¹⁰For example, CRRA utility is well deﬁned only on the positive real numbers, so for a CRRA utility consumer $c = 0$ . In other cases, for example with exponential or quadratic cases, there is nothing to prevent consumption of $− ∞$ , so for those models $c = − ∞$ , unless there is a desire to restrict the model to positive values of consumption, in which case the $c ≥ 0$ constraint will be implemented through the use of (5).