Set C(t) is the consumption of time t; beta is the discount factor
The objective function of customer (choose C(t) for on each time t) is the sum of beta^t * log(C(t)) ; t is from 0 to +oo.
The budget constrain is Y(t) - C(t) + r(t)K(t) = K(t+1) for t = 0 ... +oo
How to get the right FOC of this function to C(t) and K(t) from SegaMath
for example: FOC wrt C(t) : beta^t * 1/C(t) - lambda(t) = 0 FOC wrt K(t) : ...
Additionally, how to set the objective function as a expectation on time t (E_t(sum of beta^t * log(C(t)) ; t is from 0 to +oo) and get similar FOCs
