Hiya, I'm a bit stuck on this maximisation problem. I've done all the steps but seem to be getting too large an answer. Any help would be greatly appreciated!
A student has current income y1 and expects future income y2. She plans
current consumption c1 and future consumption c2 in order to maximise
utility
U = 2√c1 +2β√c2
c1, c2 > 0
β > 0 is her discount rate.
If she borrows now, c1 > y1, then future
consumption, after repaying the loan c1 −y1 with interest r, will be
c2 = y2 −(1+r)(c1 −y1).
Alternatively, if she saves now, c1 < y1, future consumption will be
c2 = y2 + (1+r)(y1 −c1)
after receiving interest r on her savings.
Answer the following questions:
(a) [10 marks] Find the optimal consumption plan c1, c2. Show your
workings.
(b) [15 marks] Show how an increase in the interest rate affects the level
of borrowing or saving. Show your workings