Question 1 (15 points)

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.