代写接单-Natural Resource Economics Homework 1 Matt Reimer UC Davis | ARE/ESP 175

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Natural Resource Economics Homework 1 Matt Reimer UC Davis | ARE/ESP 175

 Total Points 10 Problem 1: 

Market Equilibrium and Total Surplus [3.5 points] Consider the market for cobalt, an important mineral for the production of electronic vehicle batteries and is heavily concentrated in the Democratic Republic of Congo (DRC).1 Let the market demand function for cobalt be = 2000 250, where is the price of cobalt. Suppose the DRC is covered with many small local cobalt mines, all of which have the same production process and are producing identical products. Thus, the DRC cobalt industry is a perfectly competitive market, with each mine acting as if they can sell as much (or as little) as they want without affecting the price (i.e., they are price takers). Consider a single cobalt mine whose cost of mining units of cobalt is represented by () = 22. Thus, a single mine earns profits () = 22. 1.A. [0.5 points] Assume that a single cobalt mine chooses cobalt production to maximize profits. Find the amount of cobalt that maximizes a cobalt mines profits. 1.B. [0.5 points] Suppose that the government limits the number of mines in the DRC to 1,000 via a permit program. What is the industry supply curve? And what are the market equilibrium quantity produced and price of cobalt ? 1.C. [0.5 points] What are the producer and consumer surplus in the DRC market for cobalt? 1.D. [1 point] It turns out that mining cobalt has some negative social costsit produces mineral tailings that contaminate ground water supplies. Suppose that the total external damages are equal to = 2. Determine the socially optimal level of cobalt that should be produced. 1.E. [1 point] Suppose that the government wants to restrict the amount of cobalt produced to achieve the socially optimal level that you found in Part E. The government has decided to do this by reducing the number of cobalt mining permits. How many permits should it issue? 1See NYTimes article for more on cobalt in the DRC. 1 Problem 2: Rents, Land Use, and Social Welfare [4 points] Suppose a forested piece of land has a timber production function of () = 5 2, where is the number of workers. Suppose timber receives a price of in a perfectly competitive market. For simplicity, suppose that the supply of workers is perfectly elastic and the per-worker wage is equal to zero. 2.A. [0.5 points] What is the optimal number of workers and the rent to the land? 2.B. [0.5 points] Suppose that timber must be transported to the city to get processed. Suppose one unit of timber is transported at a cost of 3 dollars per unit of distance. Consider a plot of land that is a distance away from port. What are the rents to the land? 2.C. [0.5 points] Beyond what distance from the city would we no longer expect to see land dedicated to forestry? 2.D. [1 point] Now suppose that there is another competing use for land: agriculture. Assume that agriculture follows the production schedule () = 10 2. Just like timber, agriculture must also be transported to the city. For simplicity, assume that both the per unit output price and the per-unit-distance transportation cost of agriculture are equal to 1. Over what distance will land be devoted to agriculture and forestry? 2.E. [0.5 points] What do you expect to happen to the amount of land dedicated to forestry if the price of timber goes down? Explain. 2.F. [1 point] Now suppose that land devoted to forestry provides the social benefit of regulating climate through carbon sequestration: each unit of land devoted to forestry provides a benefit of 20 dollars. What is the socially optimal distance that separates agriculture and forestry? Problem 3: Electric Vehicles and Discounting [2.5 points] Consider the choice of buying one of two cars: an electric vehicle (EV), which costs $60,000, and a plug-in hybrid electric vehicle (PHEV), which costs $50,000. Suppose you expect to own the vehicle for ten years and that you will save $2,000 per year in gasoline expenditures if you buy the EV. Further suppose that the annual real interest rate for a savings account is = 4%. For simplicity, assume there is no resale value for either car and that you receive your gasoline savings annually starting immediately (i.e., today). 3.A. [0.5 points] Which vehicle provides a better return on investment? By how much? 3.B. [1 point] How many years will it take for the two investments to be equal? 3.C. [1 point] Now suppose that you expect gasoline savings to decrease at an annual rate of = 25%. Would this rate justify buying an EV, assuming once again that you will own it for ten years? 2 


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