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.

Answer 1

A) utility maximizing condition;

MUc/pc=MU(R)/w

R/1=C/6

C=6R

Budget constraint:

48+16*6=C+6R

144=C+6R

144=6R+6R=12R

R=144/12=12

C=144-12R=144-12*6=72

B)New utility maximizing condition;

R/1=C/8

C=8R

48+16*8=C+8R

176=8R+8R=16R

R=176/16=11

C) Substitution effect: increase in wage, increase the opportunity cost of leisure,so leisure Decreases.

Income effect: increase in wage , increase labour income. Because leisure is normal good. So income effect lead to increase in leisure.

utility maximizing condition;

MUc/pc=MU(R)/w

R/pc=C/w

C=R*w/pc

Replace C with above equation in utility function to derive Compensated demand of R.

U=(Rw/pc)*R=(R^2*w)/pc

R=(Ū*Pc/w)^0.5 ( Compensated demand of R)

Initial utility=CR=72*12=864

R=(864*1/8)^0.5=108^0.5~10.4

So substitution effect=10.4-12=-1.6

Income effect=11-10.4=0.6