5) Patrice gets utility from leisure and consumption according to utility function: U(C, L) = C + ln(L).

She receives wage w, is endowed with 24 hours in a day, and consumption has a price of $1.

a) Draw her budget and time constraints when w = 1

b) At that wage, how much will she work?

c) Calculate her labor supply as a function of w.

d) Find the wage that maximizes her labor choice or explain why no such wage exists.