Question

3. Jade is deciding how much to work in 2020. She derives utility from consumption,C, but she also really likes taking leisure time L. She must divide her available hours between work and leisure. For every hour of leisure she takes, she must work one fewer hours (meaning that the price of leisure is her hourly wage). The function that describes her preferences is given by

The marginal utilities are

U(C, L) = C(1/2)L(1/2)

MUC = 1C(−1/2)L(1/2)2

MUL = 1C(1/2)L(−1/2)2

She can earn a wage of w per hour, and suppose that the price of consumption is given by pC = 1. (10 points)

a. Write down Jade’s budget constraint if she can work 2000 hours in a year (Hint: Total value of her consumption in a year is equal to her annual income).

b. Set up Jade’s utility maximization problem and find her optimal consumption ofC and L. What would Jade’s choice of leisure and consumption be if w = 20?

c. A payroll tax is proposed that would tax Jade’s labour income by 25%. This means that Jade’s effective wage rate is now 0.75w where w is the wage rate without the tax. What is her new optimal choice for leisure and consumption?

d. On a graph with L on the horizontal axis and C on the vertical axis, depict the income and substitution effects on leisure hours associated with the tax. Will the income and substitution effects have the same sign? What is the intuition for your answer?

Answer 1