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Consider two rms supplying for the market for a homogenous good. Let x and y be the output of each rm. Both rms have identical cost structure: xed cost is 4 and marginal cost is 4. The demand curve for the good is P = 100 Q, where P is the price and Q is the total supply of the market. Model these two rms as the Cournot duopolists with discrete time periods (t = O, 1, 2, ) so that each rm assumes the other rm's output of the previous period xed. a. Write down the prot of the rst rm for the period t+1 as a function of Jew and y. b. Write down the prot maximization condition for the rst rm in terms of 2m; and y,. c. With the prot maximization conditions of the two rms, form a system of difference equation. Determine the steady state of the system. (1. Solve the system of difference equation. e. When the initial conditions are x0 = y0 = 36, determine the constants of the solution. Will it converge