Question

The manager of a local monopoly estimates that the elasticity of demand for its product is constant and equal to -3. The firm’s marginal cost is constant at $35 per unit.

a. Express the firm’s marginal revenue as a function of its price.

Instruction: Enter your response rounded to two decimal places.

MR = ____________________ × P


b. Determine the profit-maximizing price.

Instruction: Use the rounded value calculated above and round your response to two decimal places.

$ __________________________

Answer 1

a) Elasticity of demand = (dQ/dP) x (P/Q)

(dP/dQ) x Q = P / Elasticity of demand

Total Revenue = price x quantity = P x Q

Marginal Revenue = P + [Q x (dP/dQ)]

Putting the value of (dP/dQ) x Q = P / Elasticity of demand in the equation of marginal revenue above,

Marginal Revenue = P + [P / Elasticity of demand]

= P - P/3 since elasticity of demand = -3

So, marginal revenue = P - P/3 = P ( 1 - 1/3) = 2P/3 is the answer or (2/3) x P is the answer.

b) According to Lerner index of monopoly power,

(P - MC) / P = 1 / elasticity of demand

(P - 35) / P = 1 / 3

3P - 105 = P

3P - P = 105

2P = 105

P = 105/2 = 52.5 is the answer. This is the profit maximizing price which can be calculated by equating marginal revenue with marginal cost also. That is , 2P/3 = 35, P = 105/2 = 52.5.