Simulate in Dynare the response of output, ination, and interest rates assuming an economy that is struc tured as follows: Tl't : EtTTt+1 + Edit 1 . ft : Et$t+1 * E [H * Ett+1l it : bn't + 95ml} \"at = Putil + 6t Importantly, you must make some assumptions about how your representative agents form expectations. Assume a = 1, [3 = 0.99, w = 0.5, and K. = M. Assume that the shocks to the economy are persistent, with p = 0.75. Choose your own values for 925,, and qm, but keep them constant for the entire assignment. Clearly state what values you are using at the beginning of your assignment. a) Rational expectations is a widely used assumption in macroeconomics. Why do you think macroe- conomists prefer to make this assumption than assume individuals form non-rational expectations? Show how this economy would evolve under rational expectations, ie. where EtIt+1 = $t+1 and Etmirl = "n+1 in response to a persistent demand shock and a persistent ination shock. (This should produce two sets of simulations.) b) Now assume that agents form naive expectations, ie. Ele = :ct_1 and Ett+1 = 71}_1, and simulate the same two types of shocks as in part (a). Describe how the dynamics of your economy change and compare it to part a)'s economy under rational expectations. How does the standard deviation of output and ination change under the cases of a demand shock and an ination shock? Why do you obtain different results? c) Now assume that agents form trendchasing expectations, ie. Et$t+1 : xt_1 + 0.5(1rt_1 7 xt_2) and Eth = 7ft_1 + 0.5[7rt_1 7ft_2) . Again, simulate the same two types of shocks as in part (a). How do these economies differ from your rational and naive expectation cases? Why are the dynamics different