# Chapter 6

### Chapter 6 Topics

6-2

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.

6-3

Figure 6.1

6-4

Real Per Capita Income and the Investment Rate

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

6-5

### Real Income Per Capita vs. Investment Rate

6-6

Real per capita income and the rate of population growth

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

6-7

Figure 6.3

6-8

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.

6-9

Figure 6.4

6-10

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.

6-11

Equation 6.1: Production Function

Output is produced from land and labor inputs.

6-12

Equation 6.2: Evolution of the population

Population growth is higher the higher is per capita consumption.

6-13

Equation 6.3: Equilibrium Condition

In equilibrium, consumption equals output produced.

6-14

Equation 6.4: Equilibrium evolution of the population

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

6-15

Figure 6.5

6-16

### Equation 6.5

6-17

Figure 6.6

6-18

Equation 6.6: The per-worker production function

6-19

Equation 6.7: Equilibrium condition in per-worker form

6-20

### Equation 6.8

Population growth is increasing in consumption per worker,

c

6-21

### The Per-Worker Production Function

6-22

Figure 6.8

6-23

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.

6-24

Figure 6.9

The Effect of an Increase in

z

6-25

Figure 6.10

z

6-26

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.

6-27

Figure 6.11

6-28

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.

6-29

### 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.

6-30

Equation 6.9: Population growth

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

n

.

6-31

Equation 6.10: Consumption Savings Behavior

6-32

Equation 6.11: Representative firm’s production function

6-33

### Equation 6.12

6-34

Equation 6.13: Evolution of the capital stock

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

6-35

Figure 6.12

6-36

Equation 6.14: Income Expenditure Identity

The income expenditure identity holds as an equilibrium condition.

6-37

### Equation 6.15

In equilibrium, future capital equals total savings (

= I

) plus what remains of current

K

.

6-38

### Equation 6.16

Substitute for output from the production function.

6-39

### Equation 6.17

Rewrite in per-worker form.

6-40

6-41

Figure 6.13

6-42

### Equation 6.19

Equation determining the steady state quantity of capital per worker,

k

6-43

Figure 6.14

6-44

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.

6-45

Figure 6.15

6-46

Figure 6.16

Effect of an Increase in the Savings Rate at Time

T

6-47

Figure 6.17

6-48

Figure 6.18

6-49

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.

6-50

Figure 6.19

6-51

Increases in Total Factor Productivity, z

Sustained increases in

z

cause sustained increases in per capita income.

6-52

Figure 6.20

6-53

### 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.

6-54

Equation 6.20: Cobb-Douglas Production Function

6-55

6-56

6-57

Figure 6.21

6-58

Table 6.1

6-59

Figure 6.22

6-60

Table 6.2

6-61