Introduction to Modern Economic Growth income, c˜ (t) will grow Instead, in analogy with k (t), let us define C (t) A (t) L (t) c˜ (t) ≡ A (t) c (t) ≡ We will see that this normalized consumption level will remain constant along the BGP In particular, we have · c˜ (t) c˙ (t) ≡ −g c (t) c˜ (t) (r (t) − ρ − θg) = θ Moreover, for the accumulation of capital stock, we have k˙ (t) = f (k (t)) − c (t) − (n + g + δ) k (t) , where recall that k (t) ≡ K (t) /A (t) L (t) The transversality condition, in turn, can be expressed as ẵ Z t ảắ [f (k (s)) − g − δ − n] ds = (8.32) lim k (t) exp − t→∞ In addition, the equilibrium interest rate, r (t), is still given by (8.8), so r (t) = f (k (t)) − δ Since in steady state c (t) must remain constant, we also have r (t) = ρ + θg or f (k∗ ) = ρ + δ + θg, (8.33) which pins down the steady-state value of the normalized capital ratio k∗ uniquely, in a way similar to the model without technological progress The level of normalized consumption is then given by (8.34) c∗ = f (k∗ ) − (n + g + δ) k∗ , while per capita consumption grows at the rate g 395