Comparative Dynamics

We now briefly discuss how comparative dynamics are different in the neoclassical growth model than those in the basic Solow model. Recall that while comparative statics refer to changes in steady state in response to changes in parameters, comparative dynamics look at how the entire equilibrium path of variables changes in response to a change in policy or parameters.

will remain unchanged). Figure 8.2 shows diagrammatically how the comparative dynamics work out. This figure is drawn under the assumption that the change in the discount rate (corresponding to the change in the preferences of the representative household in the econ­omy) is unanticipated and occurs at some date T. At this point, the curve corresponding to c/c = 0 shifts to the right and together with this, the laws of motion represented by the phase diagram change (in the figure, the arrows represents the dynamics of the economy after the change). It can be seen that following this decline in the discount factor, the previous steady-state level of consumption, c*, is above the stable arm of the new dynamical system. Therefore, consumption must drop immediately to reach the news stable arm, so that capi­tal can accumulate towards its new steady-state level. This is shown in the figure with the arc representing the jump in consumption immediately following the decline in the discount rate. Following this initial reaction, consumption slowly increases along the stable arm to a higher level of (normalized) consumption. Therefore, a decline in the discount rate lead to a temporary decline in consumption, associated with a long-run increase in consumption. We know that the overall level of normalized consumption will necessarily increase, since the intersection between the curve forand the inverse U-shaped curve forwill necessarily be to the left side of k_gold.

Comparative dynamics in response to changes in other parameters, including the rate of labor-augmenting technological progress g, the rate of population growth n, and other aspects of the utility function, can also be analyzed similarly. Exercise 8.13 asks you to work through the comparative dynamics in response to a change in the rate of labor-augmenting technological progress, g, and in response to an anticipated future change in ρ.

8.8.