An individual needs to allocate the 168 hours available each week to work, W, hours and free time, F, hours. He earns $20 an hour (after deductions), and his utility function is given by U = 6E^1/3 F^2/3 where E denotes his weekly earnings.
Explain briefly why the Lagrangian for this problem may be written as
Hence find the optimal number of hours worked in a week.If the hourly rate of pay increases, does the optimal number of hours worked in a week increase, decrease or stay the same?

Transcribed Image Text:

L(E, F, X) = 6E"³ F3 + A(3360 – E – 20F) %3D