2. The standard model of consumer behavior assumes that income is exogenous. Ofcourse, a person's income usually depends upon the number of hours the individualworks. Suppose that an individual has T hours each day which can be allocatedtoward working time, H, or leisure time, L-that is, T = H + L. The individual earnsw dollars for each hour worked. Then the individual's income is M + wH where Mdenotes any non-labor income. The individual has preferences over leisure time, L,and a consumption good, X, which can be represented by a quasi-concave utilityfunction, U(X, L). The consumption good, X, can be purchased at the price Px. Theindividual seeks to maximize the utility subject to the constraints on time and money.(1) Formulate the individual's problem as an optimization problem with twoconstraints a time constraint and a money constraint. Derive the first-orderconditions. Give an economic interpretation of the Lagrange multipliers.(2) The two-constraints problem can be reduced to a one-constraint problem bysubstituting the time constraint into the money constraint. Formulate the choice ofX and L as a one-constraint problem. Derive the first-order conditions andcompare with the first-order conditions from (1).(3) Use comparative statics (in words) to determine whether or not an individual wil1increase the number of hours worked in response to an increase in the wage rate.Draw a diagram to illustrate the income and substitution effects of an increase inthe wage rate on the number of hours worked.

Maximizing utility refers to the economic concept of making choices in a way that leads to the…

2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has 7 hours each day which can be allocated toward working time, H, or leisure time, L—that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money.

2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has 7 hours each day which can be allocated toward working time, H, or leisure time, L—that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

2. The standard model of consumer behavior assumes that income is exogenous. Of
course, a person's income usually depends upon the number of hours the individual
works. Suppose that an individual has T hours each day which can be allocated
toward working time, H, or leisure time, L-that is, T = H + L. The individual earns
w dollars for each hour worked. Then the individual's income is M + wH where M
denotes any non-labor income. The individual has preferences over leisure time, L,
and a consumption good, X, which can be represented by a quasi-concave utility
function, U(X, L). The consumption good, X, can be purchased at the price Px. The
individual seeks to maximize the utility subject to the constraints on time and money.
(1) Formulate the individual's problem as an optimization problem with two
constraints a time constraint and a money constraint. Derive the first-order
conditions. Give an economic interpretation of the Lagrange multipliers.
(2) The two-constraints problem can be reduced to a one-constraint problem by
substituting the time constraint into the money constraint. Formulate the choice of
X and L as a one-constraint problem. Derive the first-order conditions and
compare with the first-order conditions from (1).
(3) Use comparative statics (in words) to determine whether or not an individual wil1
increase the number of hours worked in response to an increase in the wage rate.
Draw a diagram to illustrate the income and substitution effects of an increase in
the wage rate on the number of hours worked.

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