Can you do this using uhligs method please Question 3Consider the following extension to the benchmark real business cycle (RBC) model. Thesocial planner solves the problem of the representative agent (household) to maximize itsexpected lifetime utility function given by:(C:)'- – 1(H.)'+n¯Eo(4)1-71+7t0subject to the aggregate resource constraint, Eq. (5), the production function, Eq. (6), andthe capital accumulation equation, Eq. (7):C: + I = Y;(5)= Z,K ,H}-*1-a(6)Kį = (1 – 8)Kt-1+I .(7)ß is the discount factor. Utility depends positively on the consumption of goods C1, andnegatively on the supply of labour hours H. y captures the inverse of the intertemporalelasticity of substitution in consumption. 7 measures the inverse of the Frisch elasticity of3labour supply. Y; is output, I, is investment, and K is physical capital. a measures capital'sshare in output, and d is the depreciation rate of capital.(a) Write down the combined budget constraint.(b) Write down the Bellman equation for the household's optimization problem, clearlyindicating state variables and control variables.(c) Derive the first order conditions for the control variables.

Name: Can you do this using uhligs method please Question 3Consider the foll
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Can you do this using uhligs method please Question 3Consider the following extension to the benchmark real business cycle (RBC) model. Thesocial planner solves the problem of the representative agent (household) to maximize itsexpected lifetime util