Exercise 5

ECO 4554-01 Economics of State and Local Government Optimal Jurisdictions Exercise 5 Instructions Your answers must be clearly written and legible. What you submit must be a finished product, not a draft or “scratch work”. Do your calculations and scratch work elsewhere and then copy it to your final product. If your exercise is messy or hard to follow, it will not be evaluated and you will not receive credit. Show your arithmetic. To Submit: If you complete the exercise off-line, scan the completed exercise into your computer. Your scanning software may require you to indicate that this is a single, multi-page document. From the Exercise button on the Course Menu, click on Exercise 5. Then click Choose File, find the file on your computer, and attach it. Finally, click Submit. Once you have submitted an exercise, Blackboard will not allow you to change it or delete it. Exercise 5 Quiz: When you have completed the exercise, take the Exercise 5 Quiz on the course website under Course Documents. You may take the quiz as many times as you like up to the deadline. If you do not submit a completed exercise, you may not receive credit for the quiz. Formatting Quiz Answers: Dollars: No decimals unless non-zero and at least one digit to the left of the decimal even if zero. If non-zero decimals (that is, cents), you must include two digits to the right of the decimal. Include dollar sign and commas to separate thousands. Quantities: No decimals unless non-zero and at least one digit to the left of the decimal even if zero. Include commas to separate thousands. If decimals, two digits to the right of the decimal. Elasticities: Do not round intermediate calculations. No decimals unless non-zero and at least one digit to the left of the decimal even if zero. If decimals, round to two digits to the right of the decimal. Percentages, shares, and tax rates: Express as percentage, not as decimal. No decimals unless non-zero and at least one digit to the left of the decimal even if zero. If decimals, two digits to the right of the decimal. Include percent sign. Introduction The objectives of this exercise are to • reinforce your understanding of the implications of the Tiebout hypothesis. • illustrate the conflicts that arise among the different criteria for optimal size of jurisdictions. Before beginning this exercise, read the assignment in Fisher, Chapter 5, and review the lecture notes for Topic 3. You may also wish to review the Economist’s Toolkit on identifying and computing deadweight loss. Problems Tiebout and Returns to Scale 1. Figure 1 shows the average total cost (measured in hundreds of dollars per person) to a community of providing police protection as a function of the community’s population (measured in thousands of people). a. Based on the criterion of maximizing economies of scale (minimizing average total cost), what is the optimal size of a community for the provision of police protection? 1

ECO 4554-01: Economics of State and Local Government Optimal Jurisdictions Exercise 5

b. Suppose there are two types of individuals, represented by Dewey and Louie. Dewey is a “law and order type”, who has a strong preference for police protection (measured as number of daily police patrols). Louie is a “do your own thing free spirit type”, who prefers a minimal amount of police protection. There are 15,000 people of each type. Based on the Tiebout hypothesis, what is the optimal size of a community for the provision of police protection? 2. The table below and Figure 2 show the demand for and cost of police protection. At a cost of $100 per person, what is Dewey’s preferred quantity of police protection? What is Louie’s preferred quantity? Quantity (Daily Police Patrols) 0 1 2 3 4 5 6 7 8 9

Dewey’s Marginal Benefit $170 $160 $150 $140 $130 $120 $110 $100 $90 $80

Huey’s Marginal Benefit $130 $120 $110 $100 $90 $80 $70 $60 $50 $40

Average Total Cost=Marginal Cost $100 $100 $100 $100 $100 $100 $100 $100 $100 $100

3. Suppose everyone lives in the same community so as to take maximum advantage of the economies of scale. The community’s voting rule is that, in case simple majority rule results in a tie between preferred quantities, the quantity provided is the average of the two preferred quantities. Therefore, the quantity provided in this community is 5 daily police patrols. Calculate Dewey’s loss of consumer surplus from underproduction of police protection relative to his preferred quantity. Calculate Louie’s loss of consumer surplus from overproduction relative to his preferred quantity. 4. Now, suppose there are two communities, one composed of the Dewey-types and one composed of the Louie-types. These two communities are optimal sized based on the Tiebout criterion, but they are smaller than the optimal size based on economies of scale. Therefore, their cost to provide police protection is no longer $100 per capita, but rather $110 as shown in Figure 3. a. What is Dewey’s preferred quantity at $110? b. What is Louie’s preferred quantity at $110? c. Calculate Dewey’s loss of consumer surplus from the higher cost of police protection relative to his most preferred quantity at the $100 minimum cost? Also, calculate Louie’s loss of consumer surplus from the higher cost of police protection. [Note: At the higher cost, each individual’s preferred quantity is less than it would be if the police protection were produced at minimum cost. So, the loss of consumer surplus now has two pieces. First, there is a loss on the quantity they actually consume because of the higher cost (your answer in either a or b above). This is the rectangular area that shows the difference between $100 and $110 multiplied by the number of units they consume. Then, there is the loss on the units not consumed. This is the usual deadweight loss triangle between $100 and $110 and between the quantity they consume at the higher cost (your answer in either a or b above) and the quantity they would choose at the lower cost (your answer to 2 above).]

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ECO 4554-01: Economics of State and Local Government Optimal Jurisdictions Exercise 5

5. You can have one large community providing an inefficient quantity of police protection but at the lowest possible cost. Alternatively, you can have two smaller Tiebout communities, each providing the quantity of police protection that is efficient for its residents but at greater-thanminimum cost. Can you suggest one or more ways that this conflict between returns-to-scale optimality and Tiebout optimality can be overcome? That is, can you suggest one or more ways that simultaneously satisfy all three of the following conditions: • • •

Dewey lives in a community of no more than 15,000 where the quantity of police protection is exactly equal to his preferred quantity; Louie lives in a community of no more than 15,000 where the quantity of police protection is exactly equal to his preferred quantity; police protection is supplied to both communities at the minimum average total cost of $100 per person?

Tiebout and Interjurisdictional Externalities Education provided to students in Hueytown not only benefits Hueytown’s residents but also confers external benefits on residents of Deweyburg because, for example, some students educated in Hueytown may eventually relocate to Deweyburg. All the voters in Hueytown have the same demand for education for their children. All the voters in Deweyburg have the same demand for education of Hueytown’s children. The data are shown in the table below and in Figure 4. The quantities are in hundreds of high school graduates per year and the dollars are in thousands of dollars per graduate. Quantity (Number of High School Graduates Annually in Hundreds) 0 1 2 3 4 5 6

Hueytown’s Marginal Private Benefit, MB

Deweyburg’s Marginal External Benefit, MEB

Marginal Social Benefit (MSB=MB+MEB)

Marginal Cost (MC)

$9 $8 $7 $6 $5 $4 $3

$7 $6 $5 $4 $3 $2 $1

$16 $14 $12 $10 $8 $6 $4

$8 $8 $8 $8 $8 $8 $8

6. If the interjurisdictional externality is uninternalized, the residents of Hueytown choose the private equilibrium number of high school graduates. Calculate the loss in social surplus from the underproduction of high school graduates. 7. Suppose now that Hueytown and Deweyburg were consolidated into one large community in order to internalize the interjurisdictional externality. Everyone in the community pays the same tax-price for education, equal to one-half the marginal cost ($4,000). At this price, what is Hueytown’s preferred number of high school graduates in the consolidated community? What is Deweyburg’s preferred number of high school graduates in the consolidated community? 8. Suppose the rule is that, when simple majority rule results in a tie between preferred quantities, the quantity provided is the average of the preferred quantities. Calculate Hueytown’s loss of consumer surplus from underproduction of high school graduates in the consolidated community. Calculate Deweyburg’s loss of consumer surplus from overproduction of high school graduates.

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ECO 4554-01: Economics of State and Local Government Optimal Jurisdictions Exercise 5

9. Suppose now that the two communities were not consolidated, but that the state government subsidizes Hueytown’s cost to educate its children. The state taxes the residents of Deweyburg an amount equal to their marginal external benefit. It uses the revenues to provide an intergovernmental grant to Hueytown to increase the number of high school graduates. a. What happens to Hueytown’s demand (marginal benefit) curve for high school graduates when they receive the education subsidy from the state? b. With the grant, what number of high school graduates do the residents of Hueytown choose? (That is, what is their new preferred quantity?) c. How much of the marginal cost of this number of graduates is paid by the residents of Hueytown? d. How much of the marginal cost is paid in tax by the residents of Deweyburg? 10. Complete the following statement and explain your answer: Where interjurisdictional externalities exist, consolidation of communities results in an (efficient, inefficient) equilibrium, and intergovernmental grants without consolidation result in an (efficient, inefficient) equilibrium.

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ECO 4554-01: Economics of State and Local Government Optimal Jurisdictions Exercise 5

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ECO 4554-01: Economics of State and Local Government Optimal Jurisdictions Exercise 5

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