Question 1 Consider a 3 period small open economy populated by a representative agent with preferences given by: incl + lan + 32:5an (1) with initial asset position given by (L1. Suppose the age receive and endowment in each period y1,yg,y3 and that the interest rate is given by r. a) Write the agent's budget constrain in each period t = 1, 2, 3. b) Write the No Ponzi game (or don't die in debt) condition. (3) Derive the intertemporal budget constraint. d) Compute the equilibrilnn level of consumption, the trade balance and the current account in periods t = 1, 2,3. e) Assume that in period 1 the economy receives a temporary increase in the endowment equal to Ay > i}, and that y2,y3 remain unchanged. Calculate the changes in period 1 consumption, trade balance and current account A01, ATBl, CA1. f ) Now assume that the change in income at time 1 is permanent. Calculate the changes in consumption, the trade balance and the current accelmt at t + 1. Provide some intuition for your answers. g) Answer part e) and f) for the general case in which the representative agent lives for T > 3 periods