A monopoly has the following demand, marginal revenue, total cost, and marginal cost curves:

Demand P=1000−10QP=1000−10Q

MR=1000−20QTC=100Q+5Q2MC=100+10QMR=1000−20QTC=100Q+5Q2MC=100+10Q

a. Find the price and quantity that maximizes the monopoly's profits,

b. How many profits does the monopoly make at the profit-maximizing level of quantity?

c. How much output would a perfectly competitive market produce? What price would it charge?

d. Calculate the deadweight loss from monopoly.

a. Find the price and quantity that maximizes the monopoly's profits,

A profit-maximizing monopoly produces the quantity where MR=MC

• 1000−20Q=100+10Q900=30QQM=30PM=1000−10(30)=7001000−20Q=100+10Q900=30QQM=30PM=1000−10(30)=700

The price that maximizes the monopoly's profits is P=700 and the quantity that maximizes the monopoly's profits is Q = 30.

b. How many profits does the monopoly make at the profit-maximizing level of quantity?

• π=TR−TCTR=P×Q=700×30=21,000TC=100(30)+5(30)2=7,500π=21,000−7,500=$13,500π=TR−TCTR=P×Q=700×30=21,000TC=100(30)+5(30)2=7,500π=21,000−7,500=$13,500

Profits the monopoly make at the profit-maximizing level of quantity is $13,500

c. How much output would a perfectly competitive market produce? What price would it charge?

A perfectly competitive market produces at the quantity where P=MC

• 1000−10Q=100+10Q900=20QQC=45PC=1000−10(45)=5501000−10Q=100+10Q900=20QQC=45PC=1000−10(45)=550

A perfectly competitive market produces at Q = 45 and P = 550.

d. Calculate the deadweight loss from monopoly.

• • • The deadweight loss is represented by the area of the triangle between the demand curve and the marginal-cost curve.

At profit-maximizing quantity, the marginal cost is MCM=100+10(QM)=100+10(30)=400MCM=100+10(QM)=100+10(30)=400

The deadweight loss from monopoly is given by:

• DWL=12(PM−MCM)(QC−QM)DWL=12(700−400)(45−30)DWL=12(300)(15)DWL=2,250