Suppose a person’s utility for leisure (L) and consumption (Y) can be

Suppose a person’s utility for leisure (L) and consumption (Y) can be expressed as U = Y ˆ— L and this person has no non-labor income. Assuming a wage rate of $10 per hour, show what happens to the person’s labor supply when the person wins a lottery prize of $100 per day.

What will be an ideal response?

ANSWER

Rearranging yields U = (Y* + 10H) ∗ (24 – H) = 24Y* + 240H – Y*H – 10H^2. Maximizing utility with respect to H yields dU/dH = 240 – Y* – 20H = 0. Before winning the lottery, Y* = 0, so H = 12. After winning the $100 per day lottery, Y* = 100, so H = 7. Winning the lottery reduces this person’s quantity of labor supplied by 5 hours when w = $10.