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ECON*2100 Week 2 – Lecture 2. The Solow Growth Model. After Smith. Industrial revolution in 1800s, invention of steam engine Various writers recognized that investment and capital formation mattered

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econ 2100 week 2 lecture 2

ECON*2100Week 2 – Lecture 2

The Solow Growth Model

after smith
After Smith
  • Industrial revolution in 1800s, invention of steam engine
  • Various writers recognized that investment and capital formation mattered
  • 1930s: Keynes argued that increasing Aggregate Demand and consumption were necessary to achieve growth
  • 1950s: Solow argued that savings, not consumption, drives growth
basic set up
Basic set-up
  • Production function

Y = f(L, K)

  • Re-express in per-worker terms

Y/L = f(K/L)

y = f(k)

savings
Savings
  • Each period, output is either for consumption or investment

y = c + i

  • Also, income is either consumed or saved
  • Savings fraction = s

C = (1-s)Y

c = (1-s)y

savings investment
Savings = Investment

c = (1-s)y

y = (1-s)y + i

y = y – sy + i

y – y + sy = i

→ i = sy = s∙f(k)

savings investment1
Savings = Investment
  • i = s∙f(k)
  • Now add depreciation: d∙k

d∙k

steady state
Steady State
  • Change in capital each period

∆k = i - d∙k

  • Steady state: ∆k = 0
  • So in steady state, i = d∙k
steady state1
Steady State
  • Graphically:
steady state2
Steady State
  • Enlarge lower part:
steady state3
Steady State
  • Graphically:

consumption

optimal growth
Optimal growth
  • Go to the level of capital per worker that maximizes consumption
    • Too little investment means low productivity
    • Too much means excess savings

y = c + i

c = y – i

c = f(k) – s∙f(k)

optimal growth1
Optimal growth

c = f(k) – s∙f(k)

c = f(k) –d∙k

Maximize this where

f\'(k) – d

implications
Implications
  • Economies grow through savings
  • Amount of capital per worker is key to growth
  • Low-income countries should grow rapidly compared to high-income countries
  • Growth ends at a steady state level of capital per worker and per-capita income
slide14
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Population Growth

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