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Macroeconomics

Macroeconomics. Lecture 19. Review of the Previous Lecture. Sectoral Shifts Public Policy and Job Search Unemployment insurance (UI) Unemployment from real wage rigidity The minimum wage Labor unions. Topics under Discussion. Issues in Economic Growth Solow Model Production Function

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Macroeconomics

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  1. Macroeconomics Lecture 19

  2. Review of the Previous Lecture • Sectoral Shifts • Public Policy and Job Search • Unemployment insurance (UI) • Unemployment from real wage rigidity • The minimum wage • Labor unions

  3. Topics under Discussion • Issues in Economic Growth • Solow Model • Production Function • Consumption Function • Savings and Investment • Depreciation • Steady State

  4. Issues in Economic Growth • Learn the closed economy Solow model • See how a country’s standard of living depends on its saving and population growth rates • Learn how to use the “Golden Rule” to find the optimal savings rate and capital stock

  5. Per Capita Income of Selected Countries, 2004 (in US $) Saudi Arabia 8,530 Mexico 6,230 Malaysia 3,780 Brazil 2,710 Russia 2,610 Egypt 1,390 China 1,100 Indonesia 810 India 530 Pakistan 470 Bangladesh 400 Nigeria 320 Norway 43,350 Switzerland 39,880 United States 37,610 Japan 34,510 United Kingdom 28,350 Belgium 25,820 Germany 25,250 France 24,770 Australia 21,650 Italy 21,560 Kuwait 16,340 Korea 12,020 Source: World Bank

  6. The Solow Model • due to Robert Solow, won Nobel Prize for contributions to the study of economic growth • a major paradigm: • widely used in policy making • benchmark against which most recent growth theories are compared • looks at the determinants of economic growth and the standard of living in the long run

  7. The Solow Model • The Solow Growth Model is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy, and how they affect a nation’s total output of goods and services.

  8. How Solow model is different 1. K is no longer fixed:investment causes it to grow, depreciation causes it to shrink. 2. L is no longer fixed:population growth causes it to grow. 3. The consumption function is simpler.

  9. How Solow model is different 4. No G or T(only to simplify presentation; we can still do fiscal policy experiments) 5. Cosmetic differences.

  10. The production function Let’s analyze the supply and demand for goods, and see how much output is produced at any given time and how this output is allocated among alternative uses. The production function represents the transformation of inputs (labor (L), capital (K), production technology) into outputs (final goods and services for a certain time period).

  11. The production function • In aggregate terms: Y = F (K, L ) • Define: y = Y/L = output per worker k = K/L = capital per worker • Assume constant returns to scale:zY = F (zK, zL ) for any z > 0

  12. The production function • Pick z = 1/L. Then Y/L = F (K/L , 1) y = F (k, 1) y = f(k) where f(k) = F (k, 1)

  13. f(k) MPK =f(k +1) – f(k) 1 The production function Output per worker, y Note: this production function exhibits diminishing MPK. Capital per worker, k

  14. The national income identity • Y = C + I(remember, no G ) • In “per worker” terms: y = c + iwhere c = C/L and i = I/L

  15. The consumption function • s = the saving rate, the fraction of income that is saved (s is an exogenous parameter) • Note: s is the only lowercase variable that is not equal to its uppercase version divided by L • Consumption function: c = (1–s)y(per worker)

  16. Saving and investment • saving (per worker) = sy • National income identity is y = c + i Rearrange to get: i = y – c = sy(investment = saving) • Using the results above, i = sy = sf(k)

  17. Output per worker, y f(k) sf(k) y1 i1 c1 Capital per worker, k k1 Output, consumption, and investment

  18. Depreciation per worker, k k 1  Capital per worker, k Depreciation  = the rate of depreciation = the fraction of the capital stock that wears out each period

  19. Capital accumulation The basic idea: Investment makesthe capital stock bigger, depreciation makes it smaller.

  20. Capital accumulation Change in capital stock= investment – depreciation k = i– k Since i = sf(k) , this becomes: k = sf(k)– k

  21. The equation of motion for k k = sf(k)– k • the Solow model’s central equation • Determines behavior of capital over time which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g., income per person: y = f(k) consump. per person: c = (1–s) f(k)

  22. The steady state k = sf(k)– k If investment is just enough to cover depreciation [sf(k)=k ], then capital per worker will remain constant: k = 0. This constant value, denoted k*, is called the steady state capital stock.

  23. k sf(k) k* The steady state Investment and depreciation Capital per worker, k

  24. Summary • Issues in Economic Growth • Solow Model • Production Function • Consumption Function • Savings and Investment • Depreciation • Steady State

  25. Upcoming Topics • Steady State (cont.) • Movements towards steady state • An increase in savings rate

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