Problem 2 (12 points)

Alina is a single mother with children with preferences for leisure time and consumption of marketed goods equal to U(L,C) = L^2/3 C^1/3.

Each day, she has a time endowment of T = 16 hours she can spend working (N) or taking care of the kids at home (L). Her hourly wage

is $10.

a. How many hours does Alina choose to work each day if she has no income from other sources?

b. In a diagram measuring leisure time along the horizontal axis, draw Alina's optimal choice and clearly high-light the number of hours

Alina spends working each day.

Alina's boss wants her to do some over-time, if she agrees he raises her pay to $15 an hour. (on all hours).

c. Explain why even if offered a higher pay, Alina does not agree to work over-time.

d. What would happen to Alina's number of hours worked if her mother decided to help her out financially and gave her some money

each month?