Question

Exercise 4. Labor Supply with non-labor income (Cobb-Douglas) Each day you are endowed with 24 hours (T=24) that you can spend either in leisure (l) or working (L). For hour of labor you receive an hourly wage, w, but you also have non-labor income, m. Your consumption, c, is constrained by your labor and non-labor income: c= m +wL. You value consumption and leisure according to the following utility: u =cl2. a) What is your labor supply, as a function of wage, time endowment and non-labor income? Find L=f(w.Iem). b) If w=10 and m=30, what is L? With w=10 still, and m'=45, what is L'? With w=10 always, and m"=60, what is L"? Based of an increasing m on L (labor), is leisure () a normal or an inferior good? c) Keeping m=30 fixed, and changing w*=20, what happens to L*? Is the presence of non- labor income affecting the impact of wages on labor supply? Compare with the same wage change when mo=0. d) Given the wage change in part c, can you divide the substitution effect, ordinary income effect and endowment income effect? e) What is the reservation wage? That is, the smallest possible wage to have L>0. How does it depend on m?

Answer 1

A)

A) MUc/pc=MU(l)/pl

Pc=1

Pl=w

l^2/1=2Cl/w

w*l^2=2Cl

wl=2C

l=2C/w{ optimal bundle condition}

m+wT=w*(2C/w)+C

m+wT=2C+C=3C

m+wT=3(w*L){ L= labour supply & C=w*L}

L=(m+wT)/3w { labour supply function}

B) w=10 ,m=30

L=(30+10*24)/3*10=270/30=9

w=10. ,m=45

L=(45+240)/30=285/30=9.5

w=10,. m=60

L=(60+10*24)/30=300/30=10

As m Increasing m ,Labour supply Increases which means leisure is decreasing .it shows negitive relationship between income and leisure.so leisure is inferior good.

C)m=30. ,w=10

L=9

m=30, w=20

L=(30+24*20)/3*20=510/60=8.5

m=0. ,w=10

L=24*10/3*10=240/30=8

m=0. ,w=20

L=24*20/3*20=8

Presence of non labour income affecting the impact of wages on labour supply. In absence of non labour income, Increase in wages, doesn't change labour supply,it remain fixed at 8 hours. But with presence of non labour income , Increase in wages , decreases labour supply.