Chapter 8: Economic Growth

ECO 112 Principles of Macroeconomics

Today’s Roadmap

Key Concepts

What economic growth is, and the Rule of 70 for doubling time
Why small differences in growth rates compound into huge differences over decades
The history of modern economic growth, and the institutions that support it
The four supply factors, the demand factor, and the efficiency factor
Growth accounting: decomposing real GDP growth into hours worked and productivity
Why labor productivity, not more hours, drives most long-run growth
The close link between productivity growth and real wage growth
The benefits and costs of growth, and whether faster growth is always better

Why Economic Growth Matters

From Chapters 6 and 7 to Growth

Chapter 6 introduced growth in real GDP and real GDP per capita. Chapter 7 showed exactly how real GDP is measured. This chapter asks a bigger question: what makes an economy’s output grow year after year, decade after decade?

Economic growth is an increase in a nation’s potential output over time, most often measured as the percentage increase in real GDP or real GDP per capita.

A rising real GDP per capita means a rising standard of living for the typical person.
Even a small, sustained difference in the annual growth rate reshapes a country’s future entirely, which is the first idea this chapter builds.

The Rule of 70

A handy shortcut for translating a growth rate into something more intuitive, how long it takes an economy to double in size:

\[ \text{Years to double} = \frac{70}{\text{Annual percent growth rate}} \]

A faster growth rate means a shorter doubling time.
This rule works for any growing quantity: GDP, GDP per capita, population, an investment account, anything that grows at a roughly constant percentage rate.

Example: Using the Rule of 70

Country Z’s real GDP per capita grows at 2.5 percent per year. Country Y’s real GDP per capita grows at 7 percent per year.

About how many years will it take Country Z’s per-capita output to double?
About how many years will it take Country Y’s per-capita output to double?
Which country’s typical resident sees their living standard double sooner, and by roughly how many years?

Solution: Using the Rule of 70

Zenith: $70 / 2.5 = 28$ years
Yorba: $70 / 7 = 10$ years

Yorba doubles about 18 years sooner than Zenith.
A growth rate that looks only a few points higher on paper can mean an entire extra generation’s worth of head start.

Harder Problem: Rule of 70

Two more countries, worked in reverse:

Country Meridia’s real GDP per capita has doubled in about the last 14 years.
Country Larkspur’s real GDP per capita has doubled in about the last 35 years.

Both countries started at $10,000 real GDP per capita.

About what annual growth rate has each country been sustaining?
If each country keeps growing at that same rate, roughly how many times does its per-capita GDP double over the next 70 years?
Starting from $10,000, roughly what would each country’s per-capita GDP be after those 70 years?

Review: Rule of 70

Meridia’s growth rate: $70/14 = 5\%$ per year
Larkspur’s growth rate: $70/35 = 2\%$ per year

Doublings in 70 years: Meridia $70/14 = 5$; Larkspur $70/35 = 2$
Meridia: $10{,}000 \times 2^5 = \$320{,}000$
Larkspur: $10{,}000 \times 2^2 = \$40{,}000$

A growth rate only 3 percentage points higher compounds into an eightfold difference in outcomes after 70 years.

Why Small Growth Differences Compound

Growth rates compound, they apply to an ever-larger base each year, not to the original starting value. That is why a gap of just a couple of percentage points can matter enormously over a long enough time horizon.

\[ \text{Value after } n \text{ years} = \text{Starting value} \times (1 + g)^n \]

This is the same compounding math behind interest on savings, just applied to an entire economy’s output instead of a bank account.

Example: Two Growth Rates Over 50 Years

Two hypothetical economies each start with real GDP of $1 trillion.

Economy Low grows at 2 percent per year.
Economy High grows at 4 percent per year.

Using $(1+g)^{n}$, what is each economy’s real GDP after 50 years?
How many times larger is Economy High than Economy Low after 50 years?

Solution: Two Growth Rates Over 50 Years

Economy Low: $1 \times (1.02)^{50} \approx \$2.69$ trillion
Economy High: $1 \times (1.04)^{50} \approx \$7.11$ trillion

Economy High ends up roughly $7.11 / 2.69 \approx 2.6$ times larger, even though its growth rate is only twice Economy Low’s, not 2.6 times.
Doubling the growth rate more than doubles the long-run outcome, because compounding works on an ever-growing base.

The History of Modern Economic Growth

Growth Is a Recent Phenomenon

Sustained modern economic growth, output per person rising generation after generation, is historically very recent.

For most of human history, output per person changed very little across centuries. A person’s living standard at the end of their life looked much like their grandparents’.
Roughly starting with the Industrial Revolution (illustrative timeframe: the late 1700s and 1800s), output per person began rising steadily and has kept rising, in fits and starts, ever since.

The steady, generation-over-generation growth we now think of as normal is the historical exception, not the rule.

The Industrial Revolution and the Growth Takeoff

This chart uses illustrative, stylized numbers to show the shape of the story, a long, nearly flat line followed by a sharp takeoff, not precise historical estimates.

Institutional Foundations of Growth

Why did sustained growth take off when and where it did? Economists point to institutions, the rules and organizations that structure economic life, as a major part of the answer. A partial, illustrative list:

Strong property rights and the rule of law
Patents and copyrights that reward innovation
Efficient financial institutions that channel saving into investment
Free and competitive markets
Specialization and free trade

Property Rights, Patents, and Copyrights

Property rights: legal protection of the right to own, use, and sell resources and products. If a business owner cannot trust that profits and property will not simply be seized, they have little reason to invest, build, or innovate.
The rule of law: laws applied predictably and fairly, including to the government itself, so that contracts and property rights are actually enforceable.
Patents and copyrights: temporary legal monopolies granted to inventors and creators. Without them, a competitor could simply copy a costly new invention, so innovators would have little incentive to invest the time and money to create it in the first place.

Financial Institutions and the Loanable Funds Market

Recall from Chapter 6: growth requires investment in new capital, and investment requires savings to actually reach the businesses that want to build it.

Efficient financial institutions, banks, stock markets, bond markets, are the plumbing that channels household saving into business investment.
This is exactly the market for loanable funds from Chapter 6: savers supply funds, borrowers demand funds, and a well-functioning financial system matches them at a market interest rate.
Where financial institutions are weak or untrustworthy, saving has nowhere productive to go, and growth suffers even where saving rates are high.

Specialization, Trade, and the PPF

Recall the production possibilities frontier (PPF) and opportunity cost from Chapter 1.

When individuals, firms, or countries specialize in what they produce comparatively efficiently and then trade, total output rises, without any new resources or technology at all.
Free trade extends this idea across borders: a country imports what it would otherwise produce at high opportunity cost, and exports what it produces at low opportunity cost.
Specialization and trade are, in effect, a way of getting the economy closer to (and even beyond, in per-person terms) what a single closed economy’s own PPF could deliver on its own.

The Sources of Growth: Supply, Demand, and Efficiency

Potential Output and the Four Supply Factors

An economy’s potential output is the maximum sustainable output it can produce with its current resources and technology. Four supply factors increase potential output:

An increase in the quantity or quality of natural resources
An increase in the quantity or quality of human resources (a larger labor force, more education and training)
An increase in the supply of capital goods (physical capital: machines, buildings, infrastructure)
Improvements in technology, better ways of combining resources to produce output

The Demand Factor

Supply factors only make growth possible. The economy also needs the demand factor: enough total spending to actually purchase the expanding potential output.

If potential output rises but total spending does not keep pace, factories, workers, and machines sit idle instead of producing at capacity.
Growth requires both the ability to produce more and buyers willing and able to buy what is produced.

The Efficiency Factor

Even with enough supply and enough demand, an economy still needs the efficiency factor: resources must actually be used well.

Allocative efficiency: resources are directed toward producing the specific mix of goods and services society values most.
Productive efficiency: each good is produced using the least-costly combination of resources, and at the lowest possible per-unit cost.

An economy can have more resources and enough spending, and still fail to reach its full potential if resources are misallocated or wasted.

Visualizing Growth: An Outward-Shifting PPF

The four supply factors shift the whole PPF outward. Whether the economy actually reaches a point on the new curve depends on the demand and efficiency factors.

Example: Supply Factors and the PPF

An economy’s PPF currently runs from a maximum of 100 units of capital goods to a maximum of 100 units of consumer goods (a bowed-out curve between the two extremes).

Supply factors, more workers, more capital, better technology, expand the maximum along each axis by 25 percent.

The economy actually produces 80 units of capital goods and 80 units of consumer goods.

What is the new maximum along each axis?
Is the economy’s actual production point inside, on, or outside the new PPF?
If it is not on the new PPF, which two factors could explain the gap?

Solution: Supply Factors and the PPF

New maximum along each axis: $100 \times 1.25 = 125$ units.
Distance of the actual production point, $(80, 80)$, from the origin: $\sqrt{80^2 + 80^2} \approx 113.1$, compared with a new-PPF distance of $125$ along the diagonal.

Because $113.1 < 125$, the economy is producing inside its new PPF, not on it.
The demand factor may be insufficient (not enough total spending to buy all the newly possible output), or the efficiency factor may be lacking (resources misallocated or not used at lowest cost). Having more resources is not enough on its own, an economy still has to spend enough and use its resources well to actually reach its new potential.

Growth Accounting

Decomposing Real GDP Growth

Growth accounting breaks real GDP growth down into two pieces that, approximately, add together:

\[ \text{Growth in real GDP} \approx \text{Growth in hours worked} + \text{Growth in labor productivity} \]

Hours worked: the total number of hours supplied by the labor force.
Labor productivity: real output per hour of work.

This lets us ask a sharper question than “did GDP grow?”: did it grow because people worked more hours, or because each hour of work produced more?

Example: Hours Worked and Productivity

In a given year, total hours worked in the economy grow by 1.5 percent, and labor productivity (output per hour) grows by 2.0 percent.

Using growth accounting, approximately what is the growth rate of real GDP?
Which piece, hours or productivity, contributed more to growth this year?

Solution: Hours Worked and Productivity

Real GDP growth $\approx 1.5\% + 2.0\% = 3.5\%$

Productivity contributed more, 2.0 percentage points versus 1.5.
This matches the long-run pattern in the United States: most growth in output per capita has come from rising labor productivity, not from people simply working more hours.

Harder Problem: Growth Accounting

Last year, a country’s real GDP grew by 4.2 percent, while total hours worked grew by only 1.0 percent.

Approximately what was the growth rate of labor productivity last year?
Suppose next year hours worked are projected to fall by 0.5 percent (an aging population working somewhat less), but productivity growth holds steady at the rate you found in part 1. Approximately what real GDP growth would you forecast for next year?

Review: Growth Accounting

Productivity growth: $4.2\% - 1.0\% = 3.2\%$

Next year’s forecast: $3.2\% + (-0.5\%) = 2.7\%$
Even with hours worked shrinking, steady productivity growth can still deliver solid real GDP growth, this is exactly why productivity is considered the more important long-run driver.

Sources of Productivity Growth

Economists rank the sources of long-run productivity growth in the United States roughly as follows, largest contributor first:

Technological advance: new methods, products, and processes, often the single largest source.
Quantity of capital per worker (capital deepening): giving each worker more and better machines and tools to work with.
Education and training of the workforce (human capital, recall Chapter 6): a more skilled workforce produces more per hour.
Economies of scale and improved resource allocation: bigger, better-organized markets let resources move to their most productive uses.

Real Data: Labor Productivity

Series OPHNFB

What is the overall trend in this index over the full period shown?

Answer: it trends upward over the long run, each hour of work produces more output today than it did decades ago.

Does the index rise at a perfectly constant rate every quarter, or does the pace vary?

Answer: the pace varies noticeably, productivity growth speeds up in some periods and slows or even dips in others.

Based on growth accounting, if this index were flat for several years while the labor force kept growing, what would that imply about the source of any real GDP growth during that time?

Answer: it would mean growth was coming almost entirely from more hours worked rather than from productivity, which tends to produce slower, less durable gains in output per person.

Productivity Growth and Real Wages

The Productivity-Wage Link

Over the long run, a nation’s labor productivity growth rate and its average real hourly wage growth rate tend to track each other closely, roughly one-to-one.

In a competitive labor market, firms compete for workers, and a worker’s pay tends to reflect the value of what that worker produces.
If workers become more productive, firms competing for their labor bid wages up to roughly match. If productivity stalls, real wage growth tends to stall too.

This is why raising productivity, not just raising wages directly, is the durable path to a higher standard of living.

Example: Productivity and Wage Growth Over a Decade

Suppose average labor productivity grows at 2.2 percent per year, and real hourly wages grow at 2.1 percent per year, both sustained over a 10-year period.

Using $(1+g)^{n}$, what is the cumulative percentage growth in productivity over the decade?
What is the cumulative percentage growth in real wages over the decade?
How closely do the two cumulative figures track each other?

Solution: Productivity and Wage Growth Over a Decade

Productivity: $(1.022)^{10} \approx 1.243$, or about $24.3\%$ cumulative growth
Real wages: $(1.021)^{10} \approx 1.231$, or about $23.1\%$ cumulative growth

The two cumulative figures are within about 1 percentage point of each other after a full decade.
This is the roughly one-to-one relationship in action: workers captured almost the full benefit of their own rising productivity as higher real pay.

A Note on Immigration and Per-Capita Growth

Immigration’s effect on per-capita growth is more ambiguous, and more debated, than it might first appear.

Immigration expands the labor force (more hours worked, more potential output).
Immigration also expands total demand (more people buying goods and services).

Because immigration shifts both supply and demand at once, its net effect on the per-capita growth rate is not simply positive or negative, it depends on the specifics, and economists continue to debate the size and even the direction of the effect in different contexts.

Benefits and Costs of Economic Growth

Benefits of Growth

Rising living standards: more goods and services available per person, on average.
More resources for a societal safety net: a larger economy can support more generous programs for those who need help, without necessarily raising tax rates.
More resources for public goods: infrastructure, research, education.
More resources to address problems, including environmental ones: a richer society can afford to invest more in cleanup and cleaner technology.

Costs and Critiques of Growth

Environmental and resource costs: growth that relies on burning through natural resources or polluting can degrade the environment growth is supposed to help us afford to fix.
Growth does not guarantee even distribution: recall the mean-versus-median discussion from Chapter 6. Rising average output per person is fully consistent with most of the gains flowing to a relatively small share of the population.
Growth involves tradeoffs: recall Chapter 6’s saving-and-investment discussion. Building more capital goods today, the investment that fuels future growth, means giving up some consumption today. Faster growth tomorrow is not free.

Real Data: Real GDP Per Capita, a Longer Look

Series A939RX0Q048SBEA

Chapter 6 introduced this series. Looking at more history now, does the long-run trend look closer to steady compounding or to a straight line?

Answer: closer to steady compounding, the line curves upward over the long run rather than rising by the same dollar amount every year, consistent with a roughly constant percentage growth rate.

Do you see any extended flat or declining stretches? What might explain one?

Answer: yes, recessions and major shocks produce flat or declining stretches, but the long-run trend resumes climbing afterward.

Based on this chapter’s Rule of 70, roughly how many years would it take real GDP per capita to double at an illustrative 2 percent annual growth rate?

Answer: about 35 years, $70/2 = 35$.

Wrap Up

Economic growth is the sustained rise in real GDP or real GDP per capita. The Rule of 70 ($70 /$ growth rate) turns a growth rate into a doubling time, and small rate differences compound into huge gaps over decades.
Sustained modern growth is historically recent, and rests on institutions: property rights, patents, financial institutions, competitive markets, and specialization and trade.
Four supply factors (natural resources, human resources, capital, technology) shift potential output outward, but the demand factor and efficiency factor determine whether the economy actually gets there.
Growth accounting: real GDP growth $\approx$ growth in hours worked $+$ growth in labor productivity. Productivity, led by technological advance and capital deepening, drives most long-run growth.
Productivity growth and real wage growth move roughly one-to-one in competitive labor markets.
Growth brings real benefits, but also real costs and tradeoffs, and does not guarantee an even distribution of gains.

Looking ahead: this chapter studied the long-run growth trend. Chapter 9 studies the business cycle, the short-run ups and downs in output and employment that occur around that long-run trend.