PLAESE HELP WITH THIS ASSIGNMENT

a lnterutR-u 3mm polnu] Consider an individual who lives for turn periods, denoted l and 2. Her plel'erenom for consumption in each period are dwa'ibed by the lifetime utility function 1 1 U=aa (a) where C, denote; mnsurnptiou in period 1. Ca denotes consumption in perbd 2. Suppose that the consumer starts period 1 with nancial Wealth equal toll + "3,36! where B; is an inherited stool: of hand and r0 is the interest rate on bonds held between periods 0 and 1. Suppose further, that the individual receives endowments of goods in the amounts Q1 and Q; in periods 1 and 2, respectively. In period I, the individual can borrow or land at the interest rate r1 > [1 via a bond denoted 3;. Assume perfect capital mobility. so n = r'. a) Find the optimal lends oi consumption in periods 1 and 2 as functions of the individual's liletime wealth. l7, and the interest rate. Hint: Recall that Y = [l + ro)B,', + Q] + 7357. Do not forget to include all your derivation and equations. [12 points} b) Find the responses of mnsmnption in period 1. (10.. the trade balm in period 1. ATE, and the current account in period 1, ACA. to an increase in the mrld interest rate equal to Ar' > I). Do not forget to include all your derivation and equations. Renal! that [or variable XthereeponaeiaequaltoAX=X'-X.whereX'isthevalueoIXaftertheincmeinthe intaest rate and X 'B the initial value of X. [10 points]