(a) Consider the following social planning problem: maximize Et 8=0 Bs C |- 't+s 1-o subject...

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(a) Consider the following social planning problem: maximize Et 8=0 Bs C |- 't+s 1-o subject to the resource constraint Ct + Kt+1 (1 8)Kt = Al-K and given the forcing process In At+1 = pln At + ln t+1 where Ct and Kt are the planner's consumption and capital stock at date t, At is labour productivity, {ln t+1} is serially uncorrelated, 0 < < 1, 0 < 8 < 1, 0 < p < 1, and is the relative risk aversion parameter. Labour is inelastically supplied at unity. Derive the log-linearized first order condition and resource constraint. Show all your steps. (50 marks) (b) Using the basic new Keynesian model, set up the household's consumption, saving, and labour supply problem explaining the household's optimisation problem very carefully. Then derive the consumption Euler equation and interpret your results. (50 marks) (a) Consider the following social planning problem: maximize Et 8=0 Bs C |- 't+s 1-o subject to the resource constraint Ct + Kt+1 (1 8)Kt = Al-K and given the forcing process In At+1 = pln At + ln t+1 where Ct and Kt are the planner's consumption and capital stock at date t, At is labour productivity, {ln t+1} is serially uncorrelated, 0 < < 1, 0 < 8 < 1, 0 < p < 1, and is the relative risk aversion parameter. Labour is inelastically supplied at unity. Derive the log-linearized first order condition and resource constraint. Show all your steps. (50 marks) (b) Using the basic new Keynesian model, set up the household's consumption, saving, and labour supply problem explaining the household's optimisation problem very carefully. Then derive the consumption Euler equation and interpret your results. (50 marks)

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The problem you are presenting is an optimization exercise typical in macroeconomics specifically within the realm of dynamic stochastic general equilibrium DSGE models This exercise involves deriving ... View the full answer