1. Suppose there are five people - 1, 2, 3, 4, and 5 - who rank projects A, B, C, and D as follows:
Assuming the different projects correspond to different levels of a public good (where A is the lowest and D is the highest level), answer the following questions:
a. Taking pairwise votes, will any project be chosen by a majority-rule vote? If so, which one? Show your work.
b. Are each individual's preferences "single-peaked"? Which ones, if any, are not single-peaked? Show your work.
c. What problem potentially arises when preferences are "double-peaked" and majorityrule is the decision-making mechanism?
2. How do government bureaus differ from private firms? Why is there good reason to believe that bureaucrats will seek to supply more than the efficient level of their output in any year? Use a graphic analysis to show the losses in efficiency that will result if a government bureau succeeds in maximizing its annual expenditures.
3. Consider an economy that is composed of identical individuals who live for two periods. These individuals have preferences over consumption in periods 1 and 2 given by √ √ . They receive an income of $20,000 in period 1 and an income of $5,000 in period 2. They can save as much of their income as they like in bank accounts, earning an interest rate of 10% per period. They do not care about their children, so they spend all their money before the end of period 2. Each individual's lifetime budget constraint is given by + /(1 + r) = + /(1 + r), where and are incomes in periods 1 and 2, respectively. Individuals choose consumption in each period by maximizing lifetime utility subject to this lifetime budget constraint.
a. If there is no Social Security program, what is the individual's optimal consumption in each period? How much saving does he or she do in the first period?
b. Now the government decides to set up a Social Security program. This system will take $3,000 from each individual in the first period, put it in the bank, and transfer it to him or her with interest in the second period. Write out the new lifetime budget constraint. How does the system affect the amount of private savings? How does the system affect national savings (total savings in society)? What is the name for this type of social security system?
4. For each of the following, determine which group would have higher Social Security Wealth (SSW), all other things equal. Explain your answers.
a. male or female
b. born in 1925 or born in 1985
c. single or married
d. low-wage earners or high-wage earners
e. single-earner couples or double-earner couples