Economic growth and economic development 445

Introduction to Modern Economic Growth In fact, the competitive equilibrium is not in general Pareto optimal The simplest way of seeing this is that the steady state level of capital stock, k∗ , given by (9.9), can be so high that it is in fact greater than kgold Recall that kgold is the golden rule level of capital-labor ratio that maximizes the steady-state level of consumption (recall, for example, Figure 8.1 in Chapter for the discussion in Chapter 2) When k∗ > kgold , reducing savings can increase consumption for every generation More specifically, note that in steady state we have f (k∗ ) − (1 + n)k∗ = c∗1 + (1 + n)−1 c∗2 ≡ c∗ , where the first line follows by national income accounting, and the second defines c∗ as the total steady-state consumption Therefore ∂c∗ = f (k∗ ) − (1 + n) ∗ ∂k and kgold is defined as f (kgold ) = + n Now if k∗ > kgold , then ∂c∗ /∂k∗ < 0, so reducing savings can increase (total) consumption for everybody If this is the case, the economy is referred to as dynamically inefficient–it involves overaccumulation Another way of expressing dynamic inefficiency is that r∗ < n, that is, the steady-state (net) interest rate r∗ = R∗ −1 is less than the rate of popula- tion growth Recall that in the infinite-horizon Ramsey economy, the transversality condition (which follows from individual optimization) required that r > g + n, therefore, dynamic inefficiency could never arise in this Ramsey economy Dynamic inefficiency arises because of the heterogeneity inherent in the overlapping generations model, which removes the transversality condition In particular, suppose we start from steady state at time T with k∗ > kgold Consider the following variation where the capital stock for next period is reduced by a small amount In particular, change next period’s capital stock by −∆k, where ∆k > 0, and from then on, imagine that we immediately move to a new steady state 431