1. Suppose that in the economy of Topolis, people live for three years and there is exactly the same number of people born each year. Thus, at any given time there is a young person, worker, and elderly person. In Topolis, the government is facing a serious long-run fiscal budget imbalance. In order to reduce expected future deficits, the government decides to tax each person $100 per year today and in the future.
a. If the discount rate is 3%, then how will this new tax change the Generational Account of the average young person? The average worker? The average elderly person?
b. Suppose that now Topolis starts spending more on education. Specifically, in any year, it collects $40 from the worker and transfers it to the young in the form of increased education spending. What is the change in the Generational Account for the young, worker, and elderly? Assume that the discount rate remains at 3%.
c. Why is this statement false? "The government treats all generations equally only if generational accounts of all generations are equal."
2. Suppose that Russia and the U.S. have different marginal benefits of pollution abatement. Specifically, the marginal benefit of pollution abatement in Russia is MB=160-10A, and the marginal benefit of pollution abatement in the U.S. is MB=180-5A. If the marginal cost of abatement in each country is constant at MC=40, then how much would each country like to abate?
3. Suppose that the private marginal benefit associated with a good's consumption is PMB = 180 - 2Q and that the private marginal cost associated with its production is PMC = 5Q. Furthermore, the marginal external damage associated with the good's production is MD = 3Q. To correct the externality, the government decides to impose a tax of T per unit sold. What tax T should be set in order to reach the social optimum?
4. Suppose that flashlights are a private good. Vlad's demand for flashlights is Q = 25 - P and Don's demand for flashlights is Q = 30 - (3/2)P.
a. What is the equation for the Social Marginal Benefit curve (Market Demand Curve)?
b. If flashlights were instead a public good, what is the Social Marginal Benefit curve (line)?
c. Graph the individual inverse demand curves and the Social Marginal Benefit curves from (b)
5. The budget office of France has calculated its long run finances under two scenarios: Outcomes under an unchanged current policy, and outcomes under an alternate policy that increases subsidies to children that is paid for by reductions in government retirement pensions to the elderly. Details are in the table below:
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French Government Fiscal
Stance
|
|
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(Present discounted values)
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Current Policy
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Alternative Policy
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Current and future
government spending
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$50 trillion
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$50 trillion
|
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Government net Assets
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-$4 trillion
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-$4 trillion
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Generational Accounts of
living generations
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$33.5 trillion
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$ 9 trillion
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Generational Accounts of
future generations
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$18 trillion
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$6.5 trillion
|
a. What is the Fiscal Imbalance under the current policy? What is the Fiscal Imbalance under the Alternate Policy?
b. Under the alternate policy, is the government "sustainable" in the long run? Explain.
6. Suppose that iPads pollute the air with X-rays and the marginal damage is given by 3Q. Suppose that the marginal cost to the firm of producing an iPad is MC=50+Q.
a. What is the marginal private cost of the 100th unit of iPads?
b. What is the marginal social cost of the 100th unit of iPads?
7. a. Suppose that demand for a product is Q = 980 - 2P and supply is Q = -160 + 4P. Furthermore, suppose that the marginal external damage of this product is $30 per unit. Calculate and graph market equilibrium.
b. How many more units of this product will the free market produce than is socially optimal?
c. Calculate the deadweight loss associated with the externality. Draw the deadweight loss on a new graph.
8. Suppose 10 people each have the demand Q = 10 - P for streetlights, and 5 people have the demand Q = 10 - P/2 for streetlights. The cost of building each streetlight is 40. How many streetlights are socially optimal?
9. Andrew, Beth, and Cathy live in Lindhville. Andrew's demand function for bike paths, a public good, is given by Q = 16 - 2P. Beth's demand is Q = 9 - P/2, and Cathy's is Q = 17 - P. The marginal cost of building a bike path is MC = 15. The town government decides to use the following procedure for deciding how many paths to build. It asks each resident how many paths they want, and it builds the largest number asked for by any resident. To pay for these paths, it then taxes Andrew, Beth, and Cathy the prices a, b, and c per path, respectively, where a + b + c = MC. (The residents know these tax rates before stating how many paths they want).
a. If the taxes are set so that each resident shares the cost evenly (a = b = c), how many paths will get built?
b. Show that the government can achieve the social optimum by setting the correct tax prices a, b, and c. What prices should it set?