Consider the problem

, where subject to

with is given. is consumption in period t. u(c) is strictly concave and increasing. Consumers can save through a bond. is the amount of bond accumulated from period t to period t+1.

Solve for the consumer's max problem and express as a function of exogenous variables.

I first solve for the consumers life time budget constraint, which is

Then i set Lagrange and got the foc :

But now i am unsure how to continue

Any help is appreciated.

Thanks in advance