The demand function for a firm’s product is Q(P) = 50-P/10. The firm’s cost of production is C(Q) = Q^3-20Q^2+125Q. The firm’s problem is to choose the value of Q≥0 that maximizes its profit. You may occasionally find an irrational number and in those cases simplify your answer as much as possible.
(a) Calculate the firm’s inverse demand function.
(b) Calculate the firm’s marginal and average cost functions.
(c) Over what range of Q does the firm have economies to scale? Over what range of Q does it have diseconomies to scale? What is the firm’s lowest possible average cost of production?
(d) Does the firm’s profit-maximization problem satisfy the global SOC?