a}_h+\frac{\partial {\pi}_h}{\partial {a}_f}d{a}_f=-s\frac{\partial {q}_h}{\partial {a}_h}d{a}_h+\frac{\partial {\pi}_h}{\partial {a}_f}d{a}_f \). Setting this to zero and solving for s gives the optimal subsidy: \( {s}^{*}=\frac{\partial {\pi}_h}{\partial {a}_f}\frac{d{a}_f}{d{a}_h}\frac{\partial {a}_h}{\partial {q}_h} \).
These results are also described in Feenstra (2004, 286–293).
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Acknowledgments
We would like to thank Patrick Emerson, Rolf Färe, Todd Pugatch, Carol Tremblay, and two anonymous referees for helpful comments on an earlier version of the paper.
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Schroeder, E., Tremblay, V.J. A Reappraisal of Strategic Trade Policy. J Ind Compet Trade 15, 435–442 (2015). https://doi.org/10.1007/s10842-015-0195-7
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DOI: https://doi.org/10.1007/s10842-015-0195-7