Consider a person whose happiness from the consumption of goods (C) and time away from paid work (L) is characterized by the function U = C2L.(C squared L). When working they can earn $10 per hour and have 10 hours per day available for work. They receive a gift of $5 per day regardless of how much they work. Answer the following: (a) What is their reservation wage? (b) What is their optimal choice of work time and consumption of goods? (c) Show your answer in a well-labelled diagram and explain. (d) Now suppose a government program is introduced that offers a grant $40 per day and reduces the benefit by $0.50 for every dollar the person earns working. In a new diagram illustrate how the program alters their reservation wage. (You do not have to calculate this reservation wage.)