Caroline's utility function is given by U= 10.4106 + 8, where / is income and L is leisure. Caroline received $320 from her parents. Suppose total available time for her is 16 hours. a. Write down her budget constraint and show it graphically. b. Find Caroline's labor supply function. C. If the market wage is $25/hour, find Caroline's working hours and show the solution diagrammatically. Consider now a market wage of $50/hour. Suppose a welfare program is in existence. If Caroline works, then Caroline cannot receive any welfare. What is the minimum amount of the welfare payment (X) such that Caroline does not have to work but enjoys at least the same utility as working? Also show the solution diagrammatically