Consider two countries each with a monopolist that owns the only line of production of computer chips in the country. Let firm 1 be located in country 1 and firm 2 be located in country 2. Let q^j_i (i {1, 2}, j {1, 2}) denote the output quantity sold by firm i in country j. Consequently, we denote by q_i = q¹_i + q²_i the total output produced by firm i {1, 2}, and by q^j = q^j₁ +q^j₂ the total quantity sold in country j {1, 2}. The demand for computer chips in countries 1 and 2 is given by p^j = a q^j , j {1, 2}. The firms have no fixed costs of production, and identical constant marginal cost of production 0 < c < a. 3 (a) Assume, first, that the importation of computer chips into either country is prohibited because of a danger of spyware. This implies that q¹₂ = q²₁ = 0 is set as a political constraint. What quantities q¹₁ and q²₂ will the firms produce?

(b) At what prices will the firms sell their output? What are the firms' profits?

(c) Assume now that each of the countries decided that the threat of spyware is not significant, so that the firms are allowed to sell computer chips in a foreign country. However if a firm sells in a foreign country, it has to pay a tariff 0 < t < a c per each unit of output sold. Assume further, firms make their choices of pairs of quantities q¹_i , q²_i (i = 1, 2) simultaneously. What output quantities will the firms choose in equilibrium?

(d) Derive the upper bound on the tariff t that ensures that the countries trade with each other.