If the inverse demand curve a monopoly faces is P = 100 - 2Q, and MC is constant at 16, then the firm's Lerner index equals:

a. 58/16

b. 42/58

c. 58/42

d. 16/42

The answer is b: 42/58

We find the profit maximizing quantity and price by equating MR=MC:

• P=100−2QTR=P∗Q=(100−2Q)QTR=100Q−2Q2MR=TR(Q)′=100−4QP=100−2QTR=P∗Q=(100−2Q)QTR=100Q−2Q2MR=TR(Q)′=100−4Q

• MR=MC100−4Q=164Q=84QM=21PM=100−2(21)=58MR=MC100−4Q=164Q=84QM=21PM=100−2(21)=58

The Lerner index at the profit maximizing price and quantity is calculated as:

• L=P−MCPL=58−1658L=4258L=P−MCPL=58−1658L=4258

Hence the Lerner index at the profit maximizing price and quantity equals 42/58