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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.

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  • $\begingroup$ Do you mean $U(t) = c_{1,t} + \frac{1}{1 + \rho}\left(c_{2,t+1}\right)$? $\endgroup$
    – Kenneth Rios
    Commented Sep 29, 2018 at 23:29

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I think all the textbook is trying to say is that there can be no corner solutions to your maximization problem.

Not refusing consumption in any period, I think translates to consumption in each period > 0.

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