Question

2. (16 points) Monopoly and Bertrand opoly and Bertrand Duopoly. In a monopoly market, the de mand is p = 240 - 20. The firm's cost function is: for Q>O, C(Q) = 40 (a) Find the monopoly quantity and price.. Q = and PM = (b) Find the deadweight loss in the monopoly model. DWL = (c) If instead there are two identical firms that compete according to Bertrand price competition, is the equilibrium price? Pi = p = ____ (d) What is the deadweight in the Bertrand equilibrium? DWL =_

Answer 1

Inverse Demand: P=240-2Q and cost : C(Q) = 40Q

A)

Revenue = Price*Quantity; Revenue = (240-2Q)Q

Marginal Revenue: 240-4Q

The Marginal Cost: MC(Q) =40

For a monopoly Put: MR=MC and slove for Q

240-4Q = 40 => Q* = 50 and the monopolist price would be: P* = 240-2*50 = 140 ; P*=140

b)

the dead weight loss: Lets solve for P coordinates and Q values: P=MC ; 240-2Q = 40 => Q=100

Dead Weight Loss= (1/2)(100-50)(140-40)

Dead Weight Loss= 2500

Under Monopoly P=240-20 DWL = (1/2)(100-50)(140-40) = 2500 140 40 P=MC=40 50 100

c)

For a bertrand competition:

Bertrand Price would be: P1 = P2 = MC

as they are both identical so the optimal price they can charge is only MC... so they both do not have any incentive to deviate. As any firm charging more would loose all market.

d)

There would be Zero Dead Weight Loss in Bertrand equilibrium.

Under Bertrand P=240-20 DWL = 0 40 P=MC=40 100