2. The demand function for a firm’s product is Q = P!3 . The firm’s marginal cos

Question

2. 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?

Explanation / Answer

Q= P-3 (The ! mark in the question is replaced by -)

a) P= Q+3

Elasticity formula = dQ/dP * P/Q = -3 * P/Q = -3 *(Q+3)/Q or (-3-9/Q)

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