Assume the following happens with a perfect capital market under certainty and a two-period model. An individuals income stream is y1=2000, y2=2200 without any wealth or other income. Her utility function is characterised by = 12 0.85, r=4.5%. Illustrate your answers in diagram(s). [25 marks in total.] a) Work out the solution to the utility maximisation problem. (5 marks)

b) Assume there is a lending restriction with an upper limit of 50 (i.e., this individual can borrow at most 50 from the capital market). Work out her solution to the utility maximisation problem with the new constraint. (5 marks)

c) Assume instead of a lending restriction, there is a fixed transaction fee of 50 when this individual borrows from the capital market. Work out her solution to the utility maximisation problem with the new condition. (5 marks)

d) Assume no lending restriction or transaction fee. What would happen to the market opportunity line and the tangency point if the market interest rate increases? (5 marks)

e) Following on d), what interest rate makes this individual neither borrow nor save (lend) in time 1? (5 marks)