when considering intertemporal chioce, consumers can save at the interest rate r and also save at the same rate r.

Now, lets consider the intermediate scenario where :

there are 2 periods: period 1 and period 2

consumer gets endownment of y₁ in period 1 and y₂ in period 2

consumption levels c₁ and c₂ in period 1 and 2

consumer can save at the rate r_s and borrow at r_b where r_s< r_b

Q) in the case in which consumer consumes more than income in period 1, what is his budget constraint? what is the budget constraints in both periods and using the 2 budgets constraints to derive, what is the lifetime budget constraint?