Question

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 yields higher social welfare? Discuss.

Short answer

This answer cannot be written in a single sentence or a number. It involves multiple step-by-step calculations. Please refer to the solution steps provided for detailed answers to each part of the exercise.

Step-by-step solution

Calculate Output and Price without Regulation Under Competitive Conditions

Given the inverse market demand function \(P=100-Q\), and the private marginal cost of production \(MC=10+Q\), equate MC = P to find the equilibrium output and price under competitive conditions. Solve the equation \(10 + Q = 100 - Q\). Find value of \(Q\) and substitute it into \(P=100-Q\) equation to find \(P\).

Determine Socially Efficient Price and Output

To find the socially efficient output, equate the inverse demand function with the social cost, which is the sum of the private cost and the external cost (\(MC+MEC\)). Solve the equation \(10 + Q + Q = 100 - Q\). Find the value of \(Q\) and substitute it into \(P=100-Q\) to find socially efficient price \(P\).

Determine Tax for Competitive Market

The tax required for the competitive market to achieve socially efficient output equals the marginal external cost (MEC) at the socially efficient output. Therefore, the tax equals \(Q\) calculated in step 2.

Calculate Output and Price Under Monopolistic Conditions

Under monopolistic conditions, the firm will set the marginal revenue (MR) equal to the marginal cost (MC). For linear demand, MR is always twice the slope of P. Calculate MR from P and set it equal to MC. Solve for \(Q\) and replace this value in \(P=100-Q\) to calculate \(P\).

Determine Tax for Monopolistic Market

To find the tax that would make the monopolistic market produce the socially efficient output, set MR equal to \(MC + tax\), where tax equals the MEC at the socially efficient output. Solve for \(Q\) and find tax by replacing this value in MEC, which in this case is the same as \(Q\).

Compare and Discuss Social Welfare Under The Two Market Structures

This requires a comparison of the market outputs, prices and associated social costs under both market structures in order to determine which structure yields higher social welfare when not regulating pollution.

Key concepts

Inverse Market Demand

The concept of inverse market demand is crucial in understanding how prices in a market are determined based on the quantity demanded. In an inverse market demand function, the price (\(P\)) is expressed as a function of quantity (\(Q\)), usually in a linear form such as \(P=100-Q\). This means that for every unit increase in quantity, the price decreases by one unit.

• The slope of the inverse demand curve is negative, indicating a typical demand scenario: as prices increase, the quantity demanded decreases.
• Understanding this relationship helps in predicting how changes in market conditions can affect prices and demand.
• Businesses use this information to set prices in competitive or monopolistic markets.

For the dry cleaning market problem, the inverse demand function plays an essential role in determining equilibrium prices under different market conditions.

Marginal Cost

Marginal cost is the additional cost incurred in producing one more unit of a good or service. It is a key factor in decision-making for producers as it affects how much they choose to supply to the market. The private marginal cost of production for the dry cleaning firms in the problem is given by \(MC=10+Q\).

• It can vary with production level due to factors such as economies of scale or increased input prices.
• Connecting marginal cost with market demand helps determine equilibrium quantity and price.
• For firms, especially in competitive markets, producing where marginal cost equals price maximizes profit.

In the exercise presented, understanding marginal cost is vital for both determining market equilibrium without regulation and deciding on socially efficient outputs when accounting for external costs.

Externalities

Externalities are costs or benefits experienced by third parties not directly involved in a transaction. They can be negative, as seen with pollution in production, leading to social costs not reflected in market prices. The marginal external cost (MEC) in the exercise is given as the pollution produced by dry cleaning, \(MEC=Q\).

• Negative externalities, like pollution, result in higher societal costs than the production costs accounted by producers.
• To achieve social efficiency, these externalities should be internalized, meaning prices should reflect these costs.
• Taxes and regulations are ways to internalize such externalities, guiding markets towards outputs and prices that reflect true social costs.

By factoring in external costs, the exercise helps to illustrate how markets can adjust to effectively manage negative externalities and promote social welfare.

Social Welfare

Social welfare refers to the overall well-being and economic efficiency achieved in society when resources are allocated optimally. In the context of market structures, it involves examining how outputs and prices influence societal well-being in the face of both private and external costs.

• Competitive markets often aim to operate where supply meets demand, potentially leading to overproduction when external costs are ignored.
• By considering externalities, adjustments can be made to market mechanics through taxes, ensuring more socially optimal quantities are produced.
• Monopolistic markets, without regulation, tend to restrict output, which may limit negative externalities but result in underproduction relative to social needs.

The exercise encourages assessing different market structures to determine which maximizes social welfare, particularly when dealing with pollution and other external costs.