3. Anne is studying for a course that will give her a high income in the future. She has no money at present, but she knows that when she completes the course she will have 360 (special money, do not confuse with sterling). Her utility function over consumption at present (period 1) and consumption in the future (period 2) is given by U = C/5C4/5. She can borrow as much money as she likes from a government fund at an interest rate of 20%. (a) [25%] Set up the utility maximisation problem she faces, and illustrate how she will solve this using a clearly drawn diagram. (b) [25%] Solve the problem in (a) to find her planned consumption in the present and in the future. Illustrate this on your diagram. How much money does she borrow from the government fund?