Economic growth and economic development 73

Introduction to Modern Economic Growth To this, let us first write the steady state relationship between c∗ and s and suppress the other parameters: c∗ (s) = (1 − s) f (k∗ (s)) , = f (k∗ (s)) − δk∗ (s) , where the second equality exploits the fact that in steady state sf (k) = δk Now differentiating this second line with respect to s (again using the implicit function theorem), we have ∂k∗ ∂c∗ (s) = [f (k∗ (s)) − δ] ∂s ∂s We define the golden rule saving rate sgold to be such that ∂c∗ (sgold ) /∂s = (2.21) ∗ These The corresponding steady-state golden rule capital stock is defined as kgold quantities and the relationship between consumption and the saving rate are plotted in Figure 2.6 consumption (1–s)f(k*gold) s*gold savings rate Figure 2.6 The “golden rule” level of savings rate, which maximizes steady-state consumption 59