Complete as the question requires please

Question 6 (10 points) This question is about fiscal policy in the baseline real business cycle model. You do not need to derive anything and keep your answers clear and concise. a) TFP shocks can explain the positive correlation of GDP, consumption and invest- ment in the data. Government consumption shocks cannot explain these facts. Is this statement true or false? Explain. (Note: in this model, government consumption shocks are defined as the purchase of consumption goods by the government. This spending is not productive and does not enter the household's utility function.) b) The government wants to stimulate private consumption and GDP. They propose a temporary, debt-financed, tax cut. In the RBC model, will a tax cut have the desired effect on the economy? Start by considering lump sum taxes, and then discuss how this result might change for other types of taxes.Question 4 (20 points) Consider the following decentralized real business cycle model with no trend growth. There is a continuum of households and the representative household's preferences are given by: In (c - hCi-1) - (1) Where c is household consumption and C is aggregate consumption (which the house- hold takes as given). The household is infinitely lived and maximizes utility subject to their budget constraint. The household budget constraint can be written as: atkit - (1 -8)ke = wine trike + me (2) where w is the real wage, n is hours worked, & is capital, * is the rental price of capital and * are profits from firms. The representative firm produces output using capital k and labor ny: yt = Akin, (3) Total factor productivity A follows a Markov chain over the set A = {a1, .....ax} with transition probabilities given by paj. The aggregate resource constraint is Y = ath where upper case letters denote aggregate variables. a) Write down the household's problem in recursive form and write down the firm's maximization problem. Derive the household's first order conditions and the firm's opti- mal hiring rules. b) Carefully define a recursive competitive equilibrium. Take care to distinguish be- tween the aggregate and individual state variables and explain any market clearing con- ditions. c) Linearize the consumption Euler equation you found in part (a) around the deter- ministic steady state. d) With reference to your answer in part (c) (if you can), discuss how a TFP shock affects consumption in this model. Would the dynamics of consumption be different if consumption preferences were given by In (c - he-1)? (Hint: note the second term is now household consumption at t - 1, not aggregate consumption. You also do not need to derive anything for this question). e) What is the labor supply elasticity in this model? Given this value, how well will the model match the data? Explain