Consider the two$-$period consumption saving model developed

in class. Denote real labour income or endowment in period

$1$ and $2$ as y$1$ and y$2,$ respectively. r is the real interest rate

between period $1$ and period $2.$ Furthermore, assume the con$-$

sumer has zero initial assets$/$wealth $($a$0).$ The present discounted

value of real income in each of the two periods is equal, i$.$e$.,$

y$1=$ y$2/1+$r $.$ Find the marginal propensity to consume $($MPC$)$ for the

following utility function u$($c$1,$ c$2)=$ c$1^$c$2^1$

$2$ where is a constant

between zero and one. How is this different from a Keynesian

consumption function MPC$,$ if at all?