Consider a model of Cournot duopoly. Two firms produce an identical product. The inverse demand function for the product is given by p = 60 ? y, where y = y1 + y2 is the sum of the quantity produced by the two firms. Production costs are zero for both firms.

a) Find the quantity produced by each firm in the Nash equilibrium of this game. Find the price of the product and the profit of each firm.

b) Now say that marketing guru Jim has a proposal for firm 1. He would be able to convince people that the two firms' products were in fact slightly different from each other, so that the amount produced by each firm would not impact the price of the other's product as much as it did before. The inverse demand function for each product would become p1 = 60 ? y1 ? 1 2 y2 and p2 = 60 ? y2 ? 1 2 y1. What is the most that firm 1 would be willing to pay Jim? Show your work and explain in a few sentences what you did to find your answer.

3. Consider a model of Cournot duopoly. Two rms produce an identical product. The inverse demand function for the product is given by p = 60 y, where y = 3n + 312 is the sum of the quantity produced by the two rms. Production costs are zero for both rms. 3) Find the quantity produced by each rm in the Nash equilibrium of this game. Find the price of the product and the prot of each rm. b) Now say that marketing guru Jim has a proposal for rm 1. He would be able to convince people that the two rms\" products were in fact slightly different from each other, so that the amount produced by each rm would not impact the price of the other's product as much as it did before. The inverse demand function for each product would become p1 : 60 yl yg and p2 : 60 yg in. What is the most that rm 1 would be willing to pay Jim to do this? Show your work and explain in a few sentences what you did to nd your