. (20 points) Consider an individual that has a utility function: where G is uni
ID: 1119268 • Letter: #
Question
. (20 points) Consider an individual that has a utility function: where G is units of goods consumed in a day and L is hours of leisure enjoyed in a day The individual has a time endowment of 16 hours for the day. The price of goods is S5/unit. a) What is the reservation wage of this individual when non-wage income is S10? b) What is the reservation wage of this individual when non-wage income is S100? c) How much labor will this person offer to the market and how many goods will be consumed when non-wage income is S10 and the wage is S10/hour? d How much labor will this person offer to the market and how many goods will be consumed when non-wage income is S100 and the wage is $20/hour? e) How much labor will this person offer to the market and how many goods will be consumed when non-wage income is S100 and the wage is $20/hour AND there is a tax of 25% on any income earned above $150? Now consider (without the tax from part f that the individual (with non-wage income of $100 and a wage of S20hour) receives an overtime premium of 50% after 6 hours of work per day. How much labor will this person offer to the market and how many goods will be consumed?Explanation / Answer
a) The work of the student is correct. When nonwage income is $10, the reservation wage is $10/16.
b) The work of the student is correct. When nonwage income is $10, the reservation wage is $100/16.
c) Write the budget constraint between G and L.
G = [w (16 – L) + nonwage income] / 5
5G = 16w – wL + nonwage income
From the solution to part a, we know that the tangency condition is: 5G = wL.
Substitute the tangency condition in the budget constraint:
wL = 16w – wL + nonwage income
2wL = 16w + nonwage income (Equation 1)
The given information is that the wage rate is $10 and the nonwage income is also $10. Substitute this information in Equation 1.
2(10)L = 16(10) + 10
20L = 170
L = 8.50
Hours worked = 16 – 8.50 = 7.50 hours
Goods consumed = [w (16 – L) + nonwage income] / 5
= [10 (16 – 8.50) + 10] / 5
= 85 / 5
= 17 units
d) The given information is that the wage rate is $20 and the nonwage income is also $100. Substitute this information in Equation 1.
2(20)L = 16(20) + 100
40L = 420
L = 10.50
Hours worked = 16 – 10.50 = 5.50 hours
Goods consumed = [w (16 – L) + nonwage income] / 5
= [20 (16 – 10.50) + 100] / 5
= 210 / 5
= 42 units
As per Chegg policy, solutions to only four subparts can be reviewed/given. If you want solutions to the other parts, please post the question again and clearly mention the subparts of which you want solutions.
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