1. Suppose ten people each have the demand Q=20-4P for streetlights, and 5 people have the demand Q=18-2P for streetlights. The cost of building each streetlight is 3. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal?
2. Alfie, Bill, and Coco each value police protection differently. Alfie's demand for the public good is Q=55-5P, Bill's demand is Q=80-4P, and Coco's demand is Q=100 -10P. The marginal cost of providing police protection is $13.5.
a. What is the socially optimal level of police provision?
b. If each voter pays one-third of the total bill for police protection, how much will each voter wish the community to buy?
c. If the median voter wins, how much will the community buy?
3. The Partytown school district has long been controlled by the same political group, the INS. There is little chance of political competition in the near future. Thus Partyville is governed by a monopoly model of fiscal choice. The head of the school board, Mr. Big, is eager to maximize the school district budget. However, the school budget, if larger than the state minimum must be approved in a vote by the residents. If a proposed budget fails, the state minimum is the reversion amount.
In Partytown all residents have the following MB curve for school quality units:
MB = 500 - 10 * Q
All residents face a tax price of $100 per quality unit.
a. What is the efficient level of quality units in the Partytown school district?
b. The state minimum requires Q to be at least 20. What is the MB of residents at this level of Q?
c. Relative to the efficient point what is the welfare loss residents would experience at the state minimum?
d. Given Mr. Big's preference to maximize the school budget, what Q level will he propose and why?
4. The residents of Mobile City all live in mobile homes which they own. However, they rent land for their homes from absentee landowners. The rental supply of land is inelastic at 100 acres. The demand curve for acres is given by: R = $400 - $2L, where R is the monthly rent per acre and L is the quantity of acres rented.
- How many acres are rented? Explain. What is the market rent of an acre? Explain.
- Suppose the city imposes a tax of $40 per acre that by statute falls on the renter. What happens to the gross rent per acre? To the net rent per acre? What happens to the total number of acres rented? Explain. How much tax is collected?
- Given your answers to (b), what are the effects of the land tax on the welfare of mobile home residents? Explain.
- Given your answers to (b) and (c) what are the effects of the land tax on the welfare of the absentee land owners? Explain.
- Given your answers to (b), (c) and (d) is the land market efficient after the tax is imposed? Explain.
5. Explain the difference between a progressive and a regressive tax. If the average property tax on rental residential structures in the nation goes up, do you expect the result to be progressive or regressive? Explain.