Solow Model of Growth

Question 1

Description of Solow Model & Components

Answer 1

Looks at role of physical capital accumulation in economic growth

1) Model of production
2) Model of actual investment in physical capital
3) Model of required investment in physical capital

Question 2

Production function

Answer 2

Two factor inputs: Physical capital (K) & Labour (L)

• Upwards concave curve
• The inputs are combined to produce potential output

Y = Kα L1−α

• α represents the capital share of production
• This function exhibits constant returns to scale & diminishing marginal productivity when changing one factor alone

Question 3

Capital Investment

Answer 3

• K̇ = I - D
  Can see I adds to capital stock and depreciation erodes the stock
• Capital = Investment - depreciation (required investment)
• The dot over K means rate of change

Question 4

Actual investment

Answer 4

• Actual investment is constant proportion of, s, of income. Think of s as the investment rate
• I = sY

Question 5

Required Investment

Answer 5

• A constant proportion δ, of the physical capital stock, K.
• δ is the depreciation rate of capital
• Capital erodes at a constant rate, D = δK
• Also called replacement investment
• Creates an upward sloping line with slope δ
  K̇ = sY - δK

Question 6

Steady State Equilibrium

Answer 6

• When K̇ = 0, when actual investment is undertaken until it matches required investment
• On a graph where Actual investment & Required investment intersect
• Equilibrium stock of physical capital when sY = δK
• This model is stable so returns to equilibrium in the long run

Question 7

Analysis of GDP differences

Answer 7

• Countries with higher investment rates, s, will ten to have higher levels of K therefore higher Y.
• Countries with larger populations, L, tend to have higher levels of K therefore higher levels out Y
• Need to look at output per capita as hard to compare countries only on these metrics