Consider the following consumption problem commonly referred to as the "cake- eating" problem. The consumer starts with a certain amount of capital, ko (e.g. a certain size for the cake), and "eats" it over time. The consumer's problem is to maximize: 3* log(ct) max subject to the constraints: kt+1 2 k - c4 ko > 0 given a) Write down Bellman's equation for this problem.

Consider the following consumption problem commonly referred to as the "cake- eating" problem. The consumer starts with a certain amount of capital, ko (e.g. a certain size for the cake), and "eats" it over time. The consumer's problem is to maximize: 3* log(ct) max subject to the constraints: kt+1 2 k - c4 ko > 0 given a) Write down Bellman's equation for this problem.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the following consumption problem commonly referred to as the "cake-
eating" problem. The consumer starts with a certain amount of capital, ko (e.g.
a certain size for the cake), and "eats" it over time. The consumer's problem is
to maximize:
3* log(ct)
max
t=0
subject to the constraints:
ki+1
> k – Ct
ko
0 given
>
a) Write down Bellman's equation for this problem.

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