2. Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 80 hours. Her utility function is: U(C, L) = C(1/3) × [(2/3) In addition, Cindy receives $400 each week from her grandmother. a) Derive Cindy's marginal rate of substitution (MRS). b) Calculate Cindy's reservation wage. c) Suppose Cindy's wage rate is $40 per hour. Write down Cindy's budget line. Will Cindy work? If Cindy works, how many hours does she work? d) Suppose Cindy's wage increases to $50. Write down Cindy's new budget line and calculate how many hours that she works. e) Calculate the labour supply elasticity for Cindy when wage increases from $40 to $50. Is Cindy's labour supply elastic or inelastic? f) Draw a figure to illustrate the income and substation effects when the wage increases from $40 to $50. g) Calculate the income effect in (f). (Note that C(1/3) =³√/C and L2/³) = (√ī)².) h) Calculate the substitution effect in (f).
2. Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 80 hours. Her utility function is: U(C, L) = C(1/3) × [(2/3) In addition, Cindy receives $400 each week from her grandmother. a) Derive Cindy's marginal rate of substitution (MRS). b) Calculate Cindy's reservation wage. c) Suppose Cindy's wage rate is $40 per hour. Write down Cindy's budget line. Will Cindy work? If Cindy works, how many hours does she work? d) Suppose Cindy's wage increases to $50. Write down Cindy's new budget line and calculate how many hours that she works. e) Calculate the labour supply elasticity for Cindy when wage increases from $40 to $50. Is Cindy's labour supply elastic or inelastic? f) Draw a figure to illustrate the income and substation effects when the wage increases from $40 to $50. g) Calculate the income effect in (f). (Note that C(1/3) =³√/C and L2/³) = (√ī)².) h) Calculate the substitution effect in (f).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
just subparts g and h
Transcribed Image Text:2. Cindy gains utility from consumption C and leisure L. The most leisure she can
consume in any given week is 80 hours. Her utility function is:
U(C, L) = C(1/3) × [(2/3)
In addition, Cindy receives $400 each week from her grandmother.
a) Derive Cindy's marginal rate of substitution (MRS).
b) Calculate Cindy's reservation wage.
c) Suppose Cindy's wage rate is $40 per hour. Write down Cindy's budget line.
Will Cindy work? If Cindy works, how many hours does she work?
d) Suppose Cindy's wage increases to $50. Write down Cindy's new budget line
and calculate how many hours that she works.
e) Calculate the labour supply elasticity for Cindy when wage increases from $40
to $50. Is Cindy's labour supply elastic or inelastic?
f) Draw a figure to illustrate the income and substation effects when the wage
increases from $40 to $50.
g) Calculate the income effect in (f). (Note that C(1/3) =³√/C and L2/³) = (√ī)².)
h) Calculate the substitution effect in (f).
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