Question

In: Economics

Given the inverse demand function of monopoly is: ?(?) = ??? − ? the cost ?...

Given the inverse demand function of monopoly is: ?(?) = ??? − ? the cost
? function of the monopoly is: ?(?) = ?? + ?? .

(i) Find the profit maximizing price and output level of monopoly and the amount of profit.
(ii) Now assume that the same inverse demand function and cost function are faced by a competitive market. Find the profit maximizing price and output level of competitive market and the amount of profit.
(iii) Calculate the consumer surplus, producer surplus and deadweight loss due to monopoly.
(iv) Assume that government imposes the monopoly a lump-sum tax of ? = $??? on total profit. How does the tax affect the profit of the monopoly?

Expert Solution

i)

Demand function is given by

P=100-Q

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

Marginal Revenue=MR=dTR/dQ=100-2Q

Cost function is given by

C=10+4Q

Marginal Cost=MC=dC/dQ=4

Set MR=MC for profit maximization

100-2Q=4

Q*=48

P*=100-Q=100-48=$52

Total Revenue=TR=P*Q=48*52=$2496

Total Cost=TC=10+4Q=10+4*48=$202

Optimal Profit=TR-TC=2496-202=$2294

ii)

In case of perfect competitive firm, Set MC=P for profit maximization

4=100-Q

Q*=96

P=MC=$4

Total Revenue=TR=P*Q=4*96=$384

Total Cost=TC=10+4Q=10+4*96=$394

Optimal Profit=TR-TC=384-394=-$10

iii)

Q	P=100-Q	MR=100-2Q	MC
0	100	100	4
20	80	60	4
40	60	20	4
48	52	4	4
60	40	-20	4
80	20	-60	4
96	4	-92	4
100	0	-100	4

In case of Monopoly,

Consumer surplus is are below demand curve but above price line. So,

CS=1/2*(100-52)*48=$1152

Producer surplus is are above MC curve but below price line. So,

PS=(52-4)*48=$2304

Dead weight loss=1/2*(52-4)*(96-48)=$1152

iv)

Lump Sum Tax of $200 will increase the fixed cost. MC of firm remains unchanged. Hence optimal output and price remains unchanged. But, profit will decline by $200.

Rahul Sunny answered 2 days ago

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