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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A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by
the utility function u(L, r) = La and has 24 hours in the day to divide between work and
lesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) and
is able to select how many hours they wish to work at some positive wage per hour (w > 0).
Find the consumer's reservation wage as a function of m: this is the lowest wage at which the
consumer will work positive hours. Equivalently, it is the highest wage at which the consumer
will work zero hours. (Hint: this is all about the MRS when working zero hours.)
Suppose Lesley is deciding on career paths. She could choose career A, which earns $50,000 per
year and has a 10% chance of layoff each year, or career B, which earns 80,000 per year and has a
30% chance of layoff each year. When laid off, she earns 0.
Suppose her utility over annual earnings is equal to U(E) = VE
(a) What would be her preferred job if she had to choose one or the other? If she could
allocate her time to both jobs (e.g., could spend 90% of time in job A and 10% in job B) what
would be her ideal allocation of time between jobs?
A worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption.
a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure.
b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income?
c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage?
d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)?
e) What is the labor supply if V increases to 11600?
f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…
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