Question

Laura wants to buy songs which cost $2 a song. But in order to afford this, she has to babysit for her neighbor. Her neighbor has agreed to pay her $10 an hour for babysitting. Laura dislikes babysitting, but has no other way of buying her music. Her utility is given by the following function: U(x1, x2) = min{2C, 22 - L}

Where ? is the number of songs, ? is the number of hours she babysits. Laura can work a maximum of 22 hours.

a) Draw Laura’s indifference curves. Plot the number of work hours, ? (?1) on the horizontal axis and ? (?2) on the vertical axis. Show the line along which the indifference curves kink.

b) In which direction are her preferences increasing in this graph?

c) Is there a way to redefine Laura’s utility function so that her indifference curves have the usual convex (or L-shaped) shape?

d) How many hours will Laura chose to work?

e) In a more general case, suppose the hourly wage is ? for babysitting, then the labor supply curve shows the relationship between the optimal number of hours that Laura chooses to work as a function of the wage ?. Derive Laura’s labor supply function which shows her choice of hours of work, ?, as a function of wages ?.

f) Does Laura work more or less as wages increase?

Answer 1

A) at eqm in Leontieff preferences

2C = 22-L : line along which IC kink

L : labor hours

now as L is on X axis & not Leisure, so IC are L shaped, but mirror image along Y axis

B) direction of increasing Preferences.

C) yes, if we put Leisure on X axis , instead of labor hours

Let Leisure = H

Then H = 22-L

So U ( C, H) = Min { 2C, H }

D) for BC :

Total labor income = total Spending on Consumption

w*L = P*C

10L = 2C

Now as at eqm,

2C = 22-L

Then, 10L = 22-L

11L = 22

optimal labor hours L* = 2

e) general setting :

at eqm, 2C = 22-L

BC: wL = 2C

So, wL = 22-L

L* = 22/(1+w)

f) as L * & w are inversely related,

So as w rises, works for less hours