Econ 2100 week 2 lecture 2
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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

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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


Econ 2100 week 2 lecture 2

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Population Growth


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