Question

Adam has a utility function U(C,R) = CR, where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. Mark has a non-labor income of $48 per day.

(a) If Mark is paid a wage of $6 per hour, how many hours of leisure will he choose per day?
(b) As a result of a promotion, Mark is now paid $ 8 per hour. How will his leisure time change?

(c) Analyze the changes in Mark's leisure time using the substitution effect and the income effect. (Calculate the EXACT numerical changes in leisure time due to substitution and income effect. Calculate change for each substitution and income effect.)

Answer 1

Answer = Given U(C,R) = CR

Mark would always want maximum Utility.

Non-labor Income of Mark = $48 Per Day, Which is the same amount he gets after working for 8 Hours.

(a) As to maximize his utility and at the same time to earn the maximum amount, He would spend 8 hours on leisure and the remaining 16 - 8 = 8 for Work.

(b) Now at the same non-labor income and increased wage rate, he would get his previous income level by just working for 6 hours, So the leisure hours would increase to 8 + 2 = 10.

(c) With the Income Effect his leisure time has increased by 2 hours. And with the Substitution effect his leisure time would decrease by 2 hours and will be 6 hours.