Question

A monopoly faces the following inverse demand function: p(q)=100-2q, the marginal cost is $10 per unit.

What is the profit maximizing level of output, q*

What is the profit maximizing price

what is the socially optimal price

What is the socially optimal level of output?

What is the deadweight loss due to monopoly's profit maximizing price?

Answer 1

The profit is maximized wher Marginal revenue is equal to the marginal cost.

p=100-2q
TR=pq
TR=(100-2q)q
MR=dTR/dq
MR=100-4q

MC=10
MC=MR
10=100-4q
4q=100-10
4q=90
q*=22.5

p=100-2q
p*=100-2(22.5)=55

socially optimum level would be where P=MC
100-2q=10
2q=90
q=45(socially optimum quantity)

p=100-2q
p=100-2(45)=10(socially optimum price)

Deadweight loss=0.5*(Pm-MC)*(Qc-Qm)

Here Pm=Monopoly price
MC=marginal cost
Qc=quantity produced by competitive fimr
Qm=quantity produced by monopoly

Deadweight loss=0.5*(55-10)*(45-22.5)

Deadweight loss=506.25