° 1. Three furniture moving companies, Ripoff by Regulation, ICC Incognito, and Highwayman, have pooled their business to make profits as a monopoly. They now sit down to divide up the spoils. A majority of the three can determine how the spoils are divided. True or false: If there is no limit (set by an agenda, say) on the bargaining permitted, the majorities for one or another division will be cyclic; that is, the companies will not be able to agree on how to divide up the spoils.

° 2. In the United States, education through high school is supplied by local governments, with majority voting on the amount to be spent per pupil, collected through taxes.

a. Suppose that a certain community has three social classes, U (upper), M (middle), and L (lower), each of which acts as a single person having different tastes for expenditure per pupil (depending on the average number of children in school for each social class, the importance of education to the social class, and so on). Suppose that U values educational expenditures most, M next, and L least. Show the three demand curves for expenditure per pupil. How do you construct the marginal social willingness-to-pay (demand) curve for expenditure per pupil from these three separate demand curves, recognizing that all members of the community must consume the same amount of expenditure per pupil (all the children go to the same school)? Draw this social curve, along with the three separate class curves, all on the same graph.

b. If the marginal cost of additional expenditure per pupil is constant, what is the socially optimal output of expenditure per pupil? Explain why. Draw this point on the graph of (a).

c. If the marginal cost is shared equally in taxes among the three classes, at what points will each class begin to vote against more expenditure per pupil? In general will majority rule (2 out of 3 in this case, generally, 51%) produce the socially optimal expenditure? Explain.

d. Show how manipulating the burden of the school tax among the three classes could, given majority voting, yield the socially optimal output.

3. Suppose that two people, Harold Hawk and Donald Dove, are willing to announce truthfully the money value each puts on number of bombs used for the defense of their nation (of which they are the only citizens).

a. With 100 bombs in the arsenal, another bomb has a marginal valuation of $10 to Hawk and $4 to Dove. What is the whole nation's marginal valuation of a bomb?

b. With 200 bombs another bomb has a marginal valuation of $5 to Hawk and zero to Dove. What now is the whole nation's marginal valuation?

c. If bombs for the nation's arsenal can be produced by sacrificing other commodities valued at a constant marginal cost of $10 per bomb, will 100 be too few and 200 too many bombs? Why or why not? Draw a diagram with marginal cost and marginal valuation that illustrates the socially correct number of bombs.

d. Show that if bombs cost $10 each at the margin, the only division of the marginal tax burden to pay for the last bomb that both Hawk and Dove will accept is a division according to their marginal valuations of the bomb.

4. Giving bribes to traffic police is socially speaking more efficient than is taking the consequences of a traffic ticket (that is, having to go to court, paying a fine and court costs).

5. According to Problem 4, therefore, we should encourage the police to accept and the public to offer bribes.

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