Intermediate Macroeconomics

1. Intermediate Macroeconomics Chapter 3 Long-Run Economic Growth

2. Long-run Economic Growth • Growth accounting • Empirical results • Neoclassical growth model • Neoclassical growth model golden rule • Endogenous growth model • Government policy and growth Intermediate Macroeconomics

3. 1. Growth AccountingGrowth in six countries United States Canada U.K. Hong Kong Japan Brazil Intermediate Macroeconomics

4. Growth AccountingGrowth accounting equation ΔY = ΔA + εKΔK + εLΔL Y A K L Output growth rate = Productivity growth rate, ΔA/A + Capital growth rate, ΔK/K x elasticity of output with respect to capital, εK + Labor growth rate, ΔL/L x elasticity of output with respect to labor, εL Intermediate Macroeconomics

5. Empirical ResultsSolow and Denison studies Intermediate Macroeconomics

6. 3. Neoclassical Growth Model Growth in Actual and Potential U.S. GDP Actual GDP cycles around the long-run GDP growth rate (also called potential or full-employment GDP) Long run growth rate Actual Real GDP Source: Penn World tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html Intermediate Macroeconomics

7. Neoclassical Growth ModelStart with growth accounting equation Assumption 1. No technological change: ΔY = εKΔK + εL ΔL Y K L where, ΔA = 0 A Intermediate Macroeconomics

8. 3. Neoclassical Growth Model Steady State Assumption 2. Steady State - a condition of constant rates of growth in economic measures. With no technological change, a steady state is represented by identical constant growth rates in population, total output, and the level of capital. ΔL = ΔK = n = population growth rate L K Intermediate Macroeconomics

9. 3. Neoclassical Growth Model Constant returns to scale Assumption 3. Constant returns to scale production function. εK + εL = 1 Intermediate Macroeconomics

10. Neoclassical Growth ModelNeoclassical growth equation result ΔY = εKΔK + εL ΔL Y K L = εK n + εL n = (εK + εL ) n = n = population growth rate The growth rate of output is independent of savings or the level of capital. Intermediate Macroeconomics

11. 3.. Neoclassical Growth Model Simple model implications • Aggregate output grows at the same rate as population.* • Per worker output remains unchanged.* • The level of capital has no effect of aggregate or per worker output growth rates in steady state.** * Unless there is technological change, i.e. an increase in productivity. ** An increase in the savings rate and capital-labor ratio provides a temporary boost to aggregate output and per worker output growth rates. Growth rates will return to original steady state levels but at a permanently higher output per worker level. Intermediate Macroeconomics

12. 3. Neoclassical Growth Model Constant returns to scale Production function: Y = f(K, L) If constant returns: z Y = f(z K, z L) If z = 1/L: Y = f(K, 1) L L Or, Y/L = f(K/L) Intermediate Macroeconomics

13. 3. Neoclassical Growth ModelPer worker production function Output = f(K/L) Intermediate Macroeconomics

14. 3. Neoclassical Growth ModelSavings per worker Output = f(K/L) Savings = s • f(K/L) Intermediate Macroeconomics

15. 3. Neoclassical Growth ModelInvestment per worker Output = f(K/L) Steady State Equilibrium Investment = (n+d) • (K/L) Slope = n + d Savings = s • f(K/L) Intermediate Macroeconomics

16. Neoclassical Growth ModelEffect of an decrease in population growth rate Investment Slope = n + d gets smaller Output = f(K/L) Investment 1 Investment 2 A Savings B Intermediate Macroeconomics

17. 3. Neoclassical Growth Model Effect of an decrease in population growth rate U.S. Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html) International Monetary Fund, World Economic Outlook databases (www.imf,org). Intermediate Macroeconomics

18. 3. Neoclassical Growth ModelEffect of an increase in the savings rate Savings curve shifts upward Output Investment B Savings 2 Savings 1 A Intermediate Macroeconomics

19. 3. Neoclassical Growth Model Effect of an increase in the savings rate Steady State 2 Steady State 1 Steady State 2 Steady State 1 Intermediate Macroeconomics

20. 3. Neoclassical Growth ModelDeclining marginal productivity of capital Output = f(K/L) Larger increase in output per worker with one unit increase in labor Intermediate Macroeconomics

21. Neoclassical Growth ModelRich and Poor Convergence • Poor countries: • Low capital-labor ratio • Each unit of new capital yields larger increase in output per worker • Best place to invest is in labor markets with greatest marginal increase in output for each new unit of capital. • Investment and wealth should grow faster in poor than rich countries. Intermediate Macroeconomics

22. Neoclassical Growth Model Golden RuleSummary • Capital/Labor ratio that maximizes consumption in steady state. • Implies an optimal rate of savings – a country can have too high a rate of savings. Intermediate Macroeconomics

23. Neoclassical Growth Model Golden RuleConsumption • Consumption is the difference between output and investment in steady state. C = Y - I Intermediate Macroeconomics

24. 4. Neoclassical Growth Model Golden RuleConsumption = Output - Investment Output = f(K/L) Consumption Investment = (n+d) • (K/L) Intermediate Macroeconomics

25. 4. Neoclassical Growth Model Golden Rule Consumption per worker Consumption Maximum Consumption Intermediate Macroeconomics

26. 5. Endogenous Growth Model • Productivity growth: • Neoclassical model: productivity growth is exogenous; i.e., is given to us. • Endogenous growth model attempts to explain productivity growth within the model. • Marginal productivity of capital: • Neoclassical model: decreasing • Endogenous growth model: constant or even increasing Intermediate Macroeconomics

27. 5. Endogenous Growth Model Growth rate of output • Output is proportional to the level of capital, which implies non-decreasing marginal productivity of capital: Y = α٠ K • The change in output is proportional to the change in capital: ΔY = α٠ΔK • The growth rate of output equals the growth rate of capital: ΔY = ΔK Y K Intermediate Macroeconomics

28. 5. Endogenous Growth Model Savings = Investment • Savings = investment: S = I • Savings is proportional to output: S = s ٠ Y = s ٠α٠ K • Investment equals additions to the level of capital, ΔK, plus depreciation, d: I = ΔK + d ٠ K • Thus, s ٠α٠ K = ΔK + d ٠ K Intermediate Macroeconomics

29. 5. Endogenous Growth ModelSavings versus Investment Annual averages, 1950 - 2000 Venezuela Israel Nicaragua Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html). Intermediate Macroeconomics

30. 5. Endogenous Growth Model Growth of output and rate of savings • Rearrange to solve for the change in the capital stock: ΔK = s ٠α٠ K - d ٠ K • Divide both side by K: ΔK = s ٠α – d K • Substitute into the equation for the growth rate of output: ΔY = s٠α – d Y The growth rate of output is now a function of the savings rate. Intermediate Macroeconomics

31. 5. Endogenous Growth ModelEffect of investment rate on GDP growth Annual averages, 1950 - 2000 Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html). Intermediate Macroeconomics

32. Government Policies and Economic GrowthSummary • Policies that promote savings and investment • Temporary boost to aggregate growth rates in simple model. Sustained boost in endogenous growth model. • Permanently higher output per worker as long as higher savings rate is sustained. • Current consumption sacrificed. • Policies that raise productivity • Temporary increase to aggregate growth rates unless productivity growth rates sustained. • Sustained increase in output per worker. • No sacrifice of current consumption. Intermediate Macroeconomics