Problem 1 Labor Supply Kate is not sure how many hours she should spend at work and we have to help her. Her total available time is 24h. She has no other source of income but salary. She is a lawyer, and a current wage rate for lawyers (per hour) is w = $100. She only consumes bananas that cost pa = $5 per pound. a) What is her real wage rate (wage rate in terms of bananas)? b) Show her budget set on the graph. Suppose her utility function is: U (C, R) = (R) (C), where R is leisure (or relaxation time) and C is consumption of bananas, c) Find her optimal time spent at work, the relaxation time and consumption of bananas. d) How your answer in 0) would change if her wage rate was to = $200. How would you explain the change (or possibly no change) in her labor supply