Economic growth and economic development 592

Introduction to Modern Economic Growth and balanced growth path interchangeably when referring to endogenous growth models 13.1.3 Balanced Growth Path A balanced growth path (BGP) requires that consumption grows at a constant rate, say gC , which is only possible from (13.16) if the interest rate is constant Let us therefore look for an equilibrium allocation in which r (t) = r∗ for all t, where “*” refers to BGP values Combining (13.9), (13.10) and a constant interest rate with (13.8), we also obtain that V˙ (t) = Substituting this in either (13.7) or in (13.8), we obtain βL , r∗ where we have also substituted for the (constant) flow of rate of profits per period V∗ = (13.18) from (13.11) This equation is intuitive: a monopolist makes a flow profit of βL, and in BGP, this is discounted at the constant interest rate r∗ Let us next suppose that the (free entry) condition (13.14) holds as an equality, in which case we also have ηβL =1 r∗ This equation pins down the steady-state interest rate, r∗ , as: r∗ = ηβL The consumer Euler equation, (13.16), then implies that the rate of growth of consumption must be given by C˙ (t) = (r∗ − ρ) C (t) θ Moreover, it can be verified that the current-value Hamiltonian for the consumer’s (13.19) gC∗ = maximization problem is concave, thus this condition, together with the transversality condition, characterizes the optimal consumption plans of the consumer In a balanced growth path, consumption cannot grow at a different rate than total output (see Exercise 13.4), thus we must also have the growth rate of output in the economy is g ∗ = gC∗ 578