Now assume that the within$-$period utility function is log$,$ so that

$$

$$

The first order condition can be written:

$1)$ Use the information above and, in conjunction with the Euler equation and the budget constraint, derive the consumption function. Solve for Ct$+1(10$ marks$)$

$2)$ Derive partial derivative of Ct with respect to $,$ and $$and interpret $(15$ marks$).$