Y6

A worker receives utility from Income, I, and Leisure, L. The utility function is as follows: U (I,L) = I^1/2L^1/2

Income is earned through working H hours per day at a wage rate of W. When not working, the worker is on leisure hours, L.

a) The worker has 16 hours to divide between leisure and work, what is the constraint on hours worked, H, and leisure hours, L?

b) What is the worker's constrained optimization problem as a Lagrangian?

c) Solve for the worker's utility maximizing number of work hours, H*, and leisure hours, L*

d) How does the worker's optimal number of working hours change as wage goes up? Interpret this using the worker's income and substitution effect.