Question ID 2-14: Consider a person whose happiness from the consumption of goods (C) and time...

Question ID 2-14: Consider a person whose happiness from the consumption of goods (C) and time away from paid work (L) is characterized by the function U = CL^2 .(C L squared). When working they can earn $10 per hour and have 15 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?

(d) Now suppose a government program is introduced that offers a grant $50 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.)

Solutions

Expert Solution

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.

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

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

Rahul Sunny answered 1 year ago

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