Set up the maximization problem and solve for the optimal

Question

Suppose all agents in the economy have the following utility function:

U (c, l) = c^1-θ/(1 - θ) - l

where c is consumption, l is labor supply, and θ is a fixed parameter. Assume also that the only income that individuals have is labor income, with an hourly wage rate given by w taxed at rate t.

1. Set up the maximization problem and solve for the optimal labor supply function. [Note: it should depend on w and t. The fixed parameter θ will be there too.].