3.1 Introduction• In this chapter, we learn:

– Some facts related to economic growth that later chapters will seek to explain.

– How economic growth has dramatically improved welfare around the world.

• this growth is actually a relatively recent phenomenon

3.1 Introduction• In this chapter, we learn:

– Some tools used to study economic growth, including how to calculate growth rates.

– Why a “ratio scale” makes plots of per capita GDP easier to understand.

• The United States of a century ago could be mistaken for Kenya or Bangladesh today.

• Some countries have seen rapid economic growth and improvements to health quality, but many others have not.

3.2 Growth over the Very Long Run

• Sustained increases in standards of living are a recent phenomenon.

• Sustained economic growth emerges in different places at different times. – Thus, per capita GDP differs remarkably

around the world.

• The Great Divergence– The recent era of increased difference in

standards of living across countries. • Before 1700

– Per capita GPD in nations differed only by a factor of two or three.

• Today– Per capita GPD differs by a factor of 50 for

several countries.

3.3 Modern Economic Growth

• Timeline: from 1870 to 2000, United States per capita GDP . . .– . . . rose by nearly 15-fold.

• Implications for you?– A typical college student today will earn a

lifetime income about twice his or her parents.

3.4 Modern Growth around the World

• After World War II, growth in Germany and Japan accelerated.

• Convergence– Poorer countries will grow faster to “catch

up” to the level of income in richer countries.

• Brazil had accelerated growth until 1980 and then stagnated.– China and India have had the reverse

pattern.

A Broad Sample of Countries

• Over the period 1960–2007– Some countries have exhibited a negative

growth rate.– Other countries have sustained nearly 6

percent growth.– Most countries have sustained about 2

percent growth.• Small differences in growth rates result in

large differences in standards of living.

Case Study: People versus Countries

• Since 1960:– The bulk of the world’s population is

substantially richer. – The fraction of people living in poverty has

fallen.• A major reason for changes

– Economic growth in China and India– These are 40 percent of the world

population!

Case Study: Growth Rules in a Famous Example, Yt = AtKt

1/3Lt2/3

• Applying rules of growth rates• Original output equation:

• Use multiplication rule to get

• Use exponent rule to get

3.6 The Costs of Economic Growth

• The benefits of economic growth– Improvements in health– Higher incomes– Increase in the variety of goods and services

• Costs of economic growth include:– Environmental problems– Income inequality across and within

countries– Loss of certain types of jobs

• Economists generally have a consensus that the benefits of economic growth outweigh the costs.

3.7 A Long-Run Roadmap

• Are there certain policies that will allow a country to grow faster?

• If not, what about a country’s “nature” makes it grow at a slower rate?

Summary• Sustained growth in standards of living

is a very recent phenomenon.

• If the 130,000 years of human history were warped and collapsed into a single year, modern economic growth would have begun only at sunrise on the last day of the year.

Summary• Modern economic growth has taken hold in

different places at different times.

• Since several hundred years ago, when standards of living across countries varied by no more than a factor of 2 or 3, there has been a “Great Divergence.”

• Standards of living across countries today vary by more than a factor of 60.

• Since 1870– Growth in per capita GDP has averaged about

2 percent per year in the United States.– Per capita GDP has risen from about $2,500

to more than $37,000.

• Growth rates throughout the world since 1960 show substantial variation– Negative growth in many poor countries– Rates as high as 6 percent per year in several

newly industrializing countries, most of which are in Asia

• Growth rates typically change over time

• In Germany and Japan– Growth picked up considerably after World

War II.– Incomes converged to levels in the United

Kingdom.– Growth rates have slowed down as this

convergence occurred.

• Brazil exhibited rapid growth in the 1950s and 1960s and slow growth in the 1980s and 1990s.

• China showed the opposite pattern.

• Economic growth, especially in India and China, has dramatically reduced poverty in the world.

• In 1960– Two out of three people in the world lived on

less than $5 per day (in today’s prices).

• By 2000– This number had fallen to only 1 in 10.

4.1 Introduction• In this chapter, we learn:

– How to set up and solve a macroeconomic model. – How a production function can help us understand

differences in per capita GDP across countries.– The relative importance of capital per person

versus total factor productivity in accounting for these differences.

– The relevance of “returns to scale” and “diminishing marginal products.”

– How to look at economic data through the lens of a macroeconomic model.

• A model:– Is a mathematical representation of a

hypothetical world that we use to study economic phenomena.

– Consists of equations and unknowns with real world interpretations.

• Macroeconomists:– Document facts.– Build a model to understand the facts.– Examine the model to see how effective it is.

4.2 A Model of Production

• Vast oversimplifications of the real world in a model can still allow it to provide important insights.

• Consider the following model– Single, closed economy– One consumption good

Setting Up the Model

• A certain number of inputs are used in the production of the good

• Inputs– Labor (L)– Capital (K)

• Production function– Shows how much output (Y) can be

produced given any number of inputs

• Others variables with a bar are parameters.

• Production function:

Productivity parameterOutput Inputs

• The Cobb-Douglas production function is the particular production function that takes the form of

Assumed to be 1/3.Explained later.

• A production function exhibits constant returns to scale if doubling each input exactly doubles output.

Returns to Scale ComparisonFind the sum of

exponents on the inputs

• sum to 1

• sum to more than 1

• sum to less than 1

Result

• the function has constant returns to scale

• the function has increasing returns to scale

• the function has decreasing returns to scale

• Standard replication argument

– A firm can build an identical factory, hire identical workers, double production stocks, and can exactly double production.

– Implies constant returns to scale.

Allocating Resources

• The rental rate and wage rate are taken as given under perfect competition.

• For simplicity, the price of the output is normalized to one.

Firm chooses inputs to maximize profit

Rental rate of capital

Wage rate

• The marginal product of labor (MPL)– The additional output that is produced when

one unit of labor is added, holding all other inputs constant.

• The marginal product of capital (MPK)– The additional output that is produced when

one unit of capital is added, holding all other inputs constant.

• The solution is to use the following hiring rules:

– Hire capital until the MPK = r

– Hire labor until MPL = w

• If the production function has constant returns to scale in capital and labor, it will exhibit decreasing returns to scale in capital alone.

Solving the Model: General Equilibrium

• The model has five endogenous variables: – Output (Y)– the amount of capital (K)– the amount of labor (L)– the wage (w)– the rental price of capital (r)

• The model has five equations:– The production function– The rule for hiring capital– The rule for hiring labor– Supply equals the demand for capital– Supply equals the demand for labor

• The parameters in the model:– The productivity parameter– The exogenous supplies of capital and labor

• A solution to the model– A new set of equations that express the five

unknowns in terms of the parameters and exogenous variables

– Called an equilibrium

• General equilibrium– Solution to the model when more than a

single market clears

• In this model

– The solution implies firms employ all the supplied capital and labor in the economy.

– The production function is evaluated with the given supply of inputs.

– The wage rate is the MPL evaluated at the equilibrium values of Y, K, and L.

– The rental rate is the MPK evaluated at the equilibrium values of Y, K, and L.

Interpreting the Solution

• If an economy is endowed with more machines or people, it will produce more.

• The equilibrium wage is proportional to output per worker.

• Output per worker = (Y/L)• The equilibrium rental rate is

proportional to output per capital.• Output per capital = (Y/K)

• In the United States, empirical evidence shows:– Two-thirds of production is paid to labor. – One-third of production is paid to capital.– The factor shares of the payments are equal

to the exponents on the inputs in the Cobb-Douglas function.

• All income is paid to capital or labor.

– Results in zero profit in the economy– This verifies the assumption of perfect

competition.– Also verifies that production equals spending

equals income.

Case Study: What Is the Stock Market?

• Economic profit– Total payments from total revenues

• Accounting profit– Total revenues minus payments to all

inputs other than capital.• The stock market value of a firm

– Total value of its future and current accounting profits

– The stock market as a whole is the value of the economy’s capital stock.

4.3 Analyzing the Production Model

• Per capita = per person• Per worker = per member of the labor

force.– In this model, the two are equal.

• We can perform a change of variables to define output per capita (y) and capital per person (k).

• Output per person equals the productivity parameter times capital per person raised to the one-third power.

Output per person

Capital per person

Productivity parameter

• What makes a country rich or poor?

• Output per person is higher if the productivity parameter is higher or if the amount of capital per person is higher.

– What can you infer about the value of the productivity parameter or the amount of capital in poor countries?

Comparing Models with Data

• The model is a simplification of reality, so we must verify whether it models the data correctly.

• The best models:– Are insightful about how the world works– Predict accurately

The Empirical Fit of the Production Model

• Development accounting:– The use of a model to explain differences

in incomes across countries.

Set productivity parameter = 1

• Diminishing returns to capital implies that:– Countries with low K will have a high MPK– Countries with a lot of K will have a low MPK,

and cannot raise GDP per capita by much through more capital accumulation

• If the productivity parameter is 1, the model overpredicts GDP per capita.

Case Study: Why Doesn’t Capital Flow from Rich to Poor Countries?

• If MPK is higher in poor countries with low K, why doesn’t capital flow to those countries?– Short Answer: Simple production model

with no difference in productivity across countries is misguided.

– We must also consider the productivity parameter.

Productivity Differences: Improving the Fit of the Model

• The productivity parameter measures how efficiently countries are using their factor inputs.

• Often called total factor productivity (TFP)

• If TFP is no longer equal to 1, we can obtain a better fit of the model.

• However, data on TFP is not collected.

– It can be calculated because we have data on output and capital per person.

– TFP is referred to as the “residual.”

• A lower level of TFP

– Implies that workers produce less output for any given level of capital per person

4.4 Understanding TFP Differences

• Why are some countries more efficient at using capital and labor?

Human Capital

• Human capital– Stock of skills that individuals accumulate

to make them more productive– Education, training, etc.

• Returns to education– Value of the increase in wages from

additional schooling• Accounting for human capital reduces

the residual from a factor of 11 to a factor of 6.

Technology

• Richer countries may use more modern and efficient technologies than poor countries.

– Increases productivity parameter

Institutions

• Even if human capital and technologies are better in rich countries, why do they have these advantages?

• Institutions are in place to foster human capital and technological growth.– Property rights– The rule of law– Government systems– Contract enforcement

Misallocation

• Misallocation

– Resources not being put to their best use

• Examples

– Inefficiency of state-run resources– Political interference

Case Study: A “Big Bang” or Gradualism? Economic Reforms in

Russia and China

• When transitioning from a planned to a market economy, the change can be sudden or gradual.– A “big bang” approach is one where all old

institutions are replaced quickly by democracy and markets.

– A “gradual” approach is one where the transition to a market economy occurs slowly over time.

• Russia followed a “big bang” approach, yet GDP per capita has declined since the transition.

• China has seen accelerated economic growth using the “gradual” approach.

4.5 Evaluating the Production Model

• Per capita GDP is higher if capital per person is higher and if factors are used more efficiently.

• Constant returns to scale imply that output per person can be written as a function of capital per person.

• Capital per person is subject to strong diminishing returns because the exponent is much less than one.

• Weaknesses of the model:

– In the absence of TFP, the production model incorrectly predicts differences in income.

–The model does not provide an answer as to why countries have different TFP levels.

Summary• Per capita GDP varies by a factor of 50 between

the richest and poorest countries of the world.• The key equation in our production model is the

Cobb-Douglas production function:

Productivity parameterOutput Inputs

• The exponents in this production function:

– One-third of GDP is paid out to capital.

– Two-thirds is paid to labor.

– Exponents sum to 1, implying constant returns to scale in capital and labor.

• The complete production model consists of five equations and five unknowns:

- Output Y- Capital K- Labor L- Wage rate w- Rental rate r

• The solution to this model is called an equilibrium.

• The prices w and r are determined by the clearing of labor and capital markets.

• The quantities of K and L are determined by the exogenous factor supplies.

• Y is determined by the production function.

• The production model implies that output per person in equilibrium is the product of two key forces:

– Total factor productivity (TFP)– Capital per person

• Assuming the TFP is the same across countries, the model predicts that income differences should be substantially smaller than we observe.

• Capital per person actually varies enormously across countries, but the sharp diminishing returns to capital per person in the production model overwhelm these differences.

• Making the production model fit the data requires large differences in TFP across countries.

• Economists also refer to TFP as the residual, or a measure of our ignorance.

• Understanding why TFP differs so much across countries is an important question at the frontier of current economic research.

• Differences in human capital (such as education) are one reason, as are differences in technologies.

• These differences in turn can be partly explained by a lack of institutions and property rights in poorer countries.

Macroeconomics

This concludes the LectureSlide Set for Chapter 4

byCharles I. Jones

Second Edition

W. W. Norton & CompanyIndependent Publishers Since 1923