¹⁴This is a standard result, which follows from the ﬁrst-order condition and the budget constraint:

( ) u′(cut) = R βu′(cut+1) ⇒ (cut)−ρ = R β cut+1−ρ ⇒ cut+1 = (Rβ)1∕ρcut.

Consumption grows at the geometric rate (Rβ)

^1∕ρ. The present discounted value of consumption at time t must equal total wealth, so that

∑∞ ∞∑ ∞∑ R−icut+i = R −i(Rβ)i∕ρcut = (1− κu)icut = cut∕κu = bt. i=0 i=0 i=0