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 $5 per hour and have 8 hours per day available for work. They receive a gift of $10 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 $30 per day and reduces the benefit by $1 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 $10 when he does not work. Reservation wage can be found by putting this value in the MRS

Therefore, reservation wage is $0.625.

b)

The person has 8 hours available. Wage rate = $5. 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 = $5. If he works for the entire 8 hours, then he gets $40. Non-labor income = $10. So, total income = $50.

The budget equation is :

C + wL = m

C + 5L = 50

Optimal choice of work = 8-3.33 = 4.67 hours

Optimal choice of consumption of goods = $33.33

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 = $30. Total income = $30 ( from grant) + $10 (gift) = $40

Grant offered when worked for 8 hours = $30 - $1*40 = -$10. So, income if he works for entire 8 hours = 50-10 = $40.

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

Figure 2

SO, new reservation wage = $2.5

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