4. An individual has preferences represented by the utility function u(x,y) =xy where x is the number of dollars available to purchase goods this period and y is the number of dollars available to purchase goods next period. She has endowment (2000, 5000) and has access to a perfect capital market with interest rate r per period . a. If the interest rate is 33 and a third percent per period , what is the budget she faces? b. With general interest rate r > 0, what is the budget she faces? C. What is her optimal first-period consumption as a function of the interest rate, x(r)? d. For which interest rates is she a borrower and for which interest rates is she a saver? e. What is her marginal rate of substitution at her endowment