= Marginal-utility verification of optimal consumption
{title2=$e^{-bt}U'(c_t)=Y_t$}
For <concave> increasing utility, the <concave supporting-tangent inequality> gives $e^{-bt}[U(\hat c_t)-U(c_t)]\leq Y_t(\hat c_t-c_t)$. If the proposed <consumption> exhausts the state-price budget and every competitor has no larger budget, integration proves optimality. The objective must be well defined; a positive discount rate and finite utility bounds are a convenient sufficient condition.
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