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Basic Growth Model

Basic Growth Model. 1) Y = F(K,L) production function 2) S= sY savings 3) S=I investment-savings relationship 4) ∆K=I-(dK) capital accumulation 5) ∆L=nL eqn of motion of labor. Harrod-Domar (HD) Model. 1’) Y = (1/v)K  v = K/Y (ICOR) fixed coeff. prodn. fnc.  Leontief + CRS

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Basic Growth Model

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  1. Basic Growth Model • 1) Y = F(K,L) production function • 2) S= sY savings • 3) S=I investment-savings relationship • 4) ∆K=I-(dK) capital accumulation • 5) ∆L=nL eqn of motion of labor

  2. Harrod-Domar (HD) Model • 1’) Y = (1/v)K  v = K/Y (ICOR) fixed coeff. prodn. fnc.  Leontief + CRS K/L, K/Y, L/Y are all fixed ∆Y = ∆K/v g = ∆Y/Y = ∆K/Yv  using ∆K = sY-dK  g = (sY-dK)/Yv = s/v – dK/Yv = s/v – d  g = s/v – d Save more and make more productive investments  your economy will grow

  3. Solow Growth Model • 1’’) Y/L = F(K/L,1) => y = f(k) y = Y/L, k = K/L CRS, DRK g = ∆Y/Y = ∆K/Yv = (sY-dK)/Yv 4’’) ∆K/K = sY/K - d 4’’) ∆k/k = ∆K/K - ∆L/L (since k = K/L) ∆K/K = ∆k/k + ∆L/L = ∆k/k + n • ∆k/k + n = sY/K - d • ∆k/k = sY/K - d - n • ∆k = sy – (n+d)k

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