Question

(a) Consider a monopoly market with the following demand equation for a good Z.

P = 100 – 0.2 Q

Suppose fixed cost is zero and marginal cost is given by MC = 20.

Answer the following questions.

(i) Based on the information given, draw the diagram which shows the marginal revenue (MR) curve, marginal cost (MC) curve and the demand (D) curve of the monopoly. Show the value of X and Y intercepts for these curves.

(ii) Explain why the monopoly will not produce along the lower half of the demand curve.

(iii) Calculate the profit-maximizing price (P_M) and quantity (Q_M) of the monopoly in the market. Show P_M and Q_M in the diagram in part (i) and show your calculations in the spaces below.

(iv) Calculate the profit earned by the profit-maximizing monopoly. Show your calculation in the spaces below.

(v) Calculate the consumer surplus (CS) and producer surplus (PS) of the monopoly and the resulting deadweight loss (DWL). Show CS, PS, and DWL in your diagram in part (i).

(vi) Calculate the market equilibrium (i.e. P_PC and Q_PC) that maximizes social surplus. Calculate producer surplus (PS) and consumer surplus (CS) for this case. Show your calculations in the spaces below.

Answer 1

A) i) MR curve slope is double to that of Demand curve

So MR = 100 -.4Q

Graph

ii) in the lower half of the demand curve, demand is in-elastic, & Monopolist never operates on in-elastic portion of demand Curve

also in lower half, MR is negative, but MC is always positive,

so at monopoly eqm, MR should equal MC,which is not possible in lower half portion of demand curve .

.

iii) at monopoly eqm

MR = MC

100-.4Q = 20

.4Q = 80

Q* = 200

PM = 100- .2*200 = 60

graph

.

iV) π = (PM - MC)QM

= (60-20)*200

= 40*200

= 8,000

v) CS = .5*(100-60)*200

= .5*40*200

= 4000

PS = π = 8,000

( With constant MC , PS = π)

DWL = .5*(60-20)*(400-200)

= .5*40*200

= 20*200

= 4,000

graph

.

Vi) P= MC

100-.2Q = 20

Q* = 80/.2 = 400

QPC = 400

PPC = 20

CS = .5*(100-20)*400 = 40*400

= 16,000

PS = 0