Question

Question ID 2-22: 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 $10 per hour and have 10 hours per day available for work. They receive a gift of $5 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 $40 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.

Answer 1

1. Reservation wage - Assume they work 5 days a week which means 50 hours per week = $ 500 per week and added to it is $5 per day which would mean their weekly earnings will be $500+ $ 25 = $525. The reservation wage is $525 per week

2. Optimal choice of work time would be 8 hours per day @ 5 days a week = 40 hours and earnings @ $400 plus the $25 they get as gift = $ 425 dollars per week as optimal earning and $ 400 as consumption pattern

3.

Assume at a scale of 0 to 500 dollars one can earn spending 50 hours a week at 10 hours a day and 5 days of work

4. Assume this $525 earned per week and a $40 per day as government grant = $725 earned during a week.

B. $ 0.50 reduced for every dollar earned = $ 525 - 262.50 = 262.50

Total earning would be then 262.50 + $ 200 = 462.50