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Lecture 18: Growth

This lecture discusses Solow's model of growth, including growth facts, sources of growth, steady state, saving rate, per capita growth, transitional dynamics, and the Golden Rule. Figures and tables are used to illustrate the concepts.

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Lecture 18: Growth

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  1. Lecture 18: Growth • Facts • Solow’s model

  2. Growth • Facts: Figure 10-1 / table 10-1 / fig 10-2 • Sources of growth (per/capita): Capital accumulation / Technological progress • Y = F(K,NA) h.d. 1 • y= (Y/NA) = F(K/NA,1) = f(k) • figure 10-5

  3. Solow’s Growth Model A = 1, N = 1 Y= y = f(k) S = sY I = S K(t+1) = (1-d) K(t) + I(t) => k(t+1) - k(t) = s f(k(t)) - d k(t) Figures 11-1, 11-2

  4. Steady State and the Saving Rate In steady state: k(t+1)=k(t)=k* k(t+1) - k(t) = s f(k(t)) - d k(t) => sf(k*) = d k* g_y* = 0 (if n>0, g_y*=0 => g_Y=g_K=n>0) In steady state, the saving rate does NOT matter for per-capita growth. It does matter, however, for the level of per-capita output and transitional dynamics Figures 11-3, 11-4

  5. Some numbers • Y = (KN)0.5 => y = (K/N)0.5 =k0.5 • k(t+1)-k(t)= s k(t)0.5 - dk(t) • St.St: k*=(s/d)^2 ; y*=(s/d) • s0=d=0.1; s1=0.2 => • k* goes from 1 to 4 and y* from 1 to 2. • Higher saving=> need to maintain more capital • c* = y*- dk* • The Golden Rule: Table 11-1

  6. Dynamics • Dynamics: k(1) = 1+0.2-0.1 = 1.1>1 • … and so on • Figure 11-7

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