Based on the model in the image answer the following questions:a. Write down agent period 2 and period 3 budget constraint separately. b. Set up the agent's utility maximization problem showing her choice of variables clearly. Write down the first order conditions for agent's utility maximization.c. Derive the ratio of consumption in period 2 and period 3 i.e. c2/c3 in terms of the parameter of the model.d. Explain how investment on the parameter,e, depends on value of B Consider an agent who lives for three periods but consumes onlyin periods two and three where the consumptions are denoted byCz and cz respectively. Her utility is given by u (c2, c3) = log(c2)+3 log(ca), where 0 < 3 < 1 is the discount factor reflecting hertime preference. She invests an amount e in education in the firstperiod which she borrows from the market at a given interest rater > 0. Her income in the second period is w - h(e) where w is afixed wage rate per unit of human capital and h(e) is the amountof human capital that results from investment in education (e) inthe first period. Assume that h(e) is an increasing and concavefunction of e. The agent repays her education loan in the secondperiod. She has no income in the third period. But she can save(s) in the second period from her income on which she receivesthe return s (1+r) in the third period to meet her consumptionexpenditure.

Intertemporal Choices are made when the consumption is not limited to single period and expands to…

Answered: Consider an agent who lives for three…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Based on the model in the image answer the following questions:

a. Write down agent period 2 and period 3 budget constraint separately.

b. Set up the agent's utility maximization problem showing her choice of variables clearly. Write down the first order conditions for agent's utility maximization.

c. Derive the ratio of consumption in period 2 and period 3 i.e. c2/c3 in terms of the parameter of the model.

d. Explain how investment on the parameter,e, depends on value of B

Consider an agent who lives for three periods but consumes only
in periods two and three where the consumptions are denoted by
Cz and cz respectively. Her utility is given by u (c2, c3) = log(c2)+
3 log(ca), where 0 < 3 < 1 is the discount factor reflecting her
time preference. She invests an amount e in education in the first
period which she borrows from the market at a given interest rate
r > 0. Her income in the second period is w - h(e) where w is a
fixed wage rate per unit of human capital and h(e) is the amount
of human capital that results from investment in education (e) in
the first period. Assume that h(e) is an increasing and concave
function of e. The agent repays her education loan in the second
period. She has no income in the third period. But she can save
(s) in the second period from her income on which she receives
the return s (1+r) in the third period to meet her consumption
expenditure.

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