Two firms based in the home country and one firm based in the foreign country produce the same homogenous goodand export it to a third country. The importing country does not produce the good. The foreign firm produces at the marginal cost c*. The first home firm produces at the same marginal cost as the foreign firm, that is, c1=c*; the second home firm produces at the marginal cost, c2=αc1(α>1).
Assume that the demand in the third country is linear, examine how the optimal home export tax or subsidy changes as a function of a when the other countries are free traders. Show graphically and explain.