Suppose that the government introduces a tax on interest earnings. that is, borrowers face a real interest rate of r before and after the tax is introduced, but lenders receive an interest rate of (1 − x)r on their savings, where x is the tax rate. we will analyze what happens when the tax rate x increases from zero to some value greater than zero, with r assumed to remain constant. [hint: when x = 0, you would have a normal straight budget constraint like we’ve seen in the lecture.]
1.) show the effects of the increase in the tax rate on a household’s lifetime budget constraint. [hint: draw what the lifetime budget constraint looks like when x = 0. then show how that changes when x > 0.]
2.) suppose the household was initially a borrower when x = 0. graphically show how the increase in the tax rate x affect the optimal choice of consumption (in the current and future periods) and saving for this household. specifically, show how the income and substitution effects matter for your answer.
3.) suppose the household was initially a lender when x = 0. graphically show how the increase in the tax rate x affect the optimal choice of consumption (in the current and future periods) and saving for this household. specifically, show how the income and substitution effects matter for your answer.