Suppose an agent is trying to maximize utility U = log c + 8( log c + (1 - 7) log c) log is the natural log. GDP is as follows: 1000, Y1 = Yb = 1120, Yr = 700, = .8 B = .8 and 1 + r = 1.25. The only asset available is the riskless bond. 1. Write down the definition of the current account, that relates y, x and c in each state. 2. How does x1, x, and x, relate? 3. Plug those equations into the maximization problem and take first order conditions 4. What is the Euler equation? *UIUC 1 5. Solve for . Now instead, imagine there was a world without risk. Instead of being uncertain about y, the country knew they would get 2 1120 x .8 + 700 x .2 = 1036 6. What is the Euler equation now? 7. What is r? 8. Did risk lead to a higher or lower current account?