I have an OLG model with constant level of technology and population. The utility of agent who is born in period t is:
U() = c1,t + 1/1+pC2,t+1
My textbook asks me to write the maximization problem and FOC for the agent who is born in period t with the assumption that agent can not refuse the consumption in any of the periods.
I know how to write maximization problem
U() = c1,t + 1/1+pC2,t+1 - max c1,t ≥0 С2,t+1 ≥0 c1t + st = wt c2,t+1 = (1 + r,t+1)st
The only thing which I do not get is why we need the assumtion that agent can not refuse the consumption in any of the periods. What does it give us?
I am sorry of the question is obvious, I am just studying OLG model on my own and do not get everything.