[8 marks] Question 2 . Two automobile manufacturers, 1 and 2 produce each car at the same unitary cost (cost of each car) equal to c. There is a fixed total demand of exactly 100 new cars each year. Each company must choose to sell each car at a price of either 3 or 4. If both companies choose to sell at the same price, they share the market equally i.c. each firm sells 50 cars. However, if they choose to sell at different price levels, the company that charges the lowest price sells 80 cars whereas the other company sells 20 cars. Firms make decisions simultaneously. Payoff for each firm is the profit. Find all pure strategy Nash equilibrium of this game assuming that c=1. [5 marks] b. Consider two firms (i.c. Firm A and B) competing in a market characterized by the following (inverse) demand function: P =40-Q Where Q=q, +qA is the aggregate quantity. Firm A faces the following total production costs CA(qA)=20qA while Firm B's total production cost function is: "B(48)= 98 . Compute the Cournot equilibrium quantities, price and profits for each firm. [8 marks] c. Consider two farms X and Y. They send their goats to the commons. If farm X sends x goats and farm Y sends y goats to the commons, the milk production (in kiloliters, kl) per goat is: f(x, y) = 200 -(x + y) This is the same for all goats of both farms. The total cost of milk production is 25x for farm X and 25y for farm Y. The market price of milk per k/ is 1. Show that the commons will be over-exploited. [13 marks]