Chapter 6

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Transcript Chapter 6

Chapter 6

Economic Growth: Malthus and Solow

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 6 Topics

• Economic growth facts • Malthusian model of economic growth • Solow growth model • Growth accounting Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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U.S. Per Capita Income Growth

In the United States, growth in per capita income has not strayed far from 2% per year (excepting the Great Depression and World War II) since 1900.

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Figure 6.1

Natural Log of Real Per Capita Income in the United States, 1869 –2005 Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Real Per Capita Income and the Investment Rate

Across countries, real per capita income and the investment rate are positively correlated.

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Figure 6.2

Real Income Per Capita vs. Investment Rate

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Real per capita income and the rate of population growth

Across countries, real per capita income and the population growth rate are negatively correlated.

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Figure 6.3

Real Income Per Capita vs. the Population Growth Rate Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Real per capita income and per capita income growth

• There is no tendency for rich countries to grow faster than poor countries, and vice-versa.

• Rich countries are more alike in terms of rates of growth than are poor countries.

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Figure 6.4

Growth Rate in Per Capita Income vs. Real Income Per Capita for the Countries of the World Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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A Malthusian Model of Economic Growth

Model predicts that a technological advance will just increase population, with no long-run change in the standard of living.

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Equation 6.1: Production Function

Output is produced from land and labor inputs.

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Equation 6.2: Evolution of the population

Population growth is higher the higher is per capita consumption.

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Equation 6.3: Equilibrium Condition

In equilibrium, consumption equals output produced.

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Equation 6.4: Equilibrium evolution of the population

This equation describes how the future population depends on current population.

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Figure 6.5

Population Growth Depends on Consumption per Worker in the Malthusian Model Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.5

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Figure 6.6

Determination of the Population in the Steady State Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.6: The per-worker production function

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Equation 6.7: Equilibrium condition in per-worker form

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Equation 6.8

Population growth is increasing in consumption per worker,

c

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Figure 6.7

The Per-Worker Production Function

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Figure 6.8

Determination of the Steady State in the Malthusian Model Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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An increase in z in the Malthusian model

• If

z

increases, this shifts up the per-worker production function.

• In the long run, the population increases to the point where per capita consumption returns to its initial level.

• There is no long-run change in living standards.

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Figure 6.9

The Effect of an Increase in

z

in the Malthusian Model Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.10

Adjustment to the Steady State in the Malthusian Model When

z

Increases Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Population Control in the Malthusian Model

• Population control alters the relationship between population growth and per-capita consumption.

• In the long run, per capita consumption increases, and living standards rise.

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Figure 6.11

Population Control in the Malthusian Model Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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How Useful is the Malthusian Model

• Model provides a good explanation for pre-1800 growth facts in the world.

• Malthus did not predict the effects of technological advances on fertility.

• Malthus did not understand the role of capital accumulation in growth.

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Solow Growth Model

• This is a key model which is the basis for the modern theory of economic growth.

• A key prediction is that technological progress is necessary for sustained increases in standards of living.

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Equation 6.9: Population growth

• In the Solow growth model, population is assumed to grow at a constant rate

n

.

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Equation 6.10: Consumption Savings Behavior

• Consumers are assumed to save a constant fraction s of their income, consuming the rest. Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.11: Representative firm’s production function

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Equation 6.12

Constant returns to scale implies: Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.13: Evolution of the capital stock

Future capital equals the capital remaining after depreciation, plus current investment.

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Figure 6.12

The Per-Worker Production Function Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.14: Income Expenditure Identity

The income expenditure identity holds as an equilibrium condition.

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Equation 6.15

In equilibrium, future capital equals total savings (

= I

) plus what remains of current

K

.

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Equation 6.16

Substitute for output from the production function.

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Equation 6.17

Rewrite in per-worker form.

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Equation 6.18

Re-arrange, to get: Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.13

Determination of the Steady State Quantity of Capital per Worker Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.19

Equation determining the steady state quantity of capital per worker,

k

*: Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.14

Determination of the Steady State Quantity of Capital per Worker Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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An increase in the savings rate, s

• In the steady state, this increases capital per worker and real output per capita.

• In the steady state, there is no effect on the growth rates of aggregate variables.

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Figure 6.15

Effect of an Increase in the Savings Rate on the Steady State Quantity of Capital per Worker Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.16

Effect of an Increase in the Savings Rate at Time

T

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Figure 6.17

Steady State Consumption per Worker Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.18

The Golden Rule Quantity of Capital per Worker Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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An increase in the population growth rate, n

• Capital per worker and output per worker decrease.

• There is no effect on the growth rates of aggregate variables.

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Figure 6.19

Steady State Effects of an Increase in the Labor Force Growth Rate Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Increases in Total Factor Productivity, z

Sustained increases in

z

cause sustained increases in per capita income.

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Figure 6.20

Increases in Total Factor Productivity in the Solow Growth Model Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Growth Accounting

An approach that uses the production function and measurements of aggregate inputs and outputs to attribute economic growth to: (i) growth in factor inputs; (ii) total factor productivity growth.

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Equation 6.20: Cobb-Douglas Production Function

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Equation 6.21

A labor share in national income of 64% gives: Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Equation 6.22

The Solow residual is calculated as: Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.21

Natural Log of the Solow Residual, 1948 –2005 Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Table 6.1

Average Annual Growth Rates in the Solow Residual Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Figure 6.22

Percentage Deviations from Trend in Real GDP (black line) and the Solow Residual (colored line), 1948 –2005 Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Table 6.2

Measured GDP, Capital Stock, Employment, and Solow Residual Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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Table 6.3

Average Annual Growth Rates

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Table 6.4

East Asian Growth Miracles (Average Annual Growth Rates) Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

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