Question 2: Effects of redistributive policies. Show your work in all parts of t

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Question 2: Effects of redistributive policies. Show your work in all parts of this question. The country of Adventureland has two citizens - Bill and Ted. Bill has a private legal business. He earns $50 per hour. At a tax rate of 0%, Bill works 20 hours per week. At a 25% tax rate, he works only 16 hours, and at a 40% tax rate, he works 8 hours per week. Ted works in manufacturing. He works 20 hours per week and earns $6 per hour, regardless of the tax rate. * The government is considering imposing an income tax of either 25% or 40% on Bill and using the revenues to make transfer payments (welfare assistance) to Ted. The accompanying Table (below) summarizes the three possible policies. Effects of Redistributive Policies in Adventureland 0% tax rate 25% tax rate | 40% tax rate Bill's pre-tax income $1000 Bill's taxes Bill's net income Ted's pre-tax income $120 Ted's transfer $800 $200 $600 $120 $200 $400 $160 $240 $120 $160 $1000 Ted's net income $120 320 $280 Are any of the three policies obviously less than optimal? [Hint:less than optimal means lower social welfare and/or less efficient]. Briefly explain your answer. (10 points) a.

Explanation / Answer

ANSWER:

(A) Whether or not the policies raise social welfare depends on the society’s taste for redistribution.

Indeed, either of the policies makes Ted better off and makes Bill worse off than the status quo

of no taxes, so if society deems it sufficiently important to redistribute to Ted, then either policy

would raise social welfare. If society cares about only the “size of the pie,” however, then both

policies would lower social welfare. Whenever society deems that improving Ted’s income by

$200 improves social welfare more than reducing Bill’s income by $400 harms social welfare,

the 25% tax policy raises social welfare and is the optimal policy. The 40% tax policy can never

be optimal, since the 25% tax policy makes both Bill and Ted better off than the 40% tax policy.

(B) The utility function is increasing in income. Rawlsian social welfare is therefore equal to the

utility of the individual with lower income. For 0% and 25% tax rates, Ted has the lower incomes

($120 and $320, respectively). For a 40% tax rate, Bill has the lower income ($240). Since $320

> $240 > $120, Rawlsian social welfare is highest under the 25% tax rate and lowest under the

40% tax rate. To compute utilitarian social welfare, we compare:

Utilitarian social welfare with a 0% tax = 1,0001/2+ 1201/2 42.58

Utilitarian social welfare with a 25% tax = 6001/2+ 3201/2 42.38

Utilitarian social welfare with a 40% tax = 2401/2+ 2801/2 32.33

We see that the 0% tax rate is best.

(C) This change does not affect the order of tax rates according to the Rawlsian social welfare

function. To compute social welfare for the utilitarian social welfare function we compare:

utilitarian social welfare with 0% tax = 1,0001/5+ 1201/5 6.59.

utilitarian social welfare with 25% tax = 6001/5+ 3201/5 6.76.

utilitarian social welfare with 40% tax = 2401/5+ 2801/5 6.08.

We see that the 25% tax rate is best and the 40% tax rate is the worst.

(D) Since the two have different utility functions, it is no longer easy to see who is better off under

each situation. Under the 0% tax policy, we see that Ted has utility 1201/2 10.95 and Bill has

utility ¼ 1,0001/2 7.91. We see that Bill is worse off under this policy. Since the other two tax

policies make Bill worse off and Ted better off than the 0% policy, Bill’s utility will be used to

compute Rawlsian social welfare. Rawlsian social welfare is highest with 0% taxes and lowest

with 40% taxes, the policies that make Bill the best and worst off, respectively.

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