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Basic Solow Model Scott Baier

Basic Solow Model Scott Baier. Explaining Catch-up Growth. Key Aspects of the Solow Model . Saving gets channeled into investment Investment adds to the capital stock Each period some capital wears out with use. Simplest Solow Model. Assume that we save a constant amount (S= 50)

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Basic Solow Model Scott Baier

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  1. Basic Solow ModelScott Baier Explaining Catch-up Growth

  2. Key Aspects of the Solow Model • Saving gets channeled into investment • Investment adds to the capital stock • Each period some capital wears out with use.

  3. Simplest Solow Model • Assume that we save a constant amount (S= 50) • Assume an initial level of capital (K=300) • Assume 10% of the capital stock depreciates each period (Depreciation = d*K) • Observe how the capital stock changes each period

  4. Tabulation

  5. Tabulation

  6. Tabulation

  7. Tabulation

  8. Tabulation

  9. Tabulation

  10. Tabulation

  11. Tabulation

  12. Tabulation

  13. Key Observations • At some point, it will be the case that savings is exactly equal to investment and the capital stock reach a steady state. • When you are far away from the steady state, the capital stock grows faster. • More rapid growth in the capital stock implies more rapid growth in output.

  14. Steady State • When saving equals investment, the economy reaches a steady state and the capital stock stops growing. • Mathematically, the capital stock stops growing when: S = d*Kss Since we know S and d  Kss = s/d In our example, Kss = 50/.10 =500

  15. Simple Solow Model: Graphically

  16. Simple Solow Model: Graphically

  17. Simple Solow Model: Graphically

  18. Simple Solow Model: Graphically

  19. Solow Growth Model • Important Point: The steady state occurs where savings is equal to depreciation. • In the simple Solow Growth Model, S=d*K • Given values for S and d, we can find the steady-state value of K

  20. Solow Growth Model • It is unrealistic to assume that people save a constant amount. • It is more likely to be the case that saving is related to the level of income. • We assume that people save a constant fraction of income.

  21. Key Aspects of the Solow Model • Saving gets channeled into investment • Investment adds to the capital stock • Each period some capital wears out with use.

  22. Production Function

  23. Production Function and Saving Function

  24. Saving Function and Depreciation Schedule

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