Question

Consider a person whose happiness from the consumption of goods (C) and time away from paid work (L) is characterized by the function U = C2L.(C squared L). When working they can earn $15 per hour and have 10 hours per day available for work. They receive a gift of $15 per day regardless of how much they work. Answer the following:

(a) What is their reservation wage?

(b) What is their optimal choice of work time and consumption of goods?

(c) Show your answer in a well-labelled diagram and explain.

(d) Now suppose a government program is introduced that offers a grant $60 per day and reduces the benefit by $0.50 for every dollar the person earns working. In a new diagram illustrate how the program alters their reservation wage. (You do not have to calculate this reservation wage.)

Answer 1

a) Reservation wage is the minimum wage at which the worker decides to work.

Calculate the MRS

He gets non labour income of $15 when he does not work. Reservation wage can be found by putting this value in the MRS

Therefore, reservation wage is $0.75.

b)

The person has 10 hours available. Wage rate = $15. Wage rate is also called the opportunity cost of leisure because as the person enjoys one more hour of leisure, he has to forego 1 hours of wage. So, price of leisure = w = $15. If he works for the entire 10 hours, then he gets $150. Non-labor income = $15. So, total income = $150+$15 = $165

The budget equation is :

C + wL = m

C + 15L = 165

Therefore, optimal hours worked = 10-3.67 = 6.33

Optimal consumption = $110

c) The required graph is given below. The red line depicts the budget line and green line depicts the IC

Figure 1

d)

Grant offered when worked for 0 hours = $60. Total income at 0 hours of work = $60+$15 = $75

Grant offered when worked for 10 hours = $60 - $0.5*150 = -$15. So, income if he works for entire 10 hours = 165-15 = $150

The new budget line is drawn in figure 2 in black color.

Figure 2

New MRS at endowment point:

SO, new reservation wage = $3.75

Please rate if this answer helped you. Thank you.