Economic growth and economic development 525

Introduction to Modern Economic Growth It also pins down the initial level of consumption as Ô Ê (11.16) c (0) = (A − δ)(θ − 1)θ−1 + ρθ−1 − n k (0) Note also that in this simple AK model, growth is not only sustained, but it is also endogenous in the sense of being affected by underlying parameters For example, consider an increase in the rate of discount, ρ Recall that in the Ramsey model, this only influenced the level of income per capita–it could have no effect on the growth rate, which was determined by the exogenous labor-augmenting rate of technological progress Here, is straightforward to verify that an increase in the discount rate, ρ, will reduce the growth rate, because it will make consumers less patient and will therefore reduce the rate of capital accumulation Since capital accumulation is the engine of growth, the equilibrium rate of growth will decline Similarly, changes in A and θ affect the levels and growth rates of consumption, capital and output Finally, we can calculate the saving rate in this economy It is defined as total investment (which is equal to increase in capital plus replacement investment) divided by output Consequently, the saving rate is constant and given by s = = K˙ (t) + δK (t) Y (t) k˙ (t) /k (t) + n + δ A A − ρ + θn + (θ − 1)δ (11.17) , = θA where the last equality exploited the fact that k˙ (t) /k (t) = (A − δ − ρ)/θ This equation implies that the saving rate, which was taken as constant and exogenous in the basic Solow model, is again constant, but is now a function of parameters, and more specifically of exactly the same parameters that determine the equilibrium growth rate of the economy Summarizing, we have: Proposition 11.1 Consider the above-described AK economy, with a representative household with preferences given by (11.1), and the production technology given by (11.6) Suppose that condition (11.12) holds Then, there exists a unique 511