Consider a two-period economy, where the consumers can lend or borrow and the income of the consumers in both periods is exogenous, i.e. consumers have no choice of leisure. Suppose the government introduces a subsidy on the interest payments of the borrowers. That is, while lenders face a real interest rate of r before and after the subsidy is introduced, borrowers face a real interest rate of (1 x) r, where x is the subsidy rate after the subsidy is introduced.

(a) (15 points) Determine the effects of this subsidy on the consumer's lifetime budget constraints.

(b) (15 points)How does the subsidy affect the optimal choices (consumption in current and future periods and saving) and the welfare of the consumer? Explain your answer in terms of income and substitution effects. Does your answer change depending on whether the consumer is initially a lender or a borrower? (Ignore the effects coming through government, that is, we assume the subsidy is financed through a decrease in government spending)