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Solow’s Growth Model

Solow’s Growth Model. A Nobel-Prize Winning Idea!!!. Goals. To model the impact of saving on the long run standard of living To discuss convergence of standards of living over time To introduce the idea of a dynamic model, which describes the change in standard of living over time.

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Solow’s Growth Model

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  1. Solow’s Growth Model A Nobel-Prize Winning Idea!!!

  2. Goals • To model the impact of saving on the long run standard of living • To discuss convergence of standards of living over time • To introduce the idea of a dynamic model, which describes the change in standard of living over time

  3. The Production Function • Focus on one factor, physical capital • output per worker (y=Y/L) is a function of capital per worker (k=K/L), or • y = f(k)

  4. Notice • Output per worker rises with capital per worker • More machines for each worker lead to greater output • The diminishing marginal product of capital • The marginal benefit of each unit of capital is less than the previous unit,or • The slope decreases with as K/L increases

  5. Factors that affect the capital stock • Investment • depreciation

  6. Investment • Say we consume a constant proportion of output and save the rest. • That savings is used for Investment(I) • I=sY • If s=.2, 20% of our output is used for investment • If y=100, I=sy=.2x100=20 units of capital

  7. Depreciation • Some machines wear out each period. • We use d to denote the depreciation rate • If d=.1, 10% of machines wear out each period • If the capital stock (k) is 50, dxk=.1x50=5 units wear out each period

  8. Changes in the capital stock • Say Y=100, K=100,s=.2,d=.1 • We start the year with 10 units of capital • We buy sxY=.2x100=20 new units • dxK=.1*100=10 unit of capital wears out • At the end of the year we have, K+sY-dK = 10+20-10=20 units of capital • The process continues each year

  9. Let’s try a real example • Production function, y=square root(k) • s=.2,d=.1 • Say the capital stock starts at 1in year 1 • So y is the square root of 1 or 1 as well • In year 2, the capital stock is • k+sxy-dxk=1+.2x1-.1x1=1.1

  10. Let’s do it for 10 years

  11. To Finish Solow’s model • Extend the spreadsheet over more years • See Solow.xls • Draw the picture • see my graph on the board

  12. Conclusions • Higher savings rates lead to higher output per worker-- a higher standard of living • Poorer countries grow faster than rich countries • If savings is the same in all countries and technology is shared, we should see convergence in standards of living over time

  13. Important Extensions • Population growth • Acts like depreciation and lowers the standard of living • Improvements in Technology • Lead to sustained Growth over time • Human Capital • Can stop convergence in standards of living across countries

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