3. (a) Violet is planning to take a year out before starting her career and needs to finance this. She reckons that her future earnings will amount to 240. (These are special pounds and do not correspond to pounds sterling!). She has no money at the present time, but she can borrow as much money as she likes from her bank which will charge a rate of interest of 20%. The Page 2 of 3 [NBS8251] loan must be paid back with interest in the "future". Write out the equation of her budget constraint over consumption now and in the "future". Illustrate it on a carefully drawn diagram. [30 Marks] (b) Violet's utility function is U = CC2, with C representing consumption in the present and C2 consumption in the future. Set up and solve the utility maximisation problem that she faces. How much money does she borrow from the bank? What is the value of her future consumption? Illustrate your answer on your diagram. [35 Marks] (c) Suppose that the bank was to charge a higher rate of interest. If you know what sort of utility function Violet has, and what its key properties are, you will be able to work out very quickly how much she will now plan to consume in the future. What is this amount, and how would you describe the way Violet plans her lifetime expenditure? Very briefly (you do not need to do any analysis), how do you explain Violet's change of plan in the light of income and substitution effects? [35 Marks]