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Understanding the Solow Growth Model: Implications for Economic Growth and Development

This lecture explores the Solow Growth Model, highlighting its significance in understanding economic growth. Originating from insights during the Industrial Revolution, the model emphasizes investment and capital formation as crucial for growth. Unlike Keynes's focus on aggregate demand, Solow posits that savings drive growth through the formula Y = f(L, K). This lecture delves into the steady state analysis, the relationship between savings and investment, and how varying levels of capital per worker influence economic growth in different income countries.

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Understanding the Solow Growth Model: Implications for Economic Growth and Development

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  1. ECON*2100Week 2 – Lecture 2 The Solow Growth Model

  2. 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

  3. Basic set-up • Production function Y = f(L, K) • Re-express in per-worker terms Y/L = f(K/L) y = f(k)

  4. 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

  5. Savings = Investment c = (1-s)y y = (1-s)y + i y = y – sy + i y – y + sy = i → i = sy = s∙f(k)

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

  7. Steady State • Change in capital each period ∆k = i - d∙k • Steady state: ∆k = 0 • So in steady state, i = d∙k

  8. Steady State • Graphically:

  9. Steady State • Enlarge lower part:

  10. Steady State • Graphically: consumption

  11. 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)

  12. Optimal growth c = f(k) – s∙f(k) c = f(k) –d∙k Maximize this where f'(k) – d

  13. 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

  14. Next Population Growth

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