d) Explain why we can interpret o as a parameter that affects the degree of capital adjustment costs in this model. Briefly discuss how, and why, the responses of consump- tion and investment to TFP shocks vary with 6. Why do some macroeconomic modelers prefer to include capital adjustment costs in their models?c) Using guess and verify, solve the model and find the policy functions for Kt41, It and C, (Hint: start by guessing that investment and consumption are a constant share of output).\fQuestion 4 (20 points) Consider the planner's problem for a real business cycle model with inelastic labor supply (essentially the stochastic growth model) and no trend growth. Preferences are given by: In Of (1) Output is produced using capital K Y = A.K; (2) where K is the capital stock at the start of period t, and A, is a TFP shock and is governed by a discrete state Markov chain. There are adjustment costs to capital, which evolves according to the following production function: (3) When 6 = 0, this becomes the simple model we saw in class with full depreciation (i.e. where Ki+1 = It). The resource constraint is Y = ath a) Write down the recursive formulation of planner's problem. Use two constraints: the typical resource constraint and the capital production function. Denote the Lagrange multiplier on the resource constraint as A, and the one on the capital production constraint as Mig.d) In principle, could monetary policy fully stabilize the output gap and inflation after a government spending shock? (Hint: think about how the 3-equation setup above looks like the cases we studied in class)? Would there be any additional benefit from conducting optimal monetary policy under commitment?c) How, and why, does the response of GDP differ from the model with flexible prices? Do positive government spending shocks increase inflation? Provide economic intuition and (if you can) discuss the solution you found in part (b).b) Using the method of undetermined coefficients, find the response of the output gap and inflation to an exogenous increase in g, when prices are sticky and monetary policy follows the Taylor Rule above. To do this, guess that the solution for each variable is a linear function of the shock gr:Question 5 (20 points) Consider the following set of linearized equilibrium conditions for the standard New Keynesian model. The only difference from the model we saw in class is that the govern- ment can now purchase a basket of goods Gr, which is completely funded by lump sum taxes. This is like a pure government demand shock: assume that G, is not productive and does not provide utility. In percentage deviations from steady state: 4is real marginal cost, & is consumption, in, is the real wage, n, is hours worked, y, is output. In deviations from steady state: is the nominal interest rate, #, is inflation. o and 1. Government spending follows an AR(1) process 9: = p91-1 + et (12) a) Show that the natural level of output can be written as o+ yy Explain the mechanism through which an increase in government spending leads to anQuestion 6 (10 points) This question is about the standard decentralized real business cycle model. You do not need to derive anything for this question and keep your answers clear and concise. a) Briefly explain the mechanisms through which TFP shocks affect output, con- sumption, hours worked and investment in the standard RBC model. How well does the model replicate the business cycle facts seen in the data? How would adding habits in consumption affect the dynamics of consumption and investment