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

u′(cccu) = Rβu′(cccu ) ⇒ (cccu)-ρ = Rβ(cccu )-ρ ⇒ cccu = (R β)1∕ρcccu. t t+1 t t+1 t+1 t
Consumption grows at the geometric rate 1∕ρ (R β) . The present discounted value of consumption at time t must equal total wealth, so that
∞∑ -iu ∑∞ -i i∕ρ u ∑∞ ui u u u R ccct+i = R (Rβ) ccct = (1 - κ )ccct = ccct∕κ = bbbt. i=0 i=0 i=0