Question

4.1 Cindy gets utility from consumption (C) and leisure (L), and has a weekly timebudget ofT= 110 hours. Her utility function isU(C, L) =C∗L. She receives$660 each week from her great-grandmother regardless of how much Cindy works.What is Cindy’s reservation wage?

4.2What is Cindy’s optimal labor supply (h) and consumption (C) if her wage is10 dollars per hour? Show your work.4.3

4.3 What is her optimal labor supply and consumption if her wage is 5 dollars perhour? What is her utility level? Show your work.

Answer 1

4.1

Given

U(C,L)=C*L

Marginal utility from consumption=MUC=dU(C,L)/dC=L

Marginal utility from Leisure=MUL=dU(C,L)/dL=C

For optimal combination of C and L, we have

MUL/MUC=w (Reservation wage)

C/L=w

We know that C=Non labor income=$110 if person does not work (i.e. L=110-0=110)

So, Reservation wage=w=660/110=$6

4.2

Let h be number of hours worked, So,

L=110-h or h=110-L

Budget constraint is given by

C=Non labor income+w*h

C=660+10*(110-L)=660+1100-10L

C=1760-10L

For optimal combination of C and L, we have

MUL/MUC=w (Reservation wage)

C/L=w=10

C=10*L

Put C=10*L in budget constraint equation

C=1760-10L

10L=1760-10L

20L=1760

L=1760/20=88 hours

h=110-L=110-88=22 hours

C=1760-10L=1760-10*88=$880

4.3

We observe that wage rate is less than reservation work. So, Cindy will decide not to work. i.e.

h=0 (labor supply is zero)

L=110-h=110-0=110 hours

C=1760-10*L=1760-10*110=$660

Utility at this level is given by

U(C,L)=C*L

U(660,110)=660*110=72600 units