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Compare after-tax returns on all three forms of investment

1. Suppose you are a thirty-year-old worker choosing between an IRA, a ROTH IRA and a regular brokerage account. Your marginal federal tax rate is 15% now and 15% in retirement. Your investment of $1000 of reduction of current consumption will earn before tax return of 7% for 35 years (note, this means that you invest approximately $1176=$1000/(1-.15) for a regular IRA, getting back $176 as reduced taxes, in the first example, while you invest $1000 for the other two types of accounts). The tax on investment returns on a regular brokerage account is 10% (meaning you earn a 6.3% after tax annual yield).

a) Compare after-tax returns on all three forms of investment. Rank the investment options.

b) Suppose your tax rates are 30% now and 15% in retirement: what is the best option now? Please be sure to keep the initial decrease in consumption (after-tax income) constant.

c) What if the rates are 15% now and 30% in retirement?

d) Suppose the marginal tax rate now is 15%. What would future marginal tax rate have to be for a regular brokerage account to be a better option than a regular IRA?

2. Assume that there are only two goods in the economy: video games and water. The total amount of these goods are given, there is no production. The world is inhabited by two people: Ann and Bob. Assume that Ann and Bob have regular preferences (not necessarily same for Ann and Bob) over video games and water; and that they have some endowments of these two goods. Now a well-intentioned politician says that because water is scarce and it is a necessity, both Ann and Bob should get half of the overall water resources (and get to consume their respective endowents of video games). Is this likely to be an efficient policy? Use the Edgeworth-box to justify your answer.

3. Pete and Paul live in an exchange economy (so we can use the Edgeworth-box). The economy has endowment of 10 cheese slices and 10 crackers. Pete has distinguished taste, he likes to eat cheese with cracker, to the extent that he considers them perfect complements, his utility is U=min{ch, cr}, where ch=cheese consumption and cr=crackers consumption. Paul cares only about satisfying calorie requirements; he considers cheese and crackers perfect substitutes. His utility function is U=ch+cr.

a) Is Pete consuming 3 crackers and 5 cheeses slices a Pareto-optimal allocation? If not, how could you rearrange the consumption of Pete and Paul to arrive at better allocation?

b) Using Edgeworth-box, draw a Pareto-optimal allocation.

c) Using the logic of your answer for part a, draw the contract curve.

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