Chapter 18: Problem 7

In a market for dry cleaning, the inverse market demand function is given by \(P=100-Q\), and the (private) marginal cost of production for the aggregation of all dry-cleaning firms is given by \(\mathrm{MC}=10+Q\) Finally, the pollution generated by the dry cleaning process creates external damages given by the marginal external cost curve \(\mathrm{MEC}=Q\) a. Calculate the output and price of dry cleaning if it is produced under competitive conditions without regulation. b. Determine the socially efficient price and output of dry cleaning. c. Determine the tax that would result in a competitive market producing the socially efficient output. d. Calculate the output and price of dry cleaning if it is produced under monopolistic conditions without regulation. e. Determine the tax that would result in a monopolistic market producing the socially efficient output. f. Assuming that no attempt is made to monitor or regulate the pollution, which market structure vields higher social welfare? Discuss.

Short Answer

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a) In a competitive market without regulation, dry cleaning output is 45 and price is 55. b) The socially efficient output is 30 and the price is 70. c) The tax that would result in a competitive market producing the socially efficient output is 30. d) Under monopolistic conditions without regulation, the output is 30 and price is 70. e) The tax that would result in a monopolistic market producing the socially efficient output is 30. f) In the absence of regulation of pollution, a monopolistic market provides higher social welfare as it produces less than or equal to the socially efficient level, thereby causing less pollution.

Step by step solution

Part a: Calculate Competitive Output and Price

In a competitive market, firms set the private Marginal Cost (MC) equal to the price. So, \(P = MC\), inserting given values \(100 - Q = 10 + Q\). Solving this we get \(Q = 45\) and \(P = 55\) .

Part b: Determine Socially Efficient Price and Output

In a socially efficient outcome, the social cost (private MC + MEC) is equal to the price. So, \(P = MC + MEC\), inserting given values \(100 - Q = 10 + Q + Q\). Solving this we get \(Q = 30\) and \(P = 70\).

Part c: Determine the Tax for Competitive Market Efficiency

The tax required to bring the competitive market to social efficiency is the difference between the private MC and the social cost at the socially efficient point. Thus, we get \(\text{Tax} = MEC(Q) = Q = 30\) .

Part d: Calculate Monopolistic Output and Price

Under monopolistic conditions without regulation, the firm equates Marginal Revenue (MR) to Marginal Cost (MC). MR is calculated by deriving the revenue function which is \(P*Q = (100 - Q)*Q\), giving \(MR = 100 - 2Q\). Setting this equal to the marginal cost \(MC = 10 + Q\) gives \(Q = 30\), and \(P = 70\).

Part e: Determine the Tax for Monopolistic Market Efficiency

The same approach used in part c is applied in part e. The tax is equal to the marginal external cost (MEC) at the point which the social cost equals the price. Thus, we get \(\text{Tax} = MEC(Q) = Q = 30\).

Part f: Discuss Which Market Structure Provides Higher Welfare

Without regulation of pollution, competitive markets often produce a higher amount of output compared to the socially efficient level, as in this case (45 vs 30). Conversely, monopolistic markets, tend to produce less than or equal to the socially efficient level (30 in this case). Therefore, in the absence of pollution regulation, the monopolistic market may provide higher social welfare as it restricts production, thus creating less pollution.