Suppose the private market return is r=20%. The economy has progressive tax syst

Question

Suppose the private market return is r=20%. The economy has progressive tax system as
follows. Low income: t=0%, Moderate income: t=15%, High income: t=28%. Assume each group has some amount of capital that can be invested in either a private bond or state bond. Low income: $100,000 to invest, Moderate income: $75,000 to invest, High income: $250,000 to invest. Suppose the state government needs to raise $100,000.
a. What rate of return should it offer?
b. How much does the state government save or lose?
c. How much does the federal government save or lose?
d. If the state government needs to raise $325,000, what rate of return should it offer?

Explanation / Answer

a. with this above information, the return to induce a person to invest in the state bond is:

(1-tlow)r = 20% for low income group, (1-tmod)r = 17% for moderate income group, (1-thigh)r = 14.4% for high income group.

People with higher tax brackets will get maximum benefit from buying state bonds.

So, the rate of return Govt. should offer is = 14.4% , because there is an incentive for high income people to supply capital.

b. The govt. is now paying 14.4% instead of 20%. on $100,000.So saving:

100,000*20 % - 100,000*14.4%

= 100,000*(20%-14.4%)

= 100,000* 5.6%

= $5,600

c. The federal government would have collected taxes on interest = $100,000*20% = $20,000. So, it looses 28%x$20,000=$5,600

d. If the state government needs to raise $325,000, it must needs the supply of capital by moderate income group too. So, it needs to increase the rate of of return to 17% from 14.4%. The high income group must recieve some economic rent as it supply all the capital of $325,000 at rate of return(r)= 14.4%

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