Lectures 19-20: Savings and Technology•Review• Cont.: Change in Saving rate• Technological progressSolow’s Growth ModelA = 1, N = 1Y= y = f(k) S = sYI = S K(t+1) = (1-d) K(t) + I(t)=>k(t+1) - k(t) = s f(k(t)) - d k(t)Steady State and the Saving RateIn 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 dynamicsFigures 11-3, 11-4Some 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 11-1Dynamics• Dynamics: k(1) = 1+0.2-0.1 = 1.1>1 • … and so on• Figure 11-7Technological Progress•Table 12-2• Y = F(K,N,A) ….. Y=F(K,NA)• y = Y/NA = F(K/NA,1) = f(K/NA) = f(k)• I/AN = s Y/AN• In order to maintain a given k, we need to invest at least: (d+g_A + g_N) KTechnological ProgressI/AN > (d+g_A + g_N) (K/AN) => k growsFigure 12-2Table 12-1Figure 12-3 / 12-4A Decline in g_A• Table 12-2• Table 12-1• (use) Figure 12-2• Why? (we don’t know…)– Measurement error? – The rise of the Service Sector? • Figure 12-5– Decreased R&D Expenditure?•Table 12-3The New Economy and Productivity Growth5.83.13.20.20.7Industrial Mach.1.10.60.30.41.9Multifactor productivity2.11.31.1-0.61.5Manufacturing2.12.91948-19731.01.21973-19793.01.41979-19906.01.61990-19957.42.51995-2000Labor productivityElectronic Mach.Private Non-Farm BusinessSource: BLS.Investment Has IncreasedSource: BEA; Datastream; St. Louis Federal Reserve.Investment Share of GDP(Real Figures)10%12%14%16%18%20%22%196019651970197519801985199019952000The Price of New CapitalSource: BEA; St. Louis Federal Reserve.Real Interest Rates(Constant maturity nominal rates minus Un. of Michigan inflation expectations)-4-2024681012198019851990199520001 Year 10 YearChange in Relative Price of Equipment(1996 Relative price normalized to one; log
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