Question

1. A student has current income y? and expects future income y?. She plans current consumption c? and future consumption c? in order to maximise utility U = 2??c? + 2???c?, c?, c? > 0 where ? > 0 is her discount factor. If she borrows now, c? > y?, then future consumption, after repaying the loan c? – y? with interest r, will be c? = y? – (1 + r)(c? – y?). Alternatively, if she saves now, c? < y?, future consumption will be c? = y? + (1 + r)(y? – c?) after receiving interest r on her savings. The student takes the interest rate r as given. Answer the following questions: (a) [5 marks] State carefully the maximisation decision of the student. (b) [8 marks] Find the optimal plan (c?, c?). Show your workings and interpret your results. (c) [7 marks] Show how an increase in the interest rate affects the level of borrowing or saving. Show your workings.

          1. A student has current income y? and expects future income y?. She plans current consumption c? and future consumption c? in order to maximise utility
U = 2??c? + 2???c?, c?, c? > 0
where ? > 0 is her discount factor. If she borrows now, c? > y?, then future consumption, after repaying the loan c? – y? with interest r, will be
c? = y? – (1 + r)(c? – y?).
Alternatively, if she saves now, c? < y?, future consumption will be
c? = y? + (1 + r)(y? – c?)
after receiving interest r on her savings. The student takes the interest rate r as given.
Answer the following questions:
(a) [5 marks] State carefully the maximisation decision of the student.
(b) [8 marks] Find the optimal plan (c?*, c?*). Show your workings and interpret your results.
(c) [7 marks] Show how an increase in the interest rate affects the level of borrowing or saving. Show your workings.

1. A student has current income y? and expects future income y?. She plans current consumption c? and future consumption c? in order to maximise utility
U = 2??c? + 2???c?, c?, c? > 0
where ? > 0 is her discount factor. If she borrows now, c? > y?, then future consumption, after repaying the loan c? – y? with interest r, will be
c? = y? – (1 + r)(c? – y?).
Alternatively, if she saves now, c? < y?, future consumption will be
c? = y? + (1 + r)(y? – c?)
after receiving interest r on her savings. The student takes the interest rate r as given.
Answer the following questions:
(a) [5 marks] State carefully the maximisation decision of the student.
(b) [8 marks] Find the optimal plan (c?*, c?*). Show your workings and interpret your results.
(c) [7 marks] Show how an increase in the interest rate affects the level of borrowing or saving. Show your workings.

Added by Alberto L.

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