Strategic export policies
Here, x and y are the quantities of the home and foreign goods in the third country. β is a positive constant, and γ denotes the degree of product differentiation. If 0 < γ < β, the goods are substitutes. On the other hand, if –β < γ < 0 they are complements, and if γ = 0 they are independent. The home firm’s profit with a specific subsidy s offered by the home government is
π = ( p – c + s)x = (α – βx – γ y – c + s)x,
where c is the home firm’s constant marginal cost. Similarly, the foreign firm’s profit is
π* = (q – c*)y = (α – βy + γ x – c*)y.