Question

suppose that the inverse demand function, marginal revenue, marginal cost and total cost for a gizmo product produced by a monopolist are as follows

p=100 -2Q

MR= 100-4Q

MC=2

TC=10+2Q

a. Find the monopolist's profit maximizing output and price.

b. Calculate the monopolist's profit/loss ,if any

c. What is the Lerner Index for this industry

Answer 1

Profit Maximizing Condition :

MR = MC

where MR = marginal Revenue = d(TR)/dQ = d(p*Q)/dQ = 100 - 4Q, TR = Total revenue = p*Q

MC = d(TC)/dQ = 2

Thus, MR = MC => 100 - 4Q = 2 => Q = 24.5 => p = 100 - 2*24.5 = 51

Hence, Profit maximizing Output(Q) = 24.5 and Profit maximizing price(p) = 51

(b)

Profit = TR - TC = p*Q - TC

=> Profit = 51*24.5 - (10 + 2*24.5) = 1190.5

Hence, Profit = 1190.5

(c)

Lerner Index = (p - MC)/p

Here p = 51 and MC = 2

Thus, Lerner Index = (51 - 2)/51 = 0.96

Hence, Lerner Index = 0.96