1. In this exercise, we suppose that the economy is run by a benevolent social planner, who seeks to maximize the utility of the representative family. Since the planner is benevolent, he or she maximizes the lifetime utility of the representative households. On the other hands, the planner faces the aggregate resource constraint. Therefore, the social planner's problem is given as Lemax r e-pru(c(t)) at Jo subject to (a)k(0) > 0, and (b) k(t) = f(k(t)) – 8k(t) — c(t). Utility function is given as the CIES form, that is, u(c) = C1-0 - 1 1-0 ) 00 and 0 # 1. (a) Set a Hamiltonian of the social planner's problem (b) Find the four conditions of optimal solution using a Hamiltonian function. (c) Compare the four conditions with the equilibrium conditions of the Ramsey model.

1. In this exercise, we suppose that the economy is run by a benevolent social planner, who seeks to maximize the utility of the representative family. Since the planner is benevolent, he or she maximizes the lifetime utility of the representative households. On the other hands, the planner faces the aggregate resource constraint. Therefore, the social planner's problem is given as Lemax r e-pru(c(t)) at Jo subject to (a)k(0) > 0, and (b) k(t) = f(k(t)) – 8k(t) — c(t). Utility function is given as the CIES form, that is, u(c) = C1-0 - 1 1-0 ) 00 and 0 # 1. (a) Set a Hamiltonian of the social planner's problem (b) Find the four conditions of optimal solution using a Hamiltonian function. (c) Compare the four conditions with the equilibrium conditions of the Ramsey model.

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

1.
In this exercise, we suppose that the economy is run by a benevolent social planner, who
seeks to maximize the utility of the representative family. Since the planner is benevolent,
he or she maximizes the lifetime utility of the representative households. On the other
hands, the planner faces the aggregate resource constraint. Therefore, the social
planner's problem is given as
Se-ptu(c(t)) at
subject to (a)k(0) > 0, and (b) k(t) = ƒ(k(t)) – 8k(t) — c(t). Utility function is given
as the CIES form, that is,
u(c):
=
max
[c(t)]=o0
c1-0 - 1
1-0
0 0 and 0 # 1.
(a) Set a Hamiltonian of the social planner's problem
(b) Find the four conditions of optimal solution using a Hamiltonian function.
(c) Compare the four conditions with the equilibrium conditions of the Ramsey model.

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