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Consider an individual who lives for two periods. Her preference for consumption is given by the life-time utility hmction all-T leg-1 1 y + 131 This function is called the Constant Relative HiSk Aversion (UREA) utility function where pa- rameter 1: measures the degree of relative risk aversion. As discussed in the lecture. suppose that she starts period 1 with nancial wealth equal to {1 + r9139, where Bu denotes the inherited asset position and m. is the interest rate on this asset between period I] and 1. She receives endowments of goods in the amounts of Q1 and Q2 in the two periods. In period 1, she can borrow or lend at the interest rate 1r". the world interest rate. 1. 2. Derive the Euler Equation. Solve the optimal consumption path {01, Ce): trade balances {T31: T33}, and current accounts [CAM CA2}. [15] Discuss how Cl and {3'2 change when T or ,3 increases [15] From now on, assume qr = 1. so the UREA utility function is reduced to a (natural) log mction Ul-l = loci-l 3. If there were a temporary positive income shock of d such that period 1 endowment increased from Q1 to Il.',;|1+.-'1l.1 what are the changes of each period's consumption {IE-{1'1 and 41.92}: trade balance [TBl and 5.1232) and current account {$0.41 and $0.42}? [15] If there were a permanent positive income shock of a. such that period 1 endowment increased from Q1 to Q1+ and period 2 endowment increased from Q2 to Q2+. what are the changes of each period's consumption {1.01 and $02). trade balance [TBl and TBE) and current account {$044.1 and $044.2)? [15] If in period 1. she anticipated a temporary positive income shock of it such that period 2 endowment would increase from Q2 to Q2 + a, what are the changes of each period's consumption {IE-{3'1 and 02). trade balance {iTBI and dTBg} and current account {$0141 and $044.2)? [15] Finally, when world interest rate r\" T. will Cl T or 1? How about Cg? [15] . What do you learn from this exercise regarding current account determination? [l]