Research by Maria Prados and Stefania Albanesi shows that after
1995 the US economy experienced a decline in the labor force
participation of married women. The decline was particularly marked
for women with at least a college degree.
Consider Olivia a college graduate who enjoys consumption goods (C)
and leisure time (L). Upon graduating college, she is offered a job
that pays $50 an hour. Her yearly time budget is 6,000 hours. The
unit price of consumption goods is $1.
a) Write the expressions for Olivia’s time constraint and income
constraint and then combine them to find her yearly budget
constraint. b) In a diagram measuring leisure time along the
horizontal axis and consumption along the vertical axis draw
Olivia’s budget constraint. Olivia’s utility from consumption and
leisure time is U(C,L) = C1/3L2/3.
c) Write Olivia’s Utility Maximization Problem.
d) Compute first order conditions and solve for Olivia’s optimal
level of consumption and optimal number of hours of leisure.
e) What is the economic interpretation of the condition: |MRSC,L| =
MUL/MUC = w/p where w is the hourly wage rate and p a measure of
the general level of consumer goods prices?
f) In your diagram, add an indifference curve to illustrate
Olivia’s optimal bundle.
g) How many hours does Olivia work this year?
Olivia gets married to another college graduate who earns $200 an
hour. After marrying, Olivia shares expenses with her spouse.
Effectively it is as if she receives $200,000 of income from other
sources each year.
h) Write the expression of Olivia’s yearly budget constraint after
she gets married and illustrate her new budget constraint in your
diagram. i) Show that after marrying, each year Olivia wishes to
enjoy more than 6,000 hours of leisure time and so she decides to
drop out from the labor force.
j) In your diagram, illustrate Olivia’s optimal bundle after
marrying.
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