4. Consider the following two-period problem. The representative household utility function is

$$\log(c1) + \beta \log(c2),$$

where $\beta \in (0,1)$ is the discount factor, $c_t$ is consumption in period $t, \forall t = 1, 2$.

The budget constraints are

$$c1 + a2 = y_1$$

and

$$c2 = y2 + a_2(1 + r),$$

where $r$ is the exogenous net real interest rate, $a2$ is net savings at the end of period 1, and $yt$ is a deterministic endowment at period $t$, $\forall t = 1, 2$. The household faces a financial constraint:

$$a_2 \ge -\ell,$$

where $\ell \ge 0$ represents the exogenous credit limit.