Consider two countries each with a monopolist that owns the only line of production of a hand sanitizer 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 the hand sanitizer in countries 1 and 2 is given by p^j = a - q^j, j {1,2}.Thefirmshavenofixedcostsofproduction,andidenticalconstant marginal cost of production 0< c < a.

(a)Assume,first,that the countries have a free trade agreement,so that the firms are free to sell the hand sanitizer both in the domestic and foreign countries without any tariffs, and the shipping costs are negligible.Assume further, that firms make their choices of pairs of quantities q¹_i, q²_i simultaneously.What output quantities will the firms choose in equilibrium?

(b)What is the total output in each country? What are the equilibrium prices?What are the firms' equilibrium profits?

(c)Assume now that due to an outbreak of a pandemic, the government ofeachcountrywouldprefertoreducetheexportsofthe hand sanitizer.In order to induce the firms to produce more for the domestic country, the governments subsidize domestic (but not foreign production) by reducing the average cost of production by s > 0.As before, assume that firms make their choices of pairs of quantities q¹_i, q²_i simultaneously.What output quantities will the firms choose in equilibrium?

(d)Derive the lower bound on the subsidy s that ensures no export.