2 Consider the planner problem for the following Ramsey model.max t In(C,)t=0subject toG = K - 1,Ke+1 = K} 8 – 1Ko given.C-consumption, K:= capital stock and I- investments.1. Derive det FOC: s by using Lagrangian. HINT: you should obtain Euler equation.2. The policy function for consumption is given byC = CoKand the policy function for capital is given byK+ koKSolve co and ko and substitute the solved ko and co into C and I.

Define the Lagrangian function:where:β is the discount factor is the Lagrange multiplier for the…

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the planner problem for the following Ramsey model.
max t In(C,)
t=0
subject to
G = K - 1,
Ke+1 = K} 8 – 1
Ko given.
C-consumption, K:= capital stock and I- investments.
1. Derive det FOC: s by using Lagrangian. HINT: you should obtain Euler equation.
2. The policy function for consumption is given by
C = CoK
and the policy function for capital is given by
K+ koK
Solve co and ko and substitute the solved ko and co into C and I.

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Step 1: 1. Deriving the FOCs using Lagrangian

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Step 2: 2.Solving for the policy functions:

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