Tutorials in International MacroeconomicsPS1: Intertemporal approach to the current account1Model solution with growth shocksConsider the baseline model from the lecture which assumes quadratic consumption utilityand (1 +r)ฮฒ= 1.Assume that output follows a growth process, i.e.{ฮyt}is an AR(1)process with decay coefficient 0< ฯ <1.1. Set up the householdโs problem and derive the Euler equation.2. State the transversality condition.3. Derive the policy function for consumptionct=f(yt, yt-1, dt-1) by following the samesteps as in the lecture. Why does the policy function for consumption depend onyt-1?4. Also state the policy function for debtdtand for the current accountcat.2Guess and verifyConsider the same set-up as in Problem 1 on this Problem Set. As in the lecture, you hadobtained the policy function for consumption by using the intertemporal resource constraintof the economy. Another way of derivingfis called the โguess and verifyโ approach, whichworks as follows.1. Guess that the policy function is of the formct=ฮถ0+ฮถ1yt+ฮถ2yt-1+ฮถ3dt-1,for a set of unknown coefficients{ฮถ0, ฮถ1, ฮถ2, ฮถ3}.2. Insert the guess into the model equilibrium conditions (the one-period resource con-straint and the Euler equation)3. Choose coefficients{ฮถ0, ฮถ1, ฮถ2, ฮถ3}such that the model equilibrium conditions are alwayssatisfied. You should obtain the same coefficients as in the policy function of Problem1, which tells you that you have obtained the correct solution of the model.3Anticipated endowmentsConsider again the same model as in Problems 1-2 on this Problem Set, but now assume that{yt}follows the processyt=ฯyt-1+ฮตt-1,that is, an AR(1) but the shock entering from periodt-1. This specification implies thatendowment shocksytare known one period in advance!