Environmental Economics, EEP101/ECON125 Problem Set 4 Spring 2024

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Environmental Economics, EEP101/ECON125

Problem Set 4

Spring 2024

Problem set 4 covers core concepts from (you guessed it!) module 4. Internalities will be covered on the next problem set.

Part I. Market power and externalities When firms have market power (monopoly power), this represents an additional market failure. This can interact with an externality so that the Pigouvian prescription requires modification.

1. True/False: When a monopolist sells a good that creates a negative externality, it is possible that social welfare is maximized when the government introduces a subsidy for the good. (1 point, no explanation required)

# True

# False

2. True/False: When a monopolist sells a good that creates a positive externality, it is possible that social welfare is maximized when the government introduces a tax (not a subsidy) for the good. (1 point, no explanation required)

# True

# False

3. True/False: When a monopolist sells a good that creates a negative externality, it is possible that adding a tax equal to the marginal externality will cause an increase in deadweight loss as compared to having no tax at all. (1 point, no explanation required)

# True

# False

This problem asks you to solve an algebra problem for a case where there is a negative externality and a second market distortion due to market power. Albany-Berkeley Clinker (ABC), LLC is the monopoly provider of ready mix concrete in East Bay. The factory can produce a bag of concrete for a constant marginal cost of $8. Monthly demand for concrete is equal to Qd = 40, 000 − 2, 000P. Suppose that each bag of concrete causes $2 worth of social damages due to air pollution from the ABC plant.

4. Write out an equation for the monopolist’s marginal revenue curve (MR as a function of Q). (0 points; this won’t be graded, but you will need this to do other steps)

5. Assuming there is no policy, what quantity will the monopolist choose to maximize profits? (1 point)

6. What is the socially efficient quantity? (You only need to report the numerical answer, but look at the values and ask yourself whether the monopolist is providing too much or too little of the good as compared to the socially efficient quantity, remembering that the answer could go either way.) (1 point)

7. What is the deadweight loss in the case of no policy? (1 point)

8. Would this deadweight loss go up or down if we applied the Pigouvian prescription directly (i.e., added a tax of $2 per unit)? (1 point)

# Deadweight loss would rise if the tax were $2 (as opposed to no tax)

# Deadweight loss would fall if the tax were $2 (as opposed to no tax)

9. What is the optimal tax rate per bag of concrete? (If it is a subsidy, write the answer as a negative tax rate; i.e., t ∗ = −5 is a $5 subsidy.) (1 point)

Part II. The Diamond model

There are 6 Wonka Candy factories clustered into an industrial zone upwind of a city. Each factory emits 1 unit of Happy Joy into the air for each pallet of Wonka Bars it produces. These Happy Joy emissions travel to the city and cause benefits (a positive externality) to two groups of city residents. The first are school children, who receive $4 worth of extra hap-piness for each unit of emissions. The second group are nursing home residents, who receive $20 worth of extra joy for each unit of emissions.

10. True or False: The Diamond model indicates that if the government can place a uniform subsidy on each factory per unit of emissions, the resulting allocation will not be fully efficient (it will only be “second best”) because the externality benefits are heterogeneous. Explain briefly. (1 point)

# True

# False

11. According to the principle of targeting, would we rather pay factories a subsidy per unit of Happy Joy emitted or per unit of Wonka Bars sold? Briefly explain why, perhaps by giving an example of why the other option might be less efficient given something you invent about the nature of the production process. (2 points; 1 for multiple choice, a second for explanation)

# Better to subsidize Happy Joy

# Better to subsidize Wonka Bars

# It does not matter, they are the same thing

We introduced the Diamond model as a case where the Pigouvian prescription needs to be amended. This problem walks you through a closely related problem. In class, we motivated the model thinking about heterogeneous consumers, but here I ask you to think about two different firms.

Two local mines, named Asscher and Oval, extract identical diamonds. Suppose that the mines are small operations and are therefore price takers in the global diamond market, where the price per unit is currently $30. The Asscher mine is located in a low population part of Napa County where the mine creates an externality by using up fresh water supplies. The private cost of Asscher extraction is equal to T CA = 0.5Q2 A, while the total social damages from water use are equal to T EDA = QA. The Oval mine is located in Richmond, and the mine leaches chemicals into the Bay that cause significant problems. The private cost of Oval extraction is T CO = 4Q2 O and the total social damages from the chemical leakage is TEDO = 2QO.

12. Suppose that the Bay Area Social Planner could impose a per unit tax on Asscher, and a separate tax on Oval. What would be the tax on each? Call these the first-best mine-specific tax rates, labeled tFB. (1 point)

Answer for tFBA :

Answer for tFBO :

13. Now, suppose instead that the Bay Area Social Planner must choose one tax rate that will apply to both mines. According to the Diamond model, will the second-best tax be closer to the first-best mine-specific tax rate for Asscher, or the one for Oval? Briefly explain why. (1 point; the explanation will not be graded, but you should try to explain this for yourself.)

# Closer to Asscher (tFBA)

# Closer to Oval (tFBO)

14. What is the second-best tax rate on diamond extraction, assuming the tax rate must be the same for both mines? (2 points)

15. Extension question: When the government must impose a uniform tax rate for both firms, the tax rate will be “wrong,” which creates inefficiency. The second-best tax rate minimizes the deadweight loss summed across the two firms (equivalently, it maximizes the efficiency gains from taxation). Derive an expression for the deadweight loss in Asscher and the dead-weight loss from Oval as a function of the tax rate, labeled t SB. (You should then be able to confirm that the answer you gave above minimizes the sum.) (2 points)

Part III. The Weitzman model

A town council is deciding how to improve the quality of its drinking water by regulating upstream pollution. It is debating using a price mechanism or a quantity mechanism. Assume that the value of abating a pollutant is equal to MB=42-2q, where q represents units of abatement. The cost of abatement is uncertain. There is a 1/3 chance that MC=q and 2/3 chance that MC=q+9.

16. If the town uses a price instrument (i.e., offers the water filtration company a subsidy per unit of abatement), what price should it set? (1 point) Note that the expected value of MC is the weighted average of the two marginal cost curves, which is E[MC]=q+6.

17. If the town uses a quantity instrument (i.e., mandates a given quantity of abatement and then pays the firm its true cost), what quantity of abatement should it choose? (1 point)

18. True/false: Ex ante (meaning before we know which MC is correct), the town should prefer a quantity regulation because marginal benefit is relatively steep compared to marginal cost. (1 point, no explanation required)

# True

# False

19. Draw a graph below that shows the deadweight loss that results from uncertainty under a pricing policy and includes the two possible marginal cost functions and the marginal benefit function. (1 point)

20. Draw a graph below that shows the deadweight loss that results from uncertainty under a quantity policy and includes the two possible marginal cost functions and the marginal benefit function. (1 point)