A, b and c 2) Jane's Labor Supply ProblemErcome peningSuppose Jane is a qualified craftswoman who can help produce widgets. Her utilityfunction depends on her consumption of two goods: stuff and leisure. She spends herentire income on stuff. Her utility maximization problem is as follows:Utisty= wt+ Vz4-LSutilityW,Lmax Utility=JX + /24 – Lwhere PxX = w × Lz VP,and 0 0.(2d) Suppose the price of stuff went up from $10 per unit to $15 per unit. How muchdoes Jane work if her wage is $5 per hour (w = 5) ? What about w = 10 ? w = 15 ?(2e) Suppose Jane used to make a wage of $10 per hour (w = 10) when the price of stuffwas $10 (p = 10). Now that prices are $15 (p = 15), how much of a pay raise does Janeneed in order to achieve the same utility as before? This is known as the inflationproblem in macroeconomics.

A utility function refers to a function that assigns a real number to each item of consumer goods or…

Answered: Sutility LW 2 VP. where PxX = w × L and…

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Sutility LW 2 VP. where PxX = w × L and 0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.1P

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Concept explainers

Financial Statements

Financial statements (or financial reports) are the formal records of the financial activities that are undertaken by a firm. They are convenient instruments used for analyzing a company’s financial position and performance. Financial ratios are created with the help of the numerical values that are derived from the financial statements. They give meaningful information about the financial performance of the company.

Question

100%

A, b and c

2) Jane's Labor Supply Problem
Ercome pening
Suppose Jane is a qualified craftswoman who can help produce widgets. Her utility
function depends on her consumption of two goods: stuff and leisure. She spends her
entire income on stuff. Her utility maximization problem is as follows:
Utisty= wt+ Vz4-L
Sutility
W,L
max Utility=JX + /24 – L
where PxX = w × L
z VP,
and 0<L<24
.V24-L
Jane's utility maximization problem can be rewritten using the following indirect utility
function' that incorporates her budget constraint
max Indirect Utility=
"L+ /24 – L
P
' Indirect utility function is the utility function where the budget constraint is plugged-in.
Treat in a similar manner as the utility function.
This is because the budget constraint implies that for each hour she works, she can buy an
additional " unit(s) of stuff.
P
For now, assume that Jane is a price-taker in both the market for stuff (where she buys)
and the market for labor (where she sells).
(2a) Suppose the price of stuff is $10 (p=10). How much does Jane work if her wage is
$5 per hour (w = 5) ?
(2b) What about w = $10? w = $15? Sketch Jane's labor supply curve.
(2c) At w = 10, does the substitution effect dominate the income effect or vice versa ?
Briefly explain your answer.
OPTIONAL: This particular labor supply curve does not backward-bend for any positive
wage. Can you prove this? HINT: need to show that
for all w > 0.
(2d) Suppose the price of stuff went up from $10 per unit to $15 per unit. How much
does Jane work if her wage is $5 per hour (w = 5) ? What about w = 10 ? w = 15 ?
(2e) Suppose Jane used to make a wage of $10 per hour (w = 10) when the price of stuff
was $10 (p = 10). Now that prices are $15 (p = 15), how much of a pay raise does Jane
need in order to achieve the same utility as before? This is known as the inflation
problem in macroeconomics.

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