Endowment

Consumption

In this case, $e$ represent the endowment point, the value between $C_1^{\ast }$ and $Y_1$ means $S_1^{\ast }$ , and we can test the value to check whether a consumer is a saver or a borrower.

Endowment point is the combination of the $Y_1$ and $Y_2$

Notice that it is no connection with the Tax , so the Endowment point may be not on the exactly the budget constraint curve.

So the problem solving process is :

1. We first test $\frac{\delta U}{\delta S}$ to find out the optimal $S^{\ast }$
2. And then we calculate the $C_1$ and $C_2$ $Y_1$ and $Y_2$ to compare, if $Y_1>C_1$, that means the consumer is a saver, and vice versa.

What if a person can’t save (That means, there is no banks)

Then the optimal choice of would be the endowment point, the reason maybe there’s no chance to adjust the saving plan to maximize the Utility.