¹This is the optimal consumption function for a utility-maximizing consumer with $Rβ = 1$ if that consumer has quadratic utility (Hall (1978)) or if the consumer has CRRA utility and perfect foresight and anticipates $𝜃t+n = ψt+n = 1 ∀ n > 0$ . See ConsumptionFunction for a derivation of this consumption function under quadratic utility, and PerfForesightCRRA for the derivation in the perfect foresight CRRA case. Deaton (1992) argues that the ‘Permanent Income Hypothesis’ should be deﬁned as the hypothesis that consumption is determined according to (5); but this diﬀers sharply from Friedman (1957)’s deﬁnition, and has not become universally accepted.