Question

4. Steve's utility function over leisure and consumption is given by u(L,Y)= min (3L,Y). Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 5. Find the optimal leisure - consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours. Will this law induce Steve to work more hours? If so, how many? If not, explain.

Answer 1

A) u = Min ( 3L, Y)

BC : total Consumption = total labor income

Y = w(T-L)

T = total time Endowment

T-L = total work hours

L= Leisure

Then at eqm,

3L = Y

So from BC : Y = 5(T-L)

Put Y = 3L

3L = 5T - 5L

8L = 5T

L* = .625T

Work hours = T-L*

= .375T

Y* =3L* = 1.875T

.

b) after 8 hours, w' = 1.5*5 = 7.5

Since the Preferences are Leontieff type, where two goods , Leisure & Consumption are enjoyed in fixed proportions,

So no question of substitution of one good for the another,

Bcoz two are always used in fixed proportion.

So only income effect is present.

Income effect says that if wage rate rises, then both leisure & Consumption will rise.

While Leisure falls, as w rises, only due to Substitution effect

so steve will not work for more hours