1. A perennial debate is whether federal budget deficits lead to higher interest rates. The follow-ing table gives some historical data on deficits and interest rates. For each year, the deficit is the difference between revenues and expenditures measured in current dollars; a negative figure is a deficit, and a positive figure is a surplus.
Year Deficit Interest Rate 1980 $ 273.8 15.3% 1985 2212.3 9.9 1990 2221.0 10.0 1995 2164.0 8.8 2000 236.2 9.2 2005 2318.3 6.2 2010 21,293.5 3.3 Tools of Positive Analysis chapter 233
On the basis of these data, what inference could you make about the relationship between fed-eral deficits and interest rates? Explain why inferences based on these data alone might be problematic. ”
2. ” Suppose that Tang and Wilson must split a fixed 400 pounds of food between them. Tang’s utility function is U T5 sqrt ( F1 ) and Wilson’s utility function is U W5 ½ sqrt ( F2 ), where F1 and F2 are pounds of food to Tang and Wilson, respectively. a. How much utility will Tang and Wilson receive if the food is distributed evenly between them? b. If the social welfare function is U T1U w , then what distribution of food between Tang and Wilson maximizes social welfare? c. If social welfare is maximized when they each obtain the same level of utility, then what is the distribution of food between Tang and Wilson that maximizes social welfare? ”
3. ” Suppose that the income tax in a certain nation is computed as a flat rate of 5 percent, but no tax is levied above $50,000 in taxable income. Taxable income, in turn, is computed as the individual’s income minus $10,000; that is, everyone gets a $10,000 deduction. What are the marginal and average tax rates for each of the following three workers? (Evaluate the mar-ginal tax rate at each person’s current income level.) a. A part-time worker with annual income of $9,000. b. A retail salesperson with annual income of $45,000. c. An advertising executive with annual income of $600,000. Is the tax progressive, proportional, or regres-sive with respect to income? 8. Assume that in a given country, tax revenues, T , depend on income, I , according to the formula400002,.0000 Thus, for example, when a household has an income of $50,000, its tax burden is 4,000 0.2 50,000, or $6,000. Is this a progressive tax schedule? [Hint: Compute average tax rates at several different levels of income.] Now let’s generalize the tax schedule in this problem to:TatIa where a and t are numbers. (For example, in the tax schedule above, a4,000 and t 0.2.) Write down a formula for the average tax rate as a function of the level of income. Show that the tax system is progressive if a is negative, and regressive if a is positive. [Hint: The aver-age tax rate is T/I .] ”
4. Suppose that your neighbor is willing to pay you $100 to do some home repairs for her. You would be willing to do the job for $80, so you strike a deal. Now suppose that the government lev-ies a tax of $25 on all home repair transactions.” “You pack up your gear and leave your neighbor’s home, because it is no longer worthwhile for you to do the job. As a result of your leaving the job, you do not have to pay the $25 tax. Relate this scenario to the concept of excess burden. ”
5. “ In 2002, the US federal government levied a tax of 3 percent on that part of a car’s price ex-ceeding$40,000. [For example, the tax liability on a $50,000 car would be 0.03 ($50,000$40,000), or $300.] Discuss the efficiency, equity, and administrability of this “luxury car tax.””