Suppose that there is a worker who is deciding how much to work. They have a job that pays them at wage w and they can choose how many hours ` that they want to work.

a) (3 marks) The decision maker values dollars of consumption as c and has a linear dislike of labor provision. Thus, the decision maker chooses ` to maximize w` ` Find the ` which solves the decision maker's problem.

b) (3 marks) Suppose that now the decision maker is now faced with a labor tax of (where 0 < 1), so their take-home pay is only (1 )w`. How does this change the solution to the decision maker's problem?

c) (6 marks) What value of maximizes tax revenue