Suppose I care only about consumption this year and consumption next year, and suppose I earn an income this year but do not expect to earn an income next year.
A: The government announces an increase in the tax on interest income. Illustrate my before and after tax inter temporal budget constraint.
(a) Suppose I save 50% of my income after the new tax is imposed. Illustrate the amount of the tax the government will collect from me next year. Call this T.
(b) Illustrate the most I would be willing to pay next year to keep the government from imposing this tax on interest income. Call this amount L.
(c) Is L larger or smaller than T? What does your answer depend on?
(d) If consumption is always a normal good, will I consume more or less next year if the tax on interest income is removed?
(e) If consumption is always a normal good, will I consume more or less this year if the tax on interest income is eliminated?
(f) Can you re-draw your graph but this time indicate how much T′ you are paying in taxes in terms of this year’s consumption — and how much L′ you would be willing to pay to avoid the tax in terms of this year’s consumption?
B: Now suppose that my tastes over consumption now, c1, and consumption next period, c2, can be captured by the utility function u(c1,c2)= c1a c2(1−α)
(a) Suppose the interest rate is r. What does α have to be in order for me to optimally save 50% of my income this year?
(b) Assume from now on that α is as you calculated above and suppose that my current income is $200,000. Suppose the interest rate before the tax increase was 10% and the after-tax interest rate after the tax increase is 5%. How much tax revenue T does the government collect from me next period? What is the present value of that this period?
(c) What is the most (L) I would be willing to pay to avoid this tax increase (in either today’s dollars or in next period’s dollars)?
(d) Does the amount that I save today change as a result of the tax increase?
(e) Is the tax efficient? If not, how big is the deadweight loss?