Economic Growth Second Edition
Download 0.79 Mb. Pdf ko'rish
|
BarroSalaIMartin2004Chap1-2
1.2.4
The Steady State We now have the necessary tools to analyze the behavior of the model over time. We first consider the long run or steady state, and then we describe the short run or transitional dynamics. We define a steady state as a situation in which the various quantities grow at 9. Euler’s theorem says that if a function F (K, L) is homogeneous of degree one in K and L, then F(K, L) = F K · K + F L · L. This result can be proven using the equations F(K, L) = L · f (k), F K = f (k), and F L = f (k)− k · f (k). 10. Note that, in the previous section and here, we assumed that each person saved a constant fraction of his or her gross income. We could have assumed instead that each person saved a constant fraction of his or her net income, f (k) − δk, which in the market setup equals ra + w. In this case, the fundamental equation of the Solow–Swan model would be ˙ k = s · f (k) − (sδ + n) · k. Again, the same equation applies to the household-producer and market setups. 34 Chapter 1 constant (perhaps zero) rates. 11 In the Solow–Swan model, the steady state corresponds to ˙k = 0 in equation (1.13), 12 that is, to an intersection of the s · f (k) curve with the (n +δ) · k line in figure 1.1. 13 The corresponding value of k is denoted k ∗ . (We focus here on the intersection at k > 0 and neglect the one at k = 0.) Algebraically, k ∗ satisfies the condition s · f (k ∗ ) = (n + δ) · k ∗ (1.20) Since k is constant in the steady state, y and c are also constant at the values y ∗ = f (k ∗ ) and c ∗ = (1 − s) · f (k ∗ ), respectively. Hence, in the neoclassical model, the per capita quantities k, y, and c do not grow in the steady state. The constancy of the per capita magnitudes means that the levels of variables—K , Y , and C—grow in the steady state at the rate of population growth, n. Once-and-for-all changes in the level of the technology will be represented by shifts of the production function, f ( · ). Shifts in the production function, in the saving rate s, in the rate of population growth n, and in the depreciation rate δ, all have effects on the per capita levels of the various quantities in the steady state. In figure 1.1, for example, a proportional upward shift of the production function or an increase in s shifts the s · f (k) curve upward and leads thereby to an increase in k ∗ . An increase in n or δ moves the (n + δ) · k line upward and leads to a decrease in k ∗ . It is important to note that a one-time change in the level of technology, the saving rate, the rate of population growth, and the depreciation rate do not affect the steady-state growth rates of per capita output, capital, and consumption, which are all still equal to zero. For this reason, the model as presently specified will not provide explanations of the determinants of long-run per capita growth. Download 0.79 Mb. Do'stlaringiz bilan baham: |
Ma'lumotlar bazasi mualliflik huquqi bilan himoyalangan ©fayllar.org 2025
ma'muriyatiga murojaat qiling
ma'muriyatiga murojaat qiling