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

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

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.
Transcribed Image Text: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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