A worker has utility function over consumption x and leisure l given by: u(x,l)=(x*l)⁰.⁵
The worker chooses how many of the 16 hours they are awake each day to supply to the labor market, subject to a market wage of w. Assume they consume what they earn at the end of the day and that non-labor income is 8.
a. Setup the Lagrangian that describes the worker’s labor supply problem.