a) Suppose a firm has the Cobb-Douglas the production function f(x1, x2) = x0.5x2.5 where x is the amount of factor 1 that the firm uses in the production process and X2 is the corresponding amount of factor 2. Let the price of the firm's output be p and the factor prices of good 1 and good 2 be w and w2 respectively. What is the only profit level of the firm that is consistent with long-run equilibrium? Prove your answer. [5 points] b) A firm produces y units of its output using x, units of input factor 1 and x2 units of input factor 2. The prices of factor 1 and factor 2 are w and w respectively. Find the firm's inverse supply function p(y) if the two factors of production are perfect complements i.e. f(x1, x2) = min{x1, x2). 15 points]