4. Business cycles might be caused by sectoral reallocations in which technological advancementcauses new industries to flourish. Workers can move from old to the new industries, although itdoes not happen instantenously. These workers spend time away from market work, either for jobsearch or for training/education (to acquire the skills needed to work in the new industry).Suppose that there are two firms, the agricultural low-tech and the manufacturing high-tech firm.The old firm is active in both periods and it pays wage wд in each period. The manufacturing firmpays wage wM and is only active in the second period and WA WM. To work in the manufacturingfirm, the consumer should spend some of her time in the first period to be out of the labor market.The consumer chooses (c, c', l, l') to maximizeu(c, c')subject to the budget constraints:c+b≤wA (h-1)c≤wa(h-1)+wMl + b(1+r)and a time constraint0 <1 ≤h.Assume also that the consumer's utility function follows the standard conditions and that substi-tution effects dominate income effects in the consumer's decision. Note that in this model, theconsumer values consumption but does not value leisure. The amount of hours spent to work inthe manufacturing sector cannot be greater than 1, the hours spent out of labor market in the firstperiod.a. Derive the consumer's lifetime budget constraint.b. Obtain the consumer's choice of time spent out of the labor force in the first period I usingthe lifetime budget constraint you derive in question (a).

In the first period, the consumer's budget constraint is given by:where:c = consumption in the first…

a. Derive the consumer's lifetime budget constraint. b. Obtain the consumer's choice of time spent out of the labor force in the first period I using the lifetime budget constraint you derive in question (a).

a. Derive the consumer's lifetime budget constraint. b. Obtain the consumer's choice of time spent out of the labor force in the first period I using the lifetime budget constraint you derive in question (a).

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

4. Business cycles might be caused by sectoral reallocations in which technological advancement
causes new industries to flourish. Workers can move from old to the new industries, although it
does not happen instantenously. These workers spend time away from market work, either for job
search or for training/education (to acquire the skills needed to work in the new industry).
Suppose that there are two firms, the agricultural low-tech and the manufacturing high-tech firm.
The old firm is active in both periods and it pays wage wд in each period. The manufacturing firm
pays wage wM and is only active in the second period and WA WM. To work in the manufacturing
firm, the consumer should spend some of her time in the first period to be out of the labor market.
The consumer chooses (c, c', l, l') to maximize
u(c, c')
subject to the budget constraints:
c+b≤wA (h-1)
c≤wa(h-1)+wMl + b(1+r)
and a time constraint
0 <1 ≤h.
Assume also that the consumer's utility function follows the standard conditions and that substi-
tution effects dominate income effects in the consumer's decision. Note that in this model, the
consumer values consumption but does not value leisure. The amount of hours spent to work in
the manufacturing sector cannot be greater than 1, the hours spent out of labor market in the first
period.
a. Derive the consumer's lifetime budget constraint.
b. Obtain the consumer's choice of time spent out of the labor force in the first period I using
the lifetime budget constraint you derive in question (a).

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