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ECON 381

Problem Set #1

September 2023

Problem Set 1 it out of 100 points. It covers Chapters 2-3 in Goodstein and Polasky and the Lutz reading, and it is due on Tuesday, September 19^th at 11:59 PM on Brightspace. Please complete your problem set in a separate document. You may complete the problem set by hand, but the scanned version must be clearly legible for the TA. Please show your work for partial credit.

Q1 A Coase Theorem Example

Rancher Roy has his ranch next to the farm of farmer Fern. Cattle tend to roam, and sometimes they stray onto Fern's land and damage her crops.  Roy can choose the size of his herd.  His revenues are $8 for each cow he raises.  Roy’s marginal cost of production (MCP) and the cost of the damage each additional cow creates for Fern’s crops (marginal cost of damage, or MCD) are given below.

While Roy can choose his number of cattle, Farmer Fern can only choose whether to farm or not to farm, and she makes this decision based on Roy’s decision of how many cattle to graze. Her cost of production is $14, and her revenue is $20 when there are no cattle roaming loose.  For each additional cattle Roy grazes, her revenue is reduced by the amount in the MCD column above.

Note that Fern does not suffer any damages when she does not farm – no matter how many cattle Roy grazes, Fern earns profit of zero (NOT negative profit) if she does not farm.

Assume that Roy faces no start-up (fixed) costs, hence marginal costs can be added up to determine total costs at a given level of cattle grazing.

Q1-A How many cattle will Roy choose if there is no liability (Roy does not pay for any damages caused)? What will total profits be for Roy? When Roy grazes this many cattle, will Fern farm or choose not to farm (because her profits would be negative if she farmed)? What will total profits be for Fern?

Q1-B If Roy is liable for damages, he must pay the cost of the damages for a given cattle directly to Fern. In this case, Ferm will farm and earn profit of $6. How many cattle will Roy choose if Roy is liable for damages? What will profits be for Roy?

Q1-C Under the Coase Theorem, it should not matter whether Roy is or is not liable for damages. According to this theorem, how could Roy achieve the same level of cattle production in Q3-A even if he does not have grazing rights on Fern’s property? Write a short response. Hint: think about differences in profits for Roy and Fern in Q1-A and Q1-B. An answer will receive full marks if it numerically demonstrates that each party is better off than under Q1-B when property rights require Roy to be liable for damages. Your answer should suggest a viable trade amount or a range of values.

Q2 The Open Access Problem

Suppose several independent and identical firms that produce vat dyes (which are used to dye textiles, an input in clothing manufacturing) are considering whether to open up a factory along the Ohio River. If a firm decides to site a factory, they only site one (so each factory represents a unique firm). The dyes the firms produce are sold on the national market for $300,000 per ton, and the private costs of producing each ton of dye is $150,000 per ton. If the firm sites one factory along the river, the factory will produce 10 tons of vat dye each year.

Vat dyes are made from coal tar, and the chemical process of converting coal tar to dyes results in the production of toxic waste. For each new factory that arrives and starts producing along the river, the river will become more polluted with toxic waste. The factories need clean water to produce, but they are contaminating the river that they draw water from. The externality associated with new factories will raise the cost of paper production at all facilities by $20,000 per ton per factory.

Q2-A Based on the structure of costs and revenue for the firm, complete the following table. Note that the table reports costs, revenues, and profits in millions $.

HINT: Note that in the table above, average costs (revenues) reflect the average cost (revenue) per factory. The marginal costs (and revenues) reflect the additional costs (additional revenue) from an additional factory operating. That’s to say, the averages/margins do not reflect additional tons, but additional firms/factories.

Q2-B If the firms collectively chose how many factories to site along the river, how many new factories will the firms open? How much in profit will the firms earn in total? Briefly explain how you determined the number of firms when the firms choose collectively. NOTE that the table reports costs and revenues in millions $.

Q2-C If the firms choose whether to site a factory along the river independently, how many new factories will the firms open? What will total profit be among these firms? Briefly explain how you determined the number of firms when the firms choose independently. NOTE that the table reports costs and revenues in millions $.

Q2-D One of the scenarios (Q2-B or Q2-C) illustrates the open access problem. Which scenario is a demonstration of the open access problem? Briefly explain why this scenario demonstrates the open access problem.

Q2-E Clearly draw a graph (with price on the Y -axis and quantity on the X axis) that displays the marginal cost and marginal revenue curves for each additional firm and its corresponding factory. Assume that government regulation restricts lake access to the profit-maximizing number of firms.  Shade in the area of the graph that represents the resource rent that would be earned by the factories that are allowed to operate.

Q3 Public goods provision

Adam and Eve live on two sides of the Garden of Eden, a small suburban development. After they move in, an old PCB dump is discovered in between their houses. If X total tons of PCB's are removed from the dump, the two have a true willingness to pay (WTP) to finance a clean-up equal to:

ADAM'sWTP = 18 — 2 X      EVE's WTP = 10 — X

Q3-A Adam's WTP is higher than Eve's. Provide two reasons why this may be the case.

Q4-B Draw a graph with price on the Y axis and tons of PCB removed on the X axis. On this graph, draw Adam’s demand curve and Eve’s demand curve. Label them clearly. Next, derive the total demand curve for the public good, add this to your graph, and clearly label it.

Q4-C Based on your graph, what is the total WTP for 3 tons of PCB cleanup?

Q3-C If cleaning up the first 4 tons were to cost $100 in total, is their sufficient WTP in this small community to finance it?  Explain why or why not.

Q3-D Suppose the demand curves for Adam and Eve were derived from a survey that they both participated in. The survey asked them to hypothetically state their WTP for additional units of cleanup. Now suppose the study team returns to their homes and asks them to make voluntary contributions to cleaning up. Do you expect their contributions to be lower, higher, or the same as their survey responses? Explain your answer in a couple of sentences.

Q4 The value of the environment

In your own words (and 1-2 paragraphs) explain the differences between 19^th-century European Settlers versus Lekwungen peoples on Vancouver Island regarding:

(1) property ownership over land and other natural resources. The response should outline different systems of property ownership: who technically has ownership rights and who makes decisions regarding management.

(2) Incentives for effectively managing natural areas with high resource value (what we’ll refer to later as “natural capital”).

Use the assigned reading from Lutz to complete your answer. You do not need to bring additional information from outside of the reading to answer this question.