Economic Growth Explained: Growth Rate, Rule of 70, Sources and Policy

Economic growth is a sustained increase in an economy's real output per person, measured as the rise in real GDP per capita over time. It is calculated with the growth rate formula, growth rate (%) = (Real GDP this year - Real GDP last year) / Real GDP last year x 100, applied to real GDP or to real GDP per capita.

Growth is the long-run story in macroeconomics. The business cycle is output bouncing above and below the economy's capacity. Growth is that capacity itself rising, year after year, which is what lifts living standards across generations. AP Macroeconomics shows growth two ways: as an outward shift of the production possibilities curve and as a rightward shift of long-run aggregate supply in the AD-AS model.

What counts as economic growth

Three words in the definition each rule something out.

Real. Growth is measured in real GDP, which removes the effect of rising prices. If nominal GDP rises 5 percent while prices rise 5 percent, the economy produced no more goods and services than before. The guide to what GDP is covers the real versus nominal adjustment in full.

Per capita. Total real GDP can rise just because the population grows. Living standards rise only when output grows faster than the number of people sharing it, so economists judge growth by real GDP per capita: real GDP divided by population.

Sustained. A one-year bounce back from a recession is a recovery, not growth in the long-run sense. Growth means the economy's potential output, the amount it can produce with its resources fully and normally employed, keeps rising.

How growth is measured

The growth rate formula

Growth rate (%) = (Value in year 2 - Value in year 1) / Value in year 1 x 100

Apply it to real GDP to get the growth of total output, or to real GDP per capita to get the growth of output per person. The economic growth rate calculator runs the same formula.

A useful shortcut: per capita growth is approximately real GDP growth minus population growth. The shortcut is close when the rates are small, but the exact answer always comes from dividing first and then taking the percentage change.

Worked example: total versus per capita growth

A country produces real GDP of $500 billion in year 1 and $520 billion in year 2. Its population grows from 50 million to 50.5 million.

Step 1. Real GDP growth. (520 - 500) / 500 x 100 = 20 / 500 x 100 = 4 percent.

Step 2. Population growth. (50.5 - 50) / 50 x 100 = 0.5 / 50 x 100 = 1 percent.

Step 3. GDP per capita in year 1. $500 billion / 50 million = $10,000 per person.

Step 4. GDP per capita in year 2. $520 billion / 50.5 million = $10,297.03 per person (520 / 50.5 = 10.29703, in thousands of dollars).

Step 5. Per capita growth. (10,297.03 - 10,000) / 10,000 x 100 = 297.03 / 10,000 x 100 = 2.97 percent.

Check. The shortcut gives 4 - 1 = 3 percent, within 0.03 points of the exact 2.97 percent. Multiplying back, 10,297.03 x 50.5 million = $520.0 billion, so Step 4 holds. Total output grew 4 percent, but the typical person's share grew just under 3 percent.

The rule of 70

Growth rates look small, so their effect is easy to underrate. The rule of 70 turns a growth rate into something you can picture:

Years to double = 70 / annual growth rate (in percent)

Enter the rate as a whole number. At 2 percent growth, use 70 / 2, not 70 / 0.02. The rule works because growth compounds: each year's increase is calculated on a larger base than the year before. The number 70 comes from the natural logarithm of 2, which is about 0.693, so the rule is an approximation that is most accurate at low growth rates. You can run any rate through the rule of 70 calculator.

Worked example: two countries, one starting point

Countries A and B each have real GDP per capita of $10,000. A grows 2 percent per year and B grows 5 percent per year. Where is each one after 70 years?

Step 1. Doubling time for A. 70 / 2 = 35 years.

Step 2. Doublings for A in 70 years. 70 / 35 = 2 doublings, so $10,000 becomes $20,000 and then $40,000.

Step 3. Doubling time for B. 70 / 5 = 14 years.

Step 4. Doublings for B in 70 years. 70 / 14 = 5 doublings: $20,000, $40,000, $80,000, $160,000, $320,000.

Check. Compound growth gives the exact answer. For A, 1.02 raised to the 70th power is about 4.00, so $10,000 becomes about $40,000, matching the rule. For B, 1.05 raised to the 70th power is about 30.4, so the exact figure is about $304,000 rather than $320,000. The rule overshoots slightly at 5 percent because the approximation weakens as rates rise, but the conclusion stands: a 3 point gap in growth rates turns equal starting incomes into incomes several times apart within one lifetime.

Where growth comes from

Real GDP per capita rises when each worker can produce more, which is why growth is closely tied to labor productivity, output per worker or per hour worked. Productivity rises through four main sources.

Physical capital

More capital per worker raises output per worker. The catch is diminishing returns: the first truck transforms a delivery business, while the twentieth adds far less. Capital accumulation alone cannot keep per capita growth going forever, which is the central result of the Solow growth model. Capital also has to be paid for, and in the loanable funds model the funds come from saving, so higher national saving supports more investment.

Human capital

Human capital is investment in people rather than machines. Education, training and health all raise what a worker can produce with a given set of tools, and skilled workers are often the ones who adopt and improve new technology.

Technology

Technology is what lets growth continue after capital runs into diminishing returns. A new production method raises the output from the same workers and the same machines. Long-run growth in output per worker is driven mostly by this kind of improvement. Growth accounting splits measured growth into the part explained by more capital and labor and the residual left over, which is attributed to technology and efficiency.

Institutions

None of the first three sources happens without incentives. People invest in machines, schooling and research when they expect to keep the returns. Secure property rights, enforceable contracts, low inflation and honest government make that expectation reasonable. Natural resources help too, but countries with similar resources can grow at very different rates depending on their institutions.

Growth on the production possibilities curve

On a production possibilities curve, economic growth is an outward shift of the whole curve. More resources or better technology let the economy produce more of both goods than it could before.

Two movements are often confused with growth and are not:

• Moving from a point inside the curve to a point on it. That is putting idle resources back to work, such as a recovery from a recession. The economy's capacity has not changed.
• Moving along the curve. That is a change in what the economy produces, with a trade-off between the two goods.

The PPC also shows a classic growth choice. An economy that devotes more of today's output to capital goods and less to consumer goods gives up consumption now, but its curve shifts out further in the future. An economy that consumes more now grows more slowly. If technology improves in only one industry, the curve pivots outward along that good's axis only. You can shift the curve yourself in the PPC sandbox.

See it move

Make it move

The production possibilities curve, drawn by the interactive graph. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Growth in the AD-AS model

In the AD-AS model, economic growth is a rightward shift of long-run aggregate supply (LRAS). LRAS is vertical at potential output, so anything that raises potential output, more capital, more skilled workers, better technology, stronger institutions, moves it to the right.

This is different from an increase in aggregate demand. A rightward AD shift can raise real GDP in the short run, but if the economy is already at potential it mainly raises the price level once wages and input prices adjust. Only an LRAS shift raises the economy's sustainable output. The difference between the short-run and long-run supply curves is laid out in SRAS vs LRAS.

If LRAS shifts right while AD stays put, the model predicts a higher real GDP and a lower price level. In practice AD usually rises too, so growth tends to come with a stable or gently rising price level rather than falling prices.

Policies that promote growth

Because growth comes from the supply side, growth policy targets the four sources rather than short-run spending.

• Encourage saving and investment. Tax rules that reward saving or business investment increase the flow of loanable funds and the capital stock. Large persistent budget deficits can work the other way by raising real interest rates and crowding out private investment.
• Invest in education and training. Public schooling, job training and student aid build human capital.
• Support research and development. Patents, research subsidies, and public funding for basic science raise the pace of technological change.
• Build infrastructure. Roads, ports, broadband and power grids are public capital that raises private productivity.
• Strengthen institutions. Protecting property rights, enforcing contracts and keeping inflation low make long-term investment worthwhile.
• Stay open to trade. Trade lets an economy specialize and gives firms access to foreign ideas and equipment.

The full unit, with flashcards and practice questions, is in the economic growth module.

Common mistakes

• Calling a recovery growth. A move from inside the PPC to the curve, or from a recessionary gap back to potential, is not long-run growth.
• Using nominal GDP. Growth must be measured in real terms or inflation looks like extra output.
• Forgetting population. Real GDP can rise while real GDP per capita falls if population grows faster.
• Writing the rule of 70 with a decimal. 70 / 0.03 gives 2,333 years, which is wrong. Use 70 / 3, about 23 years.
• Shifting AD to show growth. Long-run growth is an LRAS shift on AD-AS and an outward PPC shift. An AD shift is a short-run change in spending.

Growth is also the reason the business cycle is drawn around a rising trend line: actual output swings above and below a potential output that keeps climbing. The link between those swings and unemployment is the subject of Okun's law explained.