人民大学：《宏观经济学》（英文版） Lecture 6 Economic growth

Intermediate macroeconomics Lecture 6 Economic growth

Intermediate Macroeconomics Lecture 6 Economic Growth

Goal Develop the solow growth Model How much of the economy's output should be consumed today and how much should be saved for the future Static analysis( ch 3)> Dynamic

Goal ◼ Develop the Solow Growth Model --- How much of the economy’s output should be consumed today and how much should be saved for the future? ◼ Static analysis (Ch. 3) → Dynamic

The accumulation of capita 1. The supply for goods Production function Y= F(K,L) CharacteristiCs: CRS ay= F(ak, aL) Y K Per capita f(k)

The Accumulation of Capital 1. The supply for goods Production function: Characteristics: CRS Per Capita --- Y F K L = ( , ) aY F aK aL = ( , ) ( ,1) Y K F L L = y f k = ( )

The accumulation of Capital The production function y y=f(k) △ y △1 △人K

The Accumulation of Capital ◼ The production function y k y=f(k) y k y MPK k  = 

The accumulation of Capital 2. The demand for goods Solow model assumes that the demand for goods comes from consumption and investment only: y=C+i ∴C (1-s)y∴i=Sy=sf(k)

The Accumulation of Capital 2. The demand for goods --- Solow model assumes that the demand for goods comes from consumption and investment only: y c i = + c s y = − (1 )  i sy sf k = = ( )

The accumulation of Capital 3. The steady-state level of capital y=f(k)

The Accumulation of Capital 3. The steady-state level of capital y k y=f(k) i=sf(k) y c i

The accumulation of Capital Change in capital stock y y=f(k) sk =sf(k) k*k

The Accumulation of Capital ◼ Change in capital stock  = − k i k  y=f(k) y k i=sf(k)  k k*

The accumulation of capita Steady-state →△k=2一dk=O 今=人来 →Sf(k)=⑤k

The Accumulation of Capital ◼ Steady-state → → →  = − = k i k  0 i k * * = sf k k ( *) * = 

The accumulation of Capital Example: Cobb-Douglas function y=K- √k Steady state:S√k*=δ人水 大 δ2

The Accumulation of Capital ◼ Example: Cobb-Douglas function Steady state: 1/ 2 1/ 2 Y K L = y k = s k k * * =  2 2 * s k  =

The accumulation of Capital s=0.15,0=0.05,k=1→k*=9 Inv dep change in k 0.850.150.05 0 1_1.050.890.160.0550.1023213 1.202|1.10.930.160.060.1043596 41.3071.140.970.170.0650.1061312 505.762.42.040.360.2880.0719967 1007.9872.832.40.420.3990.0245709 93[2.550.450.45

The Accumulation of Capital ◼ s=0.15, =0.05, k=1  → k*=9 k y c inv. dep. change in k 1 1 1 0.85 0.15 0.05 0.1 2 1.1 1.05 0.89 0.16 0.055 0.1023213 3 1.202 1.1 0.93 0.16 0.06 0.1043596 4 1.307 1.14 0.97 0.17 0.065 0.1061312 … 50 5.76 2.4 2.04 0.36 0.288 0.0719967 100 7.987 2.83 2.4 0.42 0.399 0.0245709 … 9 3 2.55 0.45 0.45 0