Environmental Economics, EEP101 /ECON125 Problem Set 5 James Sallee Spring 2024 Problem set 5 covers core concepts from module 5, as well as internalities from module 4. You may write your answers either directly on the problem set or on a blank sheet. Part 1. Coase example An externality can be corrected via a tax, leading to the efficient allocation. Likewise, two parties could mutually agree to solve the externality even without the intervention of the government. This problem illustrates this using an adaptation of a famous example of externalities, with honey bees and an orchard. The idea is that the bees benefit from the orchard, and the orchard benefits from the bees, so there is a mutual externality. In our example, we will make the benefits flow in only one direction to simplify the algebra. Still, we are doing something different than lecture in the algebra because the externality from the bees will shift the cost function of the orchard. As a result, the external benefits from bees depend on the level of production of the orchard. Suppose that a beekeeper makes honey, which she sells in a competitive market with an equilibrium price P# = 20. The total cost of producing honey is TCH = H2 4+ 8H, where H denotes the quantity of honey produced. The beckeeper is located next to an orchard that grows apples that the orchard owner sells on a competitive market at a price P4 = 40. The total cost of producing apples is TC# = 242 + 484 2H A, where A denotes the quantity of apples. Note that the cost of producing apples depends on the amount of honey. The idea is that more honey requires more bees, and the more bees there are, the easier it is to grow apples. The benefit that bees provide to the orchard is a classic example of an externality. 1. Suppose that there is no policy and there is no Coasian bargaining, so the beekeeper and the orchard owner each maximize their profits taking the behavior of the other as given. What is the equilibrium quantity of honey and the equilibrium quantity of apples? We will denote these quantities as HP and AP. (2 points) Answer H\": Answer AP: 2. Now, find the socially optimal level of honey production and apple production. We will denote these as H* and A*. (2 points) (Hint: You can write total profits as a function of both H and A and take partial derivatives, yielding two equations in 2 unknowns. Or, you can solve for AP as a function of H, and then substitute this into an expression for total profitsboth honey and applein the economy, yielding an equation with only one unknown.) Answer H*: Answer A*: 3. Assume that there is no Coasian bargaining but that the government could put a subsidy in place for apples and a subsidy for honey. What per unit subsidies would cause the agents to choose the socially optimal quantities? (Hint: Follow the Pigouvian prescription.) (2 points) Answer Subsidy for H: Answer Subsidy for A: 4. The idea behind Coasian bargaining is that private parties could negotiate to get to the private optimum by making some exchange, even without a corrective tax or other policy intervention. What is the maximum amount of money that the orchard owner would be willing to pay to get the beekeeper to change from HP to H*? And, what is the minimum amount of money that the beekeeper would be willing to accept to change her production from HP to H*? (2 points) Maximum for orchard owner: Minimum for beckeeper: Part II. Green subsidies In the lecture, 1 asserted that green subsidies were less efficient than Pigouvian taxes because, even though they can shift market shares between relatively clean and relatively dirty goods, they will get the average price of the goods wrong. If a good (like an electric car) has a negative externality, we cannot mimic a Pigouvian tax by subsidizing it (except in special extreme cases). There are two goods, F for efficient and I for inefficient. They are substitutes for each other, and the demand curves are as follows: DE =100 2P + Pr Dr=100-2P; + Pg Both are produced by perfectly competitive suppliers that have constant marginal costs. The marginal costs are MCg = 10 and MCp = 20. The externality associated with each good is a constant marginal externality: MEg =5 and M Er = 10. . If there are no policies, what are the quantities sold of E and I? (Prices will be equal to MC.) (2 points) Answer Dg: Answer Dy: 6. If there are optimal Pigouvian taxes (just use the Pigouvian prescription) imposed on both products, what are the quantities sold of E and 17 (Prices will be MC plus the tax.) (2 points) i * Answer Dy Answer Dj: 7. Now suppose that there is no tax on I, but there is a green subsidy applied to F equal to the difference in externalities, which is 5. This might be an intuitive policy because it gives a subsidy to E for the reduction in emissions compared to each unit of I. What are the quantities sold of E and I? (2 points) Answer Dgs : Answer D?S: 8. In class, we discussed how a green subsidy approach (as compared to the Pigouvian prescription) creates a distortion in market size, here meaning Dg + Dr. Which of the following is illustrated here: (No explanation required, but please think about it!) (1 point) (O The market size is too large because the price of both goods is too high under a green subsidy (0 The market size is too small because the price of both goods is too high under a green subsidy (O The market size is too large because the price of both goods is too low under a green subsidy (O The market size is too small because the price of both goods is too low under a green subsidy 9. You should have found that the green subsidy leads to a different set of quantities than the Pigouvian tax. But, mayhe you can add a tax (or subsidy) to the inefficient good in order to get back to the first best. True or False: You could obtain the optimal quantities using the green subsidy of $5 for E and a tax (or subsidy) to I. (No explanation required, but please think about it!) (1 point) O True (O False Part III. Graphing internalities Below is a depiction of a market with an internality and an externality. The internal- ity causes a pivot in the demand curve for a "green" (energy efficient) product. The good causes a positive externality (consuming the good reduces consumption of a dirt- ier good). The externality is a constant value. The graph depicts the demand curve and shows the externality's size, in which we assume it shifts the MC curve graphically. Market for Energy Efficient Good $ MC true MB positive externality perceived MB Q 10. Complete the graph by drawing (i) the social marginal cost curve, (ii) denote the mar- ket equilibrium quality absent policy as Q", (iii) denote the socially optimal quantity as Q*, (iv) shade and label an area that represents the deadweight loss from the mar- ket equilibrium, and (v) show and label the optimal tax in the graph as a height.* (3 points)Part IV. Internalities In class, we introduced the possibility that internalities and externalities could interact. One consequence is that it might modify the Pigouvian prescription in that the optimal tax rate is not simply equal to marginal damages. However, we noted that if the internality is heterogeneous, this will lead to a Diamond-like second-hest situation. We explore this graphically here. Below is a depiction of a market with an internality with two types of agents, labeled "Market for Energy Efficient Good.\" In this market, some buyers are fully rational (no internality), and some are myopic (have an internality that causes them to undervalue the good). Both types of agents have the same true marginal benefits equal to the line labeled True MB. However, the myopic agents misperceive their benefits and demand too little of the good. Their MB eurve is shifted down vertically by $9. The good is sold in a competitive market with a constant marginal cost of production equal to $22. There is also a constant positive externality per unit produced equal to $12. The corresponding social marginal cost curve is drawn. Assume that there are an equal number of myopic and rational agents so that each MB curve represents the same amount of agent. Note that the socially optimal quantity to be consumed by both myopic and rational agents is the same, and it is equal to Q. Market for Energy Efficient Good True MB $9 MC=22 SMC=10 Perceived MB of Myopics 11. If you could impose a different subsidy for rational agents and for myopic agents, what would the two subsidy rates be? Answer subsidy for rational agents: Answer subsidy for myopic agents: 12. What is the second-best subsidy for this good? Answer: :\\ 13. Suppose that this second-best subsidy is added to the market. Draw on top of this graph (or replicate your own version by hand if you prefer) and label: (i) the after- subsidy price that results from imposing the second-best tax as P and calculate this value, (i) the quantity that myopic consumers would choose as @M, (iii) the quantity that rational consumers would choose, and shade and label as @, (iv) the deadweight loss associated with myopic consumers (if any) as DW LM and (v) the deadweight loss associated with rational consumers (if any) as DW LT