In the two period savings model, a consumer is given an endowment in the first period, $Y_1$, and an endowment in the second period, $Y_2$. Given these endowments, the consumer must choose how to allocate his or her consumption in the two periods, $C_1$ and $C_2$.

The consumer then faces two budget constraints restricting how much consumption he or she can have. One is for the first period:

$$C_1 = Y_1 - S + \frac{B}{1+i}$$

Where $C_1$ is consumption in the first period, $Y_1$ is the initial amount of money that the consumer is endowed with, $S$ is the amount set aside in savings, and $B$ is the amount borrowed through a loan.

The second budget constraint is for the second period:

$$C_2 = Y_2 + (1+r)S-B$$

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