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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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