ECN 236 – Economics Of The Environment HW 2 – Due Date: Se

ECN 236 – Economics of the Environment HW # 2 – due date: September 28

Suppose that the market demand curve for coal is given by 𑃠= 80 − ð‘„, and the marginal cost of producing it is ð‘€ð¶ = ð‘„ where 𑃠is the price of coal per ton and ð‘„ is quantity in thousands of tons. a. (i) How much will be supplied by a competitive market? a. (ii) Show your result graphically. b. Compute the consumer surplus and producer surplus if coal is supplied in a competitive market. c. (i) How much will be supplied if there is only one supplier of coal (monopoly)? c. (ii) Show your result graphically. d. Compute the consumer surplus and producer surplus if coal is supplied by a monopoly. Compare the consumer surplus, producer surplus and total surplus between the two types of markets.

2. Consider the market for electricity where demand (in megawatt hours) is given by 𑄠= 50 − 𑃠and the private marginal cost of generating electricity is $10 per megawatt hour. Suppose further that pollution is generated in the production of electricity in direct proportion to the amount of electricity generated and the health damage from the pollution is $15 per megawatt hour. a. Suppose electricity is produced by many competitive producers. What price will be charged, and how much electricity is produced? b. Suppose electricity is produced by a monopolist. What price will be charged, and how much electricity is produced? c. In parts a. and b., what is the consumer surplus and producer surplus from electricity generation? In parts a. and b., what is the net surplus, after taking pollution damage into account?

In the figure below, identify a point ð· such that ð‘ and 𑌠are Pareto preferred to ð· but 𑆠is not. 4. In the figure below, the slope of the production possibility frontier is increasing (getting steeper) as garbage disposal decreases and production of wine increases. Does this make sense? Explain. ECN 236 – Economics of the Environment HW # 2 – due date: September 28, . A politician states that “total surplus is not maximized in a free-market.†Critique this statement. 6. Consider an air basin with only two consumers, Huck and Matilda. Suppose Huck’s demand for air quality is given by ð‘„ð» = 1 − 𑃠where 𑃠is Huck’s marginal willingness to pay for air quality. Similarly, Matilda’s demand is given by ð‘„ð‘€ = 2 — 2ð‘ƒ. The supply of air quality is given by ð‘„ = 𑃠where 𑃠is the marginal cost of supply. a. Graph the individual demand curves and aggregate demand curve for air quality. b. What is the efficient amount of air quality? 7. Consider an airport that produces noise (ð‘) that decays as distance (ð‘‘) from the airport increases, where distance is in miles. The relationship between distance and noise is given by the following equation. ð‘ = 1 ð‘‘2 Fritz works at the airport and his damage from noise is $1 per unit of noise. His cost of commuting is $1/mile (each way). The closest he can live to the airport is ð‘‘ = 0.1 miles. a. Write an expression for Fritz’s total cost (noise and transportation). b. How far will Fritz live from the airport? What are his total costs? c. Suppose Fritz is compensated for the noise damages. How far will Fritz live from the airport? How much will he be compensated?

8. When sulfur dioxide is emitted into the air, it is transported over long distances and is converted to sulfuric acid. This gradually falls to the ground, either as rain or snow. This is called acid deposition. In what way could acid deposition be considered a rival bad? ECN 236 – Economics of the Environment HW # 2 – due date: September 28, . Identify whether each of the following resource categories is a public good, a common-pool resource, or neither. Explain each answer. a. A pool of whales in the ocean to whale hunters. b. A pod of whales in the ocean to whale watchers c. Bottled water 10. Consider a small exchange economy with two consumers, Ned (ð‘) and Stark (ð‘†) and two commodities, food (ð¹) and electricity (ð¸). The preferences of the two consumers are given by the following equations: ð‘ˆð‘ = ð¹ð‘ à— ð¸ð‘ ð‘ˆð‘† = ð¹ð‘† à— ð¸ð‘† The initial endowments of the goods are: Ned has 12 units of food and 2 units of electricity while Stark has 8 units of food and 18 units of electricity. a. Draw an Edgeworth box for this economy. Be sure to label the axes, (including the endowment point). b. Draw in the efficient lens that corresponds to the initial endowment. Explain this lens. c. For an allocation in this economy to be Pareto efficient, it must maximize the utility of Ned given the utility of Stark. Is the initial endowment Pareto efficient? Why or why not? d. Now assume Ned gets to choose a new allocation to maximize utility, subject to the constraint that Stark’s utility be no lower than at the endowment point. Illustrate this situation on a separate graph.

Paper For Above instruction

The provided assignment encompasses various economic analyses related to environmental resources, market structures, externalities, and resource allocation. This comprehensive discussion will address each component systematically, showcasing an understanding of economic principles such as supply and demand, market equilibria, consumer and producer surpluses, externalities like pollution, and Pareto efficiency in resource allocation. The discussion integrates graphical analysis, economic modeling, and critical evaluation of market outcomes versus potential government intervention or alternative allocation mechanisms.

Analysis of Coal Market: Competition vs Monopoly

The demand function for coal is given as 𑃠= 80 − ð‘„, with a marginal cost ð‘€ð¶ = ð‘„. To determine the competitive supply quantity, we set the marginal cost equal to the market price derived from demand. Under perfect competition, firms produce where price equals marginal cost. Equating demand and marginal cost:

80 – ð‘„ = ð‘„

This simplifies to 80 = 2 ð‘„, or ð‘„ = 40. This indicates that the competitive market supplies 40 thousand tons of coal. The equilibrium price is obtained by substituting ð‘„ = 40 into the demand curve:

 𑃠= 80 – 40 = 40

Graphically, the supply curve is a horizontal line at the marginal cost of ð‘€ð¶ = 40 (since supply equals marginal cost in perfect competition), and the demand curve intersects at 40 thousand tons and a price of $40 per ton.

Consumer surplus in the competitive market is the area between the demand curve and the market price, up to the equilibrium quantity. Calculated as:

 CS = 0.5  (Base)  (Height) = 0.5  40  (80 – 40) = 0.5  40  40 = 800

Similarly, producer surplus is the area between the market price and the marginal cost (which is equal to supply in this case). Since supply is perfectly elastic at $40, producer surplus is zero beyond marginal cost, but for simplicity, assuming a perfectly competitive equilibrium with supply at marginal cost, the producer surplus is the same as the area under the price above marginal cost, which is zero at this point.

In the monopoly case, the firm maximizes profit where marginal revenue equals marginal cost. Given the demand function 𑃠= 80 – ð‘„, the total revenue (TR) is:

TR = 𑃠* ð‘„ = (80 – ð‘„) ð‘„ = 80 ð‘„ – ð‘„²

The marginal revenue (MR) is the derivative of TR with respect to ð‘„:

MR = 80 – 2 ð‘„

Setting MR equal to marginal cost:

80 – 2 ð‘„ = ð‘„

80 = 3 ð‘„

  ð‘„ = 80/3 ≈ 26.67

The monopoly supplies approximately 26.67 thousand tons of coal. The corresponding price from the demand curve:

  𑃠= 80 – 26.67 ≈ 53.33

Graphically, the monopoly’s quantity is less than the competitive supply, and the price is higher, represented as a point on the demand curve at 26.67 thousand tons revenue.

Consumer surplus under monopoly is the area between the demand curve and the monopolist’s price:

CS = 0.5  (Base)  (Height) = 0.5  (26.67)  (80 – 53.33) ≈ 0.5  26.67  26.67 ≈ 356.7

Producer surplus is the monopolist’s profit, which is the area between the price and marginal cost:

PS = (Price – Marginal Cost)  Quantity = (53.33 – 40)  26.67 ≈ 13.33 * 26.67 ≈ 356.3

Comparing the two markets, the consumer surplus and producer surplus are higher under perfect competition, indicating a more efficient allocation. In contrast, monopoly results in higher prices, lower output, and a transfer of surplus from consumers to producers, decreasing total surplus—an illustration of deadweight loss.

Electricity Market Analysis: Competition and Monopoly Externalities

The electricity demand function is ð‘„ = 50 – ð‘ƒ, with a private marginal cost of $10 per megawatt hour, and external damages of $15 per MWh pollution. In a competitive setting, the market equilibrium occurs where demand equals supply:

50 – 𑃠= 10

  𑃠= 40

Thus, the equilibrium quantity is 40 MWh at a price of $10. Consumer surplus is computed based on the difference between maximum willingness to pay and the market price:

CS = 0.5  (Base)  (Height) = 0.5  40  (50 – 10) = 0.5  40  40 = 800

The producer surplus is the total revenue minus variable costs, but since the marginal cost is constant at $10, total producer surplus is:

  PS = (Price – Marginal Cost)  Quantity = (10 – 10)  40 = 0

However, when considering external damage, the social marginal cost becomes $25 ($10 private + $15 pollution damage). The optimal (socially efficient) level of production is where social marginal benefit equals social marginal cost:

50 – 𑃠= 25

  𑃠= 25

Now, the socially optimal quantity is 25 MWh, with the price reflecting the private marginal cost of $10 but with the external damages internalized through policy instruments like taxes. The total net social surplus accounting for externality involves subtracting the external damage costs from total benefits, leading to a more efficient outcome and reduced pollution.

In the monopoly scenario, the monopolist maximizes profit where MR equals MC, with the same demand function. The marginal revenue is:

MR = 50 – 2 ð‘ƒ

50 – 2 𑃠= 10

  𑃠= 20

The monopolist produces 20 MWh and charges:

  𑃠= 50 – 20 = 30

This results in a higher price than the competitive equilibrium and reduced output, which exacerbates external damages and reduces overall welfare. The consumer surplus decreases, and the external damages are internalized less efficiently, reinforcing the need for policy measures such as emission taxes or cap-and-trade systems.

Graphical and Theoretical Analysis of Market Externalities and Efficiency

The assigned problems highlight the importance of understanding how externalities influence market outcomes and the role of government intervention. Graphically, the market with externalities can be represented with social and private marginal cost and benefit curves, illustrating the divergence between private and social optima. The graphs depict the reduction in output and increased prices when external damages are considered, aligning with the economic principle that externalities cause market failures that justify policy corrections to achieve allocative efficiency.

Production Possibility Frontier and Pareto Efficiency

The increasing slope of the production possibility frontier (PPF) indicates increasing opportunity costs; as more of one good (wine) is produced, increasingly less of the other (garbage disposal) can be produced. This makes intuitive sense because resources are not perfectly adaptable between different types of production. The marginal costs of reallocating resources typically rise, leading to a steeper PPF, which reflects real-world economic trade-offs.

Market Surplus and Welfare Analysis

The statement by the politician that "total surplus is not maximized in a free-market" warrants critique. Classical economic theory posits that under certain conditions—perfect competition, full information, no externalities—markets tend to maximize total social welfare. However, real-world markets often deviate from these conditions due to externalities, market power, or public goods, leading to potential inefficiencies. Therefore, the claim is only valid in contexts where these market failures exist, emphasizing the need for regulatory interventions in many instances.

Air Quality Management: Externalities and Pareto Efficiency

The demand functions of Huck and Matilda aggregate to determine the optimal pollution level. Drawing individual demand curves and their sum illustrates where marginal willingness to pay aligns with marginal costs of supply, defining the socially efficient level of air quality. The efficient amount is where the aggregate demand curve intersects with the supply curve (marginal cost), balancing the benefits of cleaner air against the costs of achieving it. This analysis underscores the importance of externalities in environmental resource management and the role of policies such as cap-and-trade systems or pollution taxes.

Noise Pollution and External Cost Internalization

The analysis of Fritz’s living decision based on noise and transportation costs demonstrates how external costs influence individual choices. The total cost combines noise damage and commuting cost, determining Fritz's optimal residence distance. If Fritz is compensated for noise damages, his incentive to live closer diminishes, highlighting mechanisms for internalizing external costs—such as compensation or regulations—and their impact on individual behavior and urban planning.

Acid Deposition as a Long-Distance Externality

Acid deposition exemplifies a rival bad because it affects multiple regions over long distances, and the damage from acid rain reduces the quality of environmental resources shared by all. The rivalry arises because the deposition of sulfuric acid reduces the capacity of ecosystems elsewhere, and emission reductions by one polluter benefit others, which can lead to free-riding and under-provision of abatement efforts—justifying regulatory measures at regional or international levels.

Classifying Environmental Resources

The classification of resources into public goods, common-pool resources, or neither hinges on their excludability and rivalry. Whales hunted by whale hunters are rival and excludable, classifying as a common-pool resource. A pod of whales viewed by whale watchers constitutes a non-rival, non-excludable good, thus a public good. Bottled water, which is excludable and rival, does not fit into either category and is considered a private good.

Edgeworth Box and Resource Allocation

Drawing an Edgeworth box with the given endowments and preferences illustrates potential reallocations toward Pareto improvements. The initial endowment point provides a baseline, and the efficient lens depicts the set of Pareto efficient allocations that can be achieved through reallocations without harming either consumer. The initial endowment’s Pareto efficiency depends on whether it lies on the contract curve. In this case, since both consumers can improve their utilities through reallocation, the initial endowment is not Pareto efficient. The subsequent allocation maximizing Ned’s utility under the constraint that Stark’s utility is not lower than at the endowment is represented graphically by a utility frontier constrained by the initial endowment, demonstrating the concept of constrained Pareto improvements.

Conclusion

This comprehensive analysis demonstrates how economic principles elucidate typical environmental issues and market structures. Graphical models and quantitative calculations highlight the divergence between private incentives and social welfare, emphasizing the importance of regulatory policies, externality internalization, and efficient resource allocation for sustainable environmental and economic outcomes.

References

• Baumol, W. J., & Oates, W. E. (1988). The Theory of Environmental Policy. Cambridge University Press.
• Cropper, M. L., & Oates, W. E. (1992). Environmental Economics: A Survey. Journal of Economic Literature, 30(2), 675-740.
• Hanley, N., Shogren, J. F., & White, B. (2007). Environmental Economics: In Theory and Practice. Oxford University Press.
• Tietenberg, T. H., & Lewis, L. (201