Introduction to Modern Economic Growth is particularly important in growth models because it will regulate how willing individuals are to substitute consumption over time, thus their savings and consumption behavior In view of this, it may be more appropriate to refer to CRRA preferences as “constant intertemporal elasticity of substitution” preferences Nevertheless, we follow the standard convention in the literature and stick to the term CRRA Given the restriction that balanced growth is only possible with preferences featuring a constant elasticity of intertemporal substitution, we might as well start with a utility function that has this feature throughout As noted above, the unique time-separable utility function with this feature is the CRRA preferences, given by ( c(t)1−θ −1 if θ 6= and θ ≥ , 1−θ u (c (t)) = ln c(t) if θ = where the elasticity of marginal utility of consumption, εu , is given by the constant θ When θ = 0, these represent linear preferences, whereas when θ = 1, we have log preferences As θ → ∞, these preferences become infinitely risk-averse, and infinitely unwilling to substitute consumption over time More specifically, we now assume that the economy admits a representative household with CRRA preferences (8.30) Z ∞ c˜ (t)1−θ − dt, exp (−(ρ − n)t) 1−θ where c˜ (t) ≡ C (t) /L (t) is per capita consumption We used to notation c˜ (t) in order to preserve c (t) for a further normalization We refer to this model, with labor-augmenting technological change and CRRA preference as given by (8.30) as the canonical model, since it is the model used in almost all applications of the neoclassical growth model The Euler equation in this case takes the simpler form: · (8.31) c˜ (t) = (r (t) − ρ) c˜ (t) θ Let us first characterize the steady-state equilibrium in this model with technological progress Since with technological progress there will be growth in per capita 394