Thank you! work on only a part will be fine too

Question 1: A Macroeconomic Model with Time-varying Risk Aversion (50 Marks) We use a stochastic macroeconomic model to account for the aggregate uctuations of the Canadian economy. We extend the model with TFP shocks and rigid labor supply that we have covered in the course. We also consider the same data you worked with in the more recent problem sets. The representative agent's utility function is specied as: Where 7,: denotes timevarying risk aversion, with unconditional average in, = 2. The CRRA parameter is stochastic, and its log follows an AR(1) process with normally distributed i.i.d. shocks: ln 'yt : P7 1IWti + amt: 5w N N\"): '73,)- The size of the labor force is normalized to 1 and it does not change over time. The representative agent has a time endowment of one unit per period, which is devoted entirely to work (L: = 1). The production function is Cobb-Douglas: Y} = Zth'L%_a. Total Factor Productivity (TFP) is time-varying and its log follows an AR(1) stochastic process with normally distributed i.i.d. shocks: ln Z; = pz 1n Zt_1 + 5271;, 52,, N N (0, ogz). The two shocks (6%,, 5 2,15) are negatively correlated, with correlation p772. Kt is the capital stock, which depreciates at rate 6. In this model, there is no government. We consider the HPltered data you constructed in the problem sets. Namely, retrieve the series (in levels) for consumption (Ct) and investment (1,). Compute output (Y2) as the sum of only these two variables. Take the log of the three series in levels and then apply the HP lter with smoothing parameter A = 1600. Consider the cyclical component of each series. 1. State the Social Planner's problem, derive the rst order conditions and obtain the equations representing the equilibrium dynamics. Comment on your results