Question Three a] Consider the problem of maximising profits for the production function of the form f (x) = x where x is the input bought at the price of w. i) Determine the firm's profit function and factor demand function. ii) Derive the supply function. iii) Show and explain the returns to scale of the firm's production function. b) Suppose that the market demand function for a commodity is p = a - Bq and the cost function of producing the commodity is c(q) = vq - 8q2, where a, B. V. & > 0. Assume that the firms are competitive and identical. A = Pf (x) - wx i) Find the long-run equilibrium market price and quantity. ii) Find the number of firms in the market. 1 = pxe - wie