Question

You have the following information about a monopolist

p = 20 - 2q (1)

MR = 20 - 4q (2)

MC = 8 (3)

where equation (1) denotes the monopolist demand curve, equation (2) denotes its the marginal revenue function, and equation (3) is the marginal cost, assumed to be constant here. (i) Use the Lerner index to approximate the degree of monopoly power. (ii) Calculate the deadweight loss.

Answer 1

(I) For Finding Quantity of monopoly And Price of monopoly we need to equate MR=MC

ie. 20-4q= 8

4q= 12

q _m= 3--------------------------- (1) where q_m denotes the quantity of monopoly market

P_m= 20-2q

= 20- 2x3

P_m= 14 ------------------------(2) Where P_m denotes price of monopoly market

Lerner Index= (P - MC)/ P

= (14-8)/14

= 6/14

= 0.428

(II) For deadweight loss, we require the Quantity of Competitive Market

For q_c

_{Put MC equal to Demand Curve}

_Ie., 20-2q= 8

solve for q

therefore, q_{c= 6}

DeadWeight Loss= 1/2(P-MC) x ( q_c- q_m)

= 1/2 (14 - 8) x (6 - 3)

= 1/2 x 6 x 3

= 9

Shaded region shows the deadweight loss in the graph.