$(c)$ Consider the two$-$period consumption saving model developed

$in$ class. Denote real labour income $or$ endowment $in$ period

$1$ and $2as{y}_1$ and $y_2,$ respectively. $ris$ the real interest rate

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

sumer has zero initial asset$\frac{s}{w}$ealth $(a_0).$ The present discounted

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

$y_1=\frac{y_2}{1+r}.$ Find the marginal propensity $to$ consume $(MPC)$ for the

following utility function $u(c_1,c_2)=c_1^{}{c}_2^{1-}$ where $is$ a constant

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

consumption function $MPC,ifat$ all? $(Use$ a graph $if$ needed$)$