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. Therefore, we are looking at the effects of having x increase from zero to some value greater than zero, with r assumed to remain constant.

(a) Show the effects of the increase in the tax rate on a consumer's lifetime budget constraint.

(b) How does the increase in the tax rate affect the optimal choice of consumption (in the current and future periods) and saving for the consumer? Show how income and substitution effects matter for your answer, and show how it matters whether the consumer is initially a borrower or a lender.