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