Unformatted text preview: Econ 131 Fall 2009 Problem Set #3 Answer Key 1. The government of the island of Babbage is trying to decide whether to sell the government-run recycling facility to a private firm. a. You are an economic analyst in the Minister of Planning's office and are asked to economically valuate the facility. The facility is well-maintained and productive. In your valuation, consider different types of value, whether the facility is valued as a stock or a flow. Explain how you would measure the different values. Answer: The recycling facility will present a flow of benefits and costs, hence we have to remember that for all benefits and costs, we need to calculate the net present value (NPV). Now the benefits are due to different types of value: Benefit Type of Value Measurement NPV of Profits Use Value Company's balance sheets NPV of Reduction in the use Non-use value Industry data of raw materials, such as tin NPV of Reduction in the Non-use value Industry data number of trees cut NPV of Reduction in land fill Non-use value Landfill data size NPV of "The happiness that Existence value Contingent Valuation the islanders feel knowing that such a facility exists" As for costs, they mainly comprise the pollution costs, which can be measured through scientific estimates on the effects of emissions on health. b. Now you are an economic analyst in one of the private firms that is interested in buying the facility, your manager asks you to perform an economic valuation of the facility. Answer: The private firm does not take into account of any benefits or costs, except for the profits. c. In what ways, are the valuations in (a) and (b) different? Answer: If the pollution costs are less than the use values and the existence value (which is probably the case), then the valuation in (a) would be larger. d. Putting your Ministry of Planning hat back on, what would you recommend to the government? Answer: Given the answer in (c), the government should either keep running the recycling factory to make sure the socially optimal quantity is recycled or sell the facility but make sure to implement policies that would internalize the positive and negative externalities derived from the facility in order to achieve the socially optimal level of recycling. 2. Your friend Sam is going to buy a TV and he is not sure how much he should pay for it. He suspects to watch it for an average of 10 hours a month. He values each hour of TV at $10, and his yearly discount rate is 0.05. The TV lasts for 10 years. Sam knows you are an economics wiz and asks you how much he should pay for the TV. Answer: He should pay any amount up to his NPV of the benefits. Since the yearly discount rate is 0.05, the yearly discount factor is 0.952. Now the yearly benefit that Sam derives from the TV, is equal to $10*10(hours/month)*12(month/year) = $1200 per year. Hence, NPV of Benefits=$1200(1+0.952+0.9522+0.9523+...+0.9529) = 8529.38. Although the NPV of Benefits - $8529.38, that doesn't mean Sam should actually pay that much for the TV since he is surely able to buy one for far less. The difference between the maximum he would be willing to pay (i.e. the total value of the TV) and the actual price he ends up paying would be the Consumer Surplus he receives from being able to buy the TV for less than its maximal value to him. 3. What does it mean when a person has a discount rate greater than 0, equal to 0, and less than 0? (Hint: Remember that the Net Present Value is just a weighted sum!) Answer: When the discount rate is greater than 0, this means that the weights that one puts on benefits and costs are smaller as they occur further away in the future. Hence, an individual with a positive discount rate means that he/she cares more about the present than the future (impatience). When the discount rate is equal to 0, then this means that the individual puts equal weights on benefits and costs regardless of when they occur, whether $5 mean the same for him/her whether he/she gets them now or in a million years. We can describe this preference by `indifference' between the present and the future. Finally, a negative discount rate (-1<r<0) means that the individual gives benefits and costs greater weights as they lie further away into the future. One may describe this preference by `prudence'. 4. Consider a proposal to create a new National Park in the Southern Sierra on government land currently managed by the Bureau of Land Management for cattle grazing, but also used by backpackers, fishers, and other recreational users on lakes within the proposed park's boundaries. Some effects of adopting the National Park proposal would be to stop the grazing of cattle on land and enhance opportunities for backpackers, fishers, and other recreational users. a. What criterion would you use to evaluate whether or not Congress should adopt the National Park proposal? Be explicit! Answer: As we only have to make the decision between creating the park or not creating it, then our decision criterion is that the net benefits to society (Benefits Costs) are greater than or equal to zero, or alternatively that the ratio of benefits to costs is greater than or equal to one. b. Explain how you might measure the social benefits and social costs that would be involved in adopting the proposal. Define the values you would want to measure and then explain how you might go about actually measuring them. Answer: Value Benefits Consumer surplus for backpackers, hikers Preservation of wildlife Entry fees (if included in the proposal) Tourism industry in the Southern Sierra Loss of cattle grazing Implementation and management costs How to measure it Travel costs indicates marginal benefit; surveys to try to estimate the consumer surplus Contingent valuation Entry fee*estimated number of entrants per unit of time To estimate the number of entrants, contingent valuation to estimate the number of
possible visitors of the national park Contingent valuation can be used to estimate the increase in tourists in the area (outside of the park) Market data Estimated cost of establishing the national park and hiring the employees at the national park; an estimate can be obtained from a comparable national park Costs 5. A group of neighbors want a new playground built in their neighborhood. The local government says they cannot build the playground without an estimate of the benefit it will provide. To come up with an estimate of the benefit, the neighbors hire a consultant. a. Using home prices from a nearby neighborhood with a playground, the consultant notices that the average price of the 20 homes surrounding the existing playground is $10,000 more than the average price of the nearby houses not immediately next to the park. What must be true for the consultant to conclude that the existing playground provided a benefit of at least $200,000 (20 homes * $10,000/home)? Answer: In order to conclude the playground increased the value of a surrounding house by $10,000 on average, the consultant must make sure that, on average, the houses bordering the park are identical to the houses not immediately surrounding the park. For example, if the houses are all identical, then any differences in the price could be attributable solely to the proximity of the park. b. Taking a closer look, the consultant realizes that the average number of bedrooms in the houses immediately surrounding the existing playground is one less than the average number of bedrooms in the houses not next to the park. How does this impact the initial estimate of the benefit provided by the playground? Answer: If we assume that the price of a home increases as the number of bedrooms increases (holding everything else constant), then our estimate of the value added from being near the park is likely too low. If the houses near the park are on average smaller and still more expensive, then on average, the park adds more than $10,000 in value to each nearby home. 6. The local government is considering preserving a portion of a nearby 12 acre forest for a wildlife refuge. Assume the sum of the discounted benefits (in millions of dollars) of preserving `x' acres of the forest is given by acres is given by a. The mayor suggests comparing the total costs and total benefits to determine if all 12 acres should be preserved. What is the total net present value of conserving 12 acres? Answer: The NPV of conserving all 12 acres is the sum of the discounted benefits of preserving 12 acres minus the sum of the discounted costs of conserving all 12 acres. The calculation is shown below (with NPV in millions of current dollars): . . The sum of the discounted costs of preserving `x' b. If given the option of preserving all or none of the forest, what should the city government do? Answer: If they must choose between preserving all or none, the city should preserve all of the forest. One of the legislators argues that maybe the entire forest shouldn't be preserved. From the TB and TC functions above, we know the marginal benefit (in millions of dollars) and the marginal cost of preserving `x' acres are given by and . c. What is the socially optimal size (in acres) for the wildlife refuge? Answer: The socially optimal size for the refuge will be the size where the difference between the sum of discounted benefits and the sum of discounted costs is the largest. This will occur where the MB of increasing the refuge size is equal to the MC of increasing the refuge size. Therefore, the optimal refuge size is 10 acres. d. Can the socially optimal size be determined by comparing the total costs and total benefits for a single size of the wildlife refuge? Answer: No. If a CBA is carried out for a single refuge size (as in part A), there is no way to know whether the size examined is optimal. Just because the TB exceed the TC, a different size for the refuge may result in an even larger net benefit (as was the case in part C). 7. Suppose the Federal government is considering an environmental regulation that will impose a one-time cost of $200 billion on the current generation (assume for simplicity the current generation is everyone born between the years 2000 and 2100). The proposed regulation will provide an estimated benefit of $5 billion to the current generation and to every generation in the future (again, generation 1 is everyone born between 2000 and 2100; generation 2 is everyone born between 2101 and 2200; etc.) . a. The government carries out a cost benefit analysis to determine if the regulation should be carried out. A discount rate of = .95 is used to calculate the total net present value of the benefits of the policy (present value of the benefit received by the generation `i' is times $5 billion). What is the NPV of the sum of discounted benefits? (Hint: ) NOTE: The discount rate of = .95 should actually have been labeled the discount factor. As defined in class, if r = the discount rate, then [1/(1+r)] = the discount factor. If the discount factor = .95, then the discount rate r = (1- )/ = .05263 Answer: The discounted sum of benefits over all the generations is shown below. b. Do the results of the cost benefit analysis support the use of the environmental regulation? Answer: The sum of the discounted benefits does not exceed the cost of the policy. Therefore, the CBA does not support the use of the regulation. One senator argues that discounting the welfare of future generations is not ethical. The same cost benefit analysis is carried out by the senator's staff. This time, a discount rate of = 1 is applied to the benefits from future generations. NOTE: Here again, the discount rate of = 1 should be the discount factor. If the discount factor is 1 then the discount rate is 0. c. What is the sum of the discounted benefits received by all generations using the new discount rate? Are the results of the CBA sensitive to the discount rate used? Answer: By setting equal to 1, the benefit received by any generation in the future is not discounted at all. Therefore, summing the benefits over an infinite number of generations to come will result in an infinite value for the sum of discounted benefits. In this case, the infinite benefits definitely exceed the finite cost. Therefore, the analysis would support the use of the regulation. The conclusion of the study is sensitive to the discount rate (or discount factor) chosen. d. What arguments can you think of to support the use a discount rate less than one? What arguments can you think of supporting a discount rate equal to one? NOTE: Here again, the discount rate of = 1 should be the discount factor. If the discount factor is 1 then the discount rate is 0. Answer: For simplicity, assume that each generation gains utility simply through consumption. Additionally, assume as the level of consumption increases, the marginal utility of an additional unit of consumption decreases (basic concave utility function). One argument supporting a discount rate less than one can be made by examining how the level of consumption (and overall welfare) has progressed over time. Throughout history, consumption has increased as technology has improved. If we expect this trend to continue, then the level of consumption of future generations will be higher than the current levels of consumption. If this is the case, an additional unit of consumption in the current generation would increase their utility by more than an additional unit of consumption would increase future generation's utility. Therefore, we should discount the benefits obtained in the future by a factor less than one or by a rate greater than 0. Alternatively, if we expect the level of consumption to be constant in the future, then an additional unit of consumption would be valued equally by both the current and future generations. In this case, a discount factor of 1 or discount rate of 0 (no discounting) would be justified. 8. The Forest Service would like to know whether they should set aside some national forest land, previously slated to be logged, for hiking. You are helping with a travel-cost analysis to estimate the benefits of setting aside the land. Survey data has been gathered from 500 hikers who visited a forest in a neighboring state. Using regression analysis, you have controlled for differences in income, employment status, age, and other important factors that might affect the number of hiking trips taken. Taking all these factors into account, you have developed the following relationship: Cost to Get to Hiking Area $20 40 80 Hiking Trips per Person per Year 8 6 2 a. Graph the demand curve for hiking trips as a function of the "price" -- the travel cost Answer: Plotting these points shows the demand curve is: T = 10 (1/10)P where T = # of trips/year and P = "price" (here, estimated by the cost to get to the hiking area). b. Based on demographic information about the people living in the vicinity of the proposed park, you have estimated that 50,000 people will take an average of four (4) hiking trips per year. For the average person, calculate: (i) the consumer surplus for a single visit to the new park; (ii) the total consumer surplus for an average visitor; and (iii) the total expected consumer surplus per year from the proposed park. Answers: (i) A hiker who only goes once to the new park in a year would get total value of $90 and since an average person is one who takes 4 trips a year and thus has costs of $60 per trip, the consumer surplus for a single visit is $90 - $60 = $30. Or, the average person takes 4 trips per year and (according to the "demand curve") has a cost of $60 per trip. His/her first trip is worth $90, the second trip is worth $80, the third trip is worth $70 and the fourth trip is worth $60. (ii) The total value for the average visitor (who takes 4 trips a year) = (90+80+70+60) = $300 and total cost is 60(4)=$240. Thus the CS = 300 240 = $60. Using the estimated demand curve, T= 10 (1/10)P would give the average visitor's CS as: CS = (1/2)(40)(4)= $80. [Can you explain why there is this discrepancy between the two estimates of CS?] (iii) If the average person would get $80 of CS from the new park and there are 50,000 "average" persons, then the total yearly CS would be (50,000)(80)=$4 million per year. ...
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This note was uploaded on 12/09/2009 for the course ECON 131 taught by Professor Groves during the Fall '09 term at UCSD.
- Fall '09
- Environmental Economics