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The assignment is due during class 7 at the beginning of class. Return your HAND- WRJTTEN assignment in class. Team work on assignments is allowed and encouraged. There is no minimum team size (i.e., you can work individually if you prefer}, but the maximum team size is 5. Please clearly indicate the names of the team members on the front page of the assignment. Problem 1 Consider a market with only 2 rms that compete on the quantity sold. We use the Cournot model of duopoly to model this scenario. The inverse demand curve of the market is given by p=100q Where 30 indicates the market price, (1 = q1 + qg is the market quantity, (11 indicates the quantity sold by rm 1 and q; is the quantity sold by rm 2. Firms have the same total cost function T01 = 1013] T02 10132 A. Compute the CournotrNash equilibrium of the game between the two rms. How much does each rm produce in equilibrium? What is the equilibrium price? What is the prot of each rm? B. The scientist Sheldon Cooper developed a new machine to produce the good, which would decrease variable cost of production. Sheldon approaches the manager of Firm 1, to sell his innovation. If Firm 1 buys the innovation, its total variable cost of production will be W01 2 5th Sheldon asks for a price of F = 200 to sell his product. So if Firm 1 wants to use the innovation, it must spend 200. Consider the following game. Before starting the Cournot game, Firm 1 can buy Sheldon's invention, spending F = 200, and its total cost function will be T01 : 200 + 5q1. If Firm 1 does not buy Sheldon's machine, its cost is the same as in Part A, i.e. T01 : 10111. Firm 2 does not have this possibility. Solve this game by backward induction. What are the equilibrium quantities, price and prots of the rms