Question

A maximizing worker with u(z, f) = z1/2f1/2 earns 60 dollars per day in non-labour income and is paid a wage of 5 dollars per hour. How many hours will she work. If she joins a union she will be paid a wage of 20 dollars per hour but she will have to pay a membership fee. What is the maximum daily fee she would pay to join this union?

Answer 1

Given data:

A maximizing worker with u (z, f) = z1/2f1/2

Earns 60 dollars per day in non-labour income

Is paid a wage of = 5 dollars per hour.

How many hours will she work =?

If she joins a union she will be paid a wage = 20 dollars per hour

But she will have to pay a membership fee.

What is the maximum daily fee she would pay to join this union =?

Utility maximizing condition:

MUz/pz = MUf/pf

(0.5*f^0.5)/(1*z^0.5) = (0.5*z^0.5)/(5*f^0.5)

5f = z

Budget constraint:

60+24*5 = pz*z+pf*f

60+120 = 1*(5f)+5f = 10f

F = 180/10 = 18

Z = 60+(24-18)*5 = 60+30 = 90

With wage = 20

New Z = 60+(24-18)*20 = 60+120 = 180

So

Maximum daily fee = 180 – 90 = 90