Consider two countries, A and B, each with a monopolist that owns the only active coal mine in the country. Let Firm 1 be the one located in country A, and Firm 2 the one in country B. Let qj for i=1,2, j = A, B denote the quantity that Firm i sells in country j. Let q, be the total quantity produced by firm i, and let Q, be the total quantity sold in country j. The inverse demand (i.e., unit sales price) for coal in country j is given by d, = 90 - Q and the cost of production for Firm i is given by c.(q) = 10q (a) Assume that the countries do not have a trade agreement and no importation of coal from another country is allowed. What are the values of 924 and qua? What are the values of q14 and 928? Justify your answers. (b) Now suppose that countries A and B sign a free trade agreement that allows for- eign firms to sell coal in a country without tariffs. There are shipping costs. If Firm i sells q where j is not the home country then the cost to ship is 100. Assuming that the firms announce their production quantities simultaneously. What are the pure strategy Nash equilibria? (Reminder: a strategy profile consists of four components.) You will need to use partial derivatives to answer this question.