Lecture 5
THE SOLOW MODEL

1. Assumptions

• Output depends on two factors of production and technology:
  Y = AF(K,L)

• Constant-returns-to-scale technology:
  y = Af(k), where y=Y/L, k=K/L

• Saving equals fixed proportion of output:
  S = sY (s is the savings ratio)

• Labor force grows at the rate of n

2. Model

• Saving (in period t) equals investment (in period t):
  S(t) = I(t)

• Investment leads to addition to capital stock:
  I(t) = K(t+1) - K(t)

• Change in capital-labor ratio over time:
  dk/dt = sAf(k) - nk

3. Results

• In steady state, capital and labor grow at same rate:
  dk/dt=0

• Capital-labor ratio = k*

• Higher savings ratio leads to greater capital-labor ratio:
  k* increases with s

• Higher population growth leads to lower capital-labor ratio:
  k* decreases with n

• Higher savings ratio does not lead to faster growth:
  In steady state, output, capital and labor all grow at the same rate, n.

• One-time improvement in technology
  • Increase in A leads to higher k*
  • No increase in growth rate of output

• Continual technical progress
  • Leads to increase in growth rate of output

4. Criticism

• Model does not explain why technical progress occurs
• Model does not explain what determines a country's savings ratio
• Increase in savings ratio has no effect on economic growth (Questionable)

5. Convergence hypothesis

• Consider two countries with same technology, savings ratio and population growth
• Let Country A's initial capital-labor ratio be less than Country B's
• A given increase in capital stock will produce a larger increase in output in Country A than in Country B (why?)
• Result:
  • Country A will tend to grow faster than Country B
  • In steady-state, both countries will:
    (a) Grow at the same rate
    (b) Have the same per-capita income
• Evidence from developing countries?