Question

Home Tools homework1.pdfx Sign In 212 d Share 95% 7. The country of Tinyland has two citizens, Bill and Ted. Bill owns a business. He earns $50 per hour. When no tax, Bl works 20 hours. At a 25% tax rate he works 16 hours, and at a 40% tax rate he works only 8 hours per week Ted has a manufacturing job. He works 20 hours per week and earns S6 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 to Ted. The following table summarizes the three possible policies 25%) | 40 | Pre-Tax Income | $1,000 | $800 | $400 0 $200 $160 $1,000 $600 | $240 $120 120 $120 0 $200 $160 $120 $320 $280 Bill Taxes Net Income Pre-Tax Income Ted Transfer Payment Net Income (a) Suppose that Bill and Ted care only about net income, i.e., they utility function is linear in net income y, u(y)-y (i) Does either policy proposal more efficient than the status quo of no taxes? Why? (ii Are either policy proposal obviously less than optimal? Explain (b) Suppose that Bill and Ted have the same utility function u(y)-y1/2 where y ¡s consumption (which is equal to net income) (i) Rank the three tax policies for a utilitarian social welfare function. (ii) Rank the three tax policies for a Rawlsian social welfare function. Show the detail of your computation/argument for your conclusion. (c) How would your answer change to (a) if the utility function is instead u(y) = y1/5 Answer both (a.i) and (a.ii, and explain why I>

Answer 1

Under the 0% tax rate policy:

Under this policy, it is given that Bill’s net income, Y_B, is 1000 and Ted’s net income,

Y_T , is 120.

We can calculate Bill’s utility, U_B , using his utility function:

UB(Y_B)=YB

⇒U_B(Y_B)=1000= 31.62.

Similarly, we can calculate Ted’s utility, U_T , using his utility function:

UT(YT )=YT

⇒U_T(Y_T )=120=10.95.

Using a utilitarian social welfare function we can calculate the level of social welfare under this tax policy:

SW =U_B(Y_B)+U_T(Y_T )

⇒SW = 31.62 +10.95 = 42.57 .

Under the 25% tax rate policy:

Under this policy, it is given that Bill’s net income, Y_B, is 600 and Ted’s net income, Y_T , is 320.

We can calculate Bill’s utility, U_B , using his utility function:

UB(Y_B)=YB

⇒U_B(Y_B)= 600= 24.49 .

Similarly, we can calculate Ted’s utility, U_T , using his utility function:

UT(YT )=YT

⇒U_T(Y_T )= 320=17.89 .

Using a utilitarian social welfare function we can calculate the level of social welfare under this tax policy:

SW =U_B(Y_B)+U_T(Y_T )

⇒SW = 24.49 +17.89 = 42.38.

Under the 40% tax rate policy:

Under this policy, it is given that Bill’s net income, Y_B, is 240 and Ted’s net income, Y_T , is 280.

We can calculate Bill’s utility, U_B , using his utility function:

UB(Y_B)=YB

⇒U_B(Y_B)= 240=15.49 .

Similarly, we can calculate Ted’s utility, U_T , using his utility function:

UT(YT )=YT

⇒U_T(Y_T )= 280=16.73.

Using a utilitarian social welfare function we can calculate the level of social welfare under this tax policy:

SW =U_B(Y_B)+U_T(Y_T )

⇒SW =15.49 +16.73 = 32.22.

Ranking of the Tax Policies according to the level of social welfare using a utilitarian social welfare function:

Ranks	Social Welfare Levels		Tax Policies
1st (best)	42.58		0%
2nd	42.38		25%
3rd	32.23		40%