Question

In: Economics

​​​​ Suppose that dry cleaning market is perfectly competitive. In a market for dry cleaning, the...

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  1. Suppose that dry cleaning market is perfectly competitive. In a market for dry cleaning, the inverse market demand function is given by P = 300 -3 Q and the (private) marginal cost of production for the aggregation of all dry-cleaning firms is given by MC = 15 + 2Q Finally, the pollution generated by the dry-cleaning process creates external damages given by the marginal external cost curve MEC = Q.
    1. Without regulation, what are the profit-maximizing price and quantity?
    2. Determine the socially efficient price and quantity.
    3. Assume the government addresses the pollution problem by implementing a 80 cents tax per unit. Does the tax policy achieve the goal of socially efficient allocation of resources? Explain why or why not.
    4. Suppose now that the market is monopolistic instead of perfectly competitive. What are the socially efficient price and quantity?

Solutions

Expert Solution

a)

Set MC=P for profit maximization in case of perfectly competitive market

15+2Q=300-3Q

5Q=285

Q=285/5=57

P=300-3Q=300-3*57=$129

Without regulation, profit maximizing price is $129 and quantity is 57 units.

b)

In this case

MSC=MPC+MEC=15+2Q+Q=15+3Q

Set MC=P for profit maximization in case of perfectly competitive market

15+3Q=300-3Q

285=6Q

Q=285/6=47.50

P=300-3P=300-3*47.50=157.50

Socially efficient price is $157.50 and quantity is 47.50 units.

c)

Marginal private cost will increase by $0.80 for each in this case

MC'=15+2Q+0.80=15.80+2Q

Set MC'=P for profit maximization in case of perfectly competitive market

15.80+2Q=300-3Q

284.20=5Q

Q=284.20/5=56.84

P=300-3Q=300-3*56.84=$129.48

New equilibrium price is $129.48 and quantity is 56.84 units. We can see that output is quite different from socially efficient combination. So, tax policy does not achieve the goal of socially efficient allocation of resources.

d)

In case of monopoly, socially efficiency cannot be achieved as P is not same as MSC. Monopolist chooses the output level such that MR=MSC.

However monopolist maximizes its profit by selecting output level such that MR=MSC

Given P=300-3Q

Total Revenue =TR=P*Q=(300-3Q)*Q=300Q-3Q2

MR=dTR/dQ=300-6Q

Equate MR=MSC for profit maximization in case of monopoly.

300-6Q=15+3Q

285=9Q

Q=31.6667

P=300-3Q=300-3*31.6667=$205

But this is not socially efficient output and price combination.


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