answe all

Question Three Two power plants provide power to all of Cambridge: an MIT plant and a Harvard plant. Both power plants burn coal to produce electricity, and consequently produce smog as a by-product. The MIT power plant could reduce its smog, but at a total cost: Claim} = 5 ' 1i; where my indicates the total number of units of smog abated by MIT. The Harvard plant is slightly less efcient, and its total cost or cutting down on smog by in\" is: CHI:IH) = 7- 1%! + 10 '1'}:- The Cambridge government hires a team of environmentalists who calculate that the total benet of smog abatement to the city of Cambridge is 100 - {EH + EH). 1. Calculate the socially optirual level of abatement for each power plant. 2. The Cambridge government consist imng a tax on power production. {a} What tax should it impose to reach the abatement amouan you calculated in part {1}?\" {b} Write down each rm's optimization problem under the tax, and show that each will privately choose the socially optimal abatement amount. 3. Suppose that instead of taxation, the Cambridge government tries to regulate quantities. Homver, the city of lCambridge cannot write a law liar each rm, so it simmy declares that all Cambridge power plants must cut down on smog by :9 E 1 units each year. Show that this is not etlicient 1with HU'l'H math and intuition. 4. Suddenly, an economist is voted in as Mayor of Cambridge. She declares that Cambridge power plants must cut down on smog by 5 units ousmH. Additionally, she declares that rms will be able to competitively trade permits that will allow them NOT to abate. One of the mayor's old classmates from graduate school runs the MIT power plant, so the Mayor grants MIT 5 permits and Harvard [1 permits. its a result, Harvard is expected to abate by 5 units, and MIT [since it owns all the permits} is not expected to abate at all. {a} Harvard will surely want to buy some of MIT's permits. Explain intuitively [no math}, why" this trade might happen. {b} Denote the number of permits that MIT holds as y,\" [so that I,\" = 5 yMls and denote the competitive price of permits as p. Derive the amount of permits that MIT will eventually hold as a function of p. {c} Calculate theamountofpermitsthat Hanrardwillholdasafunctionofp. {d} Using that fact that ya; + my = 5, calculate p. {e} If the new mayor had divided the permits up dii'r'erently, what outcomes would have changed and what would have stayed the same? Question Four Vermont. Hardwood crafts solid wood furniture using a combination of time-tested hand construction and modern finishing techniques. Residual wood finishing chemicals are washed away as run-off and deposited in the nearby lake, a favorite fishing site for locals. A variety of technologies, including 'Hint: we can think of a Pigouvian tax here as a subsidy on abatement. So taxes on pollution provide firms an incentive to abate. high volume, low pressure sprayers and on-site solvent recovery sills are available for implementation. These technologies allow the manufacturer to reduce chemical emissions at a cost: Ci(a) = 20 - a2 where a is the level of pollution abatement. A city planner determines that the benefit to the residents of pollution abatement is 10 per unit. 1. Sketch a graph depicting the private marginal costs and benefits of abatement, and label the private market equilibrium. On the same set of axis, sketch the social marginal costs and benefits of abatement, and label the efficient outcome. Indicate the DWL if the city takes no action. 2. Calculate the level of pollution abatement that is socially efficient. 3. If the city institutes a per-unit tax on chemical emissions, what specific tax (7*) will reach the socially optimal amount of abatement? The city planner is considering either taxing the firm's pollution or requiring the firm to reach a minimum level of pollution abatement. However, given constant progress in abatement technologies the costs of abatement might reduce to: C2(a) = 20 . a2 - a. Thus while the social benefits of abatement are known, the social costs are uncertain. 4. Suppose that the planner institutes the per-unit tax calculated in (b). Assume that the true costs of abatement are revealed as C2(a) = 20- a - a. Illustrate the problem graphically and indicate the DWL relative to the social optimum. What level of abatement will be undertaken by the firm? Calculate the DWL. 5. Suppose instead that the planner institutes a mandatory minimum abatement at the socially optimal level found in (2). Again, assume that the true costs of abatement are revealed as Cz(a) = 20 . a2 - a. Illustrate the problem graphically and indicate the DWL relative to the social optimum. What level of abatement will be undertaken by the firm? Calculate the DWL. 6. Given the uncertainty in abatement costs, which strategy makes the most sense for reducing pollution in this context? 7. Intuitively discuss what is driving this result.Question Five Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all aspects of life in the city. There are only two residents willing to live within city-limits, Abe and Betty. Abe earns an income of 460, and Betty earns an income of 440. A traveling salesman is visiting the town, offering odor conversion units which conveniently inputs garlic odor and outputs clean air. Preferences over clean air (C) and all private consumption goods (r;) for individual i are given by: Vi = 5 . In(r;) + In(C) The total provision of clear air is given as the sum of individual purchases: C = CA + CB (+Cc when the local government purchases clean air in parts (4)-(5)). The price of clean air is 2 while the price of all other consumption goods is 1. 1. For both Abe and Betty, calculate each individual's private provision of clean air, taking the other's provision as given. That is, solve for CA as a function of Cs in Abe's optimization problem (and solve for C's as a function of CA in Betty's optimization problem). Can you explain the sign on the contribution of the other resident in these response functions? 2. If the government does not intervene, what level of clean air will be provided? How many units are provided by Abe? How many by Betty? 3. What is the socially optimal level of clean air provision? (You may assume a utilitarian social welfare function) Does this value differ from that found in (2)? Explain in the context of externalities. 4. Suppose the local government is dissatisfied with the level of private provision. The govern- ment taxes both Abe and Betty 30 each in lump-sum fashion (net-of-tax incomes are effectively reduced to 440 and 410 respectively) to provide 30 units of clean air. Both Abe and Betty are free to purchase additional units of clean air if they find it privately optimal to do so. What is the total level of clean air provided? Clearly explain the impact of the taxation/provision by the local government on the private provision by each resident. How does this answer compare to (2)?(c) Federal Block Grant Suppose instead that the federal government provides l\\.'Iaine with a blocl: grant of equivalent size to the federal grant calculated in (b). l. \""hat is Maine's eEective price per unit of improving education quality under this proposal? 2. How would you expect the quality provided to change under this proposal, relative to no federal intervention? Should this be an income effect. a substitution effect. or a combination of both? Provide intuition for how each price effect impacts the provided level of quality for the education program. 3. Present the state's revised problem graphically. as above. labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. 4. Solve mathematically for the revised level ofquality provided for the education prograrri and the total size of the grant. 5. The size of the federal grant under this proposal is (by construction) the same as in [b]. Explain any dierence between the number of education quality units provided here vs. under the grant in (b). In particulan which is larger. and why? (d) Federal Conditional Block Grant Suppose instead that the federal government provides Maine with a conditional block grant of equivalent size to the federal grant calculated in (b), whereby the grant is provided to the state with a mandate that the grant be spent only on improving the quality of Maine's education program. 1. How does this problem dier from the unconditional grant in part (c)? For what parameter values will the level of provided education be the same as in (c). and for which values will it differ? 2. Present the state's revised problerri relative to no federal government intervention graphically, labeling the original and revised budget constraints as well as the original and revised number of education quality units purchased. Draw two sets of graphs one for the set of parameter values where the provided education is the same as in (c) and one where provided education differs from that in (c). 3. Solve mathematically for the revised level of quality provided for the education pro- gram. 4. Assuming validity of the behavioral "ypaper elfect,' how would you expect the real world response to (d) to compare to the theoretical response assessed above? {e} Optimal Program If the federal government is specically concerned with perceived under-provision of educa- tion quality in Maine, which intervention assessed above is most eEective? Alternatively. if the federal govemment is only concerned with the overall welfare of Maine. which interven- tion assessed above is most effective. Provide intuition for similarities or differences in your responses. Question 2 The remote island nation of \"'heredat has two types of citizens; earls and plebs. \"rheredat is a small, beautiful island composed of a bunch of villages connected to each other by dirt walking paths. Due to rough seas and dangerous shoals around the island, the citizens use these paths as their sole method for transportation in the country. Unfortunately, \"'rheredat is plagued by the virurlike weed accumula, which if left alone quickly over-grows the walking paths and makes walking along the paths dangerous. especially at night. Question 1 In a drastic response to the news that Maine students score worse on the SAT than do students from any other state in the Union, shamed Maine politicians have decided to abolish all private provision of education and move to a purely public education system. That is1 the state of Maine would directly employ teachers and operate schools and provide education to any resident. The state government has W total resources available to divide between units of educational quality {E} and spending on all other public goods (G). Aggregate preferences within the state over E and G are given by U =o-ln(G}+[lo]-ln[E} where o: E {0,1}. The cost of each unit of education quality is 355. {a} State Provision Only 1. If the state of Maine maximizes the aggregate utility function above1 how many units of education quality will Maine prm'ide? 2. What fraction of total resources is spent on education, and what fraction of total resources is spent on other public goods? How do these fractions depend on the price pg of educational quality and total Maine government resources W? 3. [kmonstrate the optiinal choice graphically, using a standard budget constraint and indierence curve analysis. Part of Maine's new education strategy has been to give students access to top-notch, expe- rienced teachers. But because most good teachers move to warmer states like Florida, Maine has had to increase class sizes in order to achieve its strategy. The Federal Government is concerned that these larger class size; are detrimental to educational achievement, and thus it has vowed to improve Maine's educational system. To gure out how best to do this, the US Department of Education has (wisely!) asked you to evaluate several proposals. 1 In parts (bl-(d) below. evaluate the impact of the federal government intervention relative to the setup in (a). (b) Federal Matching Grant Suppose the federal government provides Maine with an extremely generous IBfor-one match- ing grant, such that each $1 in state spending on the education program is matched by 5,3 from the federal government. 1. What is Maine's effective price per unit of improving education quality under this proposal? 2. Before solving the problem mathematically1 how wmd you expect the quality provided to change under this proposal. relative to no federal intervention? Should this be an income effect1 a substitution effect, or a combination of both? Provide intuition for how each price elfect impacts the provided level of quality for the education program. 3. Present the state's revised problem graphically, as above, labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. 4. Solve mathematically for the revised level of quality provided for the education program and the total size of the grant. 5. How much does federal spending crowd out state spending