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Introduction to Modern Economic Growth Proof See Exercise 2.15 Ô Therefore, the comparative statics and dynamics are very similar to the model without technological progress The major difference is that now the model generates growth in output per capita, so can be mapped to the data much better However, the disadvantage is that growth is driven entirely exogenously The growth rate of the economy is exactly the same as the exogenous growth rate of the technology stock The model specifies neither where this technology stock comes from nor how fast it grows 2.7 Comparative Dynamics In this section, we briefly undertake some simple “comparative dynamic” exercises By comparative dynamics, we refer to the analysis of the dynamic response of an economy to a change in its parameters or to shocks Comparative dynamics are different from comparative statics in Propositions 2.3, 2.8 or 2.13 in that we are interested in the entire path of adjustment of the economy following the shock or changing parameter The basic Solow model is particularly well suited to such an analysis because of its simplicity Such an exercise is also useful because the basic Solow model, and its neoclassical cousin, are often used for analysis of policy changes, medium-run shocks and business cycle dynamics, so understanding of how the basic model response to various shocks is useful for a range of applications We will see in Chapter that comparative dynamics are more interesting in the neoclassical growth model than the basic Solow model Consequently, the analysis here will be brief and limited to a diagrammatic exposition Moreover, for brevity we will focus on the continuous time economy Recall that the law of motion of the effective capital-labor ratio in the continuous time Solow model is given by (2.45) k˙ (t) /k (t) = sf (k (t)) /k (t) − (δ + g + n) The right hand side of this equation is plotted in Figure 2.13 The intersection with the horizontal axis gives the steady state (balanced growth) equilibrium, k∗ This figure is sufficient for us to carry out comparative dynamic exercises Consider, for example, a one-time, unanticipated, permanent increase in the saving rate from s to s0 This shifts to curve to the right as shown by the dotted line, with a new 92