The demand function for a firm’s product is Q = P!3 . The firm’s marginal cost of production is constant at MC(Q) = 12.
(a) Calculate the elasticity of demand, as a function of Q.
(b) Does the firm’s profit maximization problem satisfy the global SOC?
(c) Using your answers to (a) and (b), what is the firm’s profit-maximizing markup? (Justify your answer carefully. Do not forget about the possibility of a boundary solution.)
(d) Based on your answer to (c), what is the firm’s profit-maximizing price?
(e) Based on your answer to (d), what is the firm’s profit-maximizing quantity?