Suppose that only two firms supply the market and each firm chooses its output in period t + 1 to maximize profit in the belief that the other firm will maintain its output level at the period t value. Let the demand function be p(x + y) = 126-(x + y) Now suppose the firms have cost functions given by 1 C(x) = x, C(y) = y (i) Derive the linear second order difference equation. (5 marks) (ii) Given x(0) = 28 and x(1) = 56, solve the difference equation for x. (10 marks)