Question

A monopoly faces the demand curve P = 100 -.01Q, where P is price and Q is weekly production measured in cents per unit. The firm’s cost function is C = 50Q + 20,000. Assuming the firm maximizes profit,a. What is the level of production, price, and total profit per week?b. If the government decides to put a tax of 20 cents per unit ON THE BUYERS of this product, what will be the new level of production, price the buyer pays, price the monopoly receives, and profit per week?c. What is the incidence of the tax on the buyers and on the monopoly?

Answer 1

a)

Inverse demand function is given by

P=100-0.01 Q

Total Revenue=P*Q=(100-0.01Q)*Q=100Q-0.01Q²

Marginal Revenue=MR=dTR/dQ=100-0.02Q

Given, C=50Q+20000

Marginal Cost=MC=dC/dQ=50

Set MR=MC for profit maximization

100-0,02Q=50

0.02Q=50

Q=50/0.02=2500

P=100-0.01 Q=100-0.01*2500=$75

Optimal output is 2500 units and price is $75

Total Revenue per week=TR=P*Q=75*2500=187500

Total Cost per week=TC=50Q+20000=50*2500+20000=145000

Profit per week=TR-TC=187500-145000=$42500

b)

In this case, tax is on buyers, P goes to seller of (P+Tax) paid by consumer. So, new demand curve curve is given by

P+0.20=100-0.01Q

P=99.80-0.01Q

TR=P*Q=(99.80-0.01Q)*Q=99.80Q-0.01Q²

Marginal Revenue=MR=dTR/dQ=99.80-0.02Q

Set MR=MC for profit maximization

99.80-0.02Q=50

Q=(99.80-50)/0.02=2490

P=99.80-0.01Q=99.80-0.01*2490=$74.90

In equilibrium consumer effectively pays $75.10 ($74.90+$0.20). and seller gets $74.90. Optimal output is 2490 units.

Total Revenue per week=TR=P*Q=74.90*2490=186501

Total Cost per week=TC=50Q+20000=50*2490+20000=144500

Profit per week=TR-TC=186501-144500=$42001

c)

Price after tax for consumer=$75.10

Price before tax for consumer=75

Incidence of tax=75.10=75.00=$0.10