exercise 4 answers

1

ECO 4554-01 Economics of State and Local Government

Public Choice

Exercise 3 Answers

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 3. 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 3 Quiz: When you have completed the exercise, take Exercise 3 Quiz on the course website under Course Documents. 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

• practice using linear demand functions to solve economic problems • reinforce your understanding of the median voter theorem, the Lindahl equilibrium, and the

reversion model • reinforce your understanding of the problems with simple majority rule

Before beginning this exercise, read Fisher, Chapter 3, and the Additional Reading Assignments for Topic 2. There are three representative individuals in the community. They have different incomes, but all have the same preferences (demands). The community operates a recreational facility. The demand functions are shown below where Q is the number of hours per week that the facility operates and MB is the marginal benefit:

Huey: MB=120-6Q. Dewey: MB=75-5Q.

ECO 4554-01: Economics of State and Local Government Public Choice

Exercise 3 Answer

2

Louie: MB=24-2Q. The marginal cost of operating the facility is $63 per hour.

Problems 1. Median Voter Theorem

a. Each individual’s preferred number of hours is the quantity at which his marginal benefit equals his share of marginal cost. If marginal cost is divided equally among the three so that each pays a tax-price of $21, what is each individual’s preferred quantity? [Recall that consumers choose the quantity that makes their marginal benefit equal to the price they must pay.]

b. Using simple majority rule, how many operating hours per week will be chosen? Answers:

a. Set each person’s demand function equal to his tax-price ($21) and solve for Q:

High income: MB=120-6Q=$21⇒Q=16.5 Middle income: MB=75-5Q=$21⇒Q=10.8 Low income: MB=24-2Q=$21⇒Q=1.5

b. The median voter is the middle income person, so the quantity chosen is his preferred

quantity, 10.8 2. Simple Majority Rule Does Not Necessarily Choose the Efficient Quantity

a. To determine the efficient quantity, you must know the marginal social benefit as well as the marginal cost. To find the marginal social benefit function, add the individual marginal benefit functions. [Remember that this is a public good so you are “adding vertically”. Each individual’s quantity consumed is equal to the total quantity supplied so they all consume the same quantity. The marginal social benefit of that quantity is the sum of the individual marginal benefits.]

b. The efficient quantity is the quantity at which marginal social benefit equals marginal cost.

What is the efficient number of operating hours? c. How does the efficient number of hours compare with the number of hours chosen by simple

majority rule? Answers: a. MSB=(120+75+24)-(6+5+2)Q=219-13Q b. MSB=MSC or 219-13Q=63 so Q*=12 c. Simple majority rule chooses 10.8 hours which is less than the efficient number of

hours, 12. 3. Lindahl Equilibrium


Exercise 3 Answer

3

In a Lindahl equilibrium, each individual pays a tax-price equal to his marginal benefit. What is the Lindahl equilibrium tax-price for each individual at the efficient quantity?

Answers: For each person, substitute the efficient quantity for Q and solve for their marginal benefits. With Lindahl tax-prices, each person’s tax-price equals his marginal benefit.

High income: $48 Middle income: $15 Low income: $0

With a set of Lindahl tax-prices, each individual prefers the efficient quantity. Therefore, simple majority rule results in choice of the efficient quantity, but so does any other voting rule. Simple majority rule is no worse, but also no better, than other voting rules. The lesson of the Lindahl equilibrium is that, when the equilibrium quantity is determined by simple majority rule voting, the closer the distribution of taxes is to the distribution of benefits, the closer the equilibrium quantity is likely to be to the efficient quantity.

4. Simple Majority Rule Does Not Reflect Intensity or Strength of Preferences

a. Suppose Huey’s demand increases so that his demand function is now MB=150-6Q. If his tax-price is still $21, what is his new preferred quantity?

b. How many hours are chosen now using simple majority rule? c. How does the increase in Huey’s demand affect the quantity chosen by simple majority rule? d. How would a change in Louie’s demand affect the quantity chosen by simple majority rule? Answers: a. 21.5 b. 10.8 c and d. A change in the preference intensity of either the high income or the low income

individual has no effect on the quantity chosen using simple majority rule. The middle income individual still has the median preferred quantity, and therefore, his preferred quantity is still the quantity chosen using simple majority rule. Changes in preference intensity among non-median voters have no effect on the outcome (provided preferences don’t change so much that the middle income person is no longer the median voter).

5. Monopoly Bureaucratic Voting Models

a. Dewey is the median voter. Draw a diagram showing Dewey’s marginal benefit curve and his

tax-price of $21. Indicate on your diagram his preferred quantity. b. Suppose simple majority is the voting rule but voters can only vote on proposals presented to

them by the bureaucrats. If voters accept the bureaucrat’s proposal, that becomes the new equilibrium quantity. If voters reject the proposal, the facility’s operating hours revert to last


Exercise 3 Answer

4

year’s level of 8. Indicate the reversion quantity on your diagram. Now, outline or shade in the area that represents Dewey’s loss of consumer surplus if the quantity is 8 instead of being equal to his preferred quantity.

c. What is the greatest number of hours that the bureaucrats can get the voters to approve?

Explain how you determine this quantity.

Answers: a.

b and c. Dewey’s loss of consumer surplus if the quantity reverts to 8 instead of his

preferred number of 10.8 is area A. The loss would be the same if the quantity were 13.6, as shown by area B, which is just equal to area A. Therefore, Dewey is indifferent between 8 and 13.6 because they both involve the same loss. So 13.6 is the largest number of hours that the bureaucrats can get Dewey (the median voter) to approve.