Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 16, Problem 16.9P
To determine
To find:
Wage to be offered to construction worker
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Assume that the individual has a utility function given by U(I, x) =
0.5 In(1) + 0.5 In(x), with px = 1, T = 16, and Y = 32. There are no
taxes on labor earnings (for simplicity).
(a) What is the individual's reservation wage in this case?
(b) If the individual is offered a wage of w = 12, how many hours of
leisure does she consume?
(c) There is a new government policy designed to provide transfers to
individuals with low consumption. All individuals with a total in-
come (i.e., non - labor and labor income) no more than 82 dollars are
given a transfer of 50 dollars. What is this individual's labor supply
decision in this case?
A student has a part-time job in a restaurant. For this she is paid $8 per hour. Her utility function for earning $I and spending S hours studying is U(I,S) = I^1/4 S^3/4 (The utility function is a measure of the `usefulness' or `worth' to the student of a certain combination of money and study time). The total amount of time she spends each week working in the restaurant and studying is 100 hours. How should she divide up her time in order to maximise her utility?
Consider a representative agent with the utility function
U = ln(Ct)+ Nt
The budget constraint is
Ct = wtNt +Dt
where wt is the wage and Dt is non-wage income (i.e. a dividend from
ownership in the firm). The agent lives for only one period (period t), and
hence its problem is static.
(a) Derive an optimality condition characterizing optimal household behav-
ior.
(b) Solve for the optimal quantities of consumption and labor.
Plz do fast asap, urgent.
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