Macroeconomics guide, Unit 2, step 4 of 23Previous step Next step

Step 4: The Business Cycle and Economic Growth

By the EconTutorials team. 11-minute read with 6 practice questions.

SyllabusAP Macro 2.7 · Cambridge 4.4 · IB 3.1

In 30 seconds

Real GDP does not rise smoothly. It moves in a business cycle of expansion, peak, contraction (recession) and trough around a rising long-run trend called potential output.
$ \text{Output gap} = \dfrac{\text{Actual GDP} – \text{Potential GDP}}{\text{Potential GDP}} \times 100 $. A negative gap means recession and spare capacity; a positive gap means overheating and rising inflation.
Actual growth uses idle resources (moving towards the PPC). Potential growth shifts the PPC outward. Only technology escapes diminishing returns, so only technology can keep growth going for ever.
Growth compounds. The rule of 70 gives the doubling time: $ \text{years to double} \approx 70 \div \text{growth rate (\%)} $.

Video lesson coming soonA short animated lesson for this step will appear here.

The four phases of the business cycle

Think about a busy high-street café over several years. In good years the queue is out of the door, the owner hires extra staff and buys a second coffee machine. Then times turn: customers cut back, shifts are reduced and a barista is let go. A year or two later, trade picks up again. Whole economies behave in a similar way. Real GDP does not rise in a straight line; it swings above and below a rising long-run trend.

Key termBusiness cycle: the recurring pattern of expansion and contraction in real GDP around its long-run trend.

Expansion. Real GDP is rising. Firms hire, unemployment falls, and confidence and investment grow. Tax revenue rises, so the budget deficit narrows on its own.
Peak. The upper turning point. Output is at its highest for the cycle, unemployment at its lowest, and inflation pressure usually builds as demand presses against supply.
Contraction (recession). Real GDP is falling. Firms cut output and lay off workers, and investment falls first and hardest. A common rule of thumb defines a recession as two consecutive quarters of falling real GDP.
Trough. The lower turning point. Output is at its lowest and unemployment at its highest. Recovery begins as stocks run down, interest rates fall and delayed spending returns.

A depression is a long, severe recession. There is no formal threshold, but US output fell roughly 26% between 1929 and 1933.

Key termPotential output: the level of real GDP an economy can sustain when all resources are used at normal rates and unemployment equals its natural rate (also called full-employment output or trend output).

The output gap

The most important number in short-run policy is the gap between what the economy is producing and what it could produce. It tells policymakers whether to cut interest rates, raise taxes or expect inflation to speed up.

\[ \text{Output gap} = \frac{\text{Actual GDP} – \text{Potential GDP}}{\text{Potential GDP}} \times 100 \]

Gap	Meaning	Unemployment	Inflation
Negative	Actual < potential: recession, spare capacity	Above the natural rate	Weak pressure
Zero	Actual = potential: full employment	At the natural rate	Stable
Positive	Actual > potential: overheating	Below the natural rate	Speeds up

Okun’s law links the gap to jobs. As a rough rule, each 1 percentage point of negative output gap goes with about 0.5 percentage points of unemployment above the natural rate.

Worked example

Actual real GDP is $1,140 billion and potential output is $1,200 billion. The natural rate of unemployment is 4%. Find the output gap and estimate unemployment.

Step 1$ \text{Output gap} = \dfrac{1{,}140 – 1{,}200}{1{,}200} \times 100 = \dfrac{-60}{1{,}200} \times 100 = -5\% $

Step 2$ \text{Cyclical unemployment} \approx 0.5 \times 5 = 2.5 \text{ percentage points} $

Step 3$ \text{Unemployment} \approx 4\% + 2.5\% = 6.5\% $

The economy is 5% below potential, in recession with spare capacity. The $60 billion of output it failed to produce is lost for good: output is a flow, and the economy does not later produce above potential to make up for it.

Common mistakeGetting the sign the wrong way round, or dividing by actual GDP. A negative gap means a recession; a positive gap sounds good but means overheating and rising inflation. Always divide by potential GDP, and always state the sign and what it means.

The catch, as with the natural rate in Step 2, is that potential output cannot be observed. It must be estimated, and estimates are often revised later.

What causes the cycle?

Economists agree on the phases but disagree about the causes, and the answer shapes whether governments should step in.

Demand shocks. A fall in confidence, a stock market crash, a housing bust or a drop in exports cuts spending, so firms cut output. This is the Keynesian view: recessions are failures of demand that governments can and should correct.
Supply shocks. An oil price spike, a pandemic, a war or a failed harvest raises costs and reduces output. These recessions come with inflation, which is what made 1973 different from 2008.
Money and finance. Too much credit inflates asset prices, the bubble bursts, banks stop lending and the real economy follows. Hyman Minsky argued that long periods of stability encourage ever riskier borrowing.
Real business cycle theory. Kydland and Prescott argued that cycles are efficient responses to real shocks, mainly in technology, so policy is at best useless. Critics say it struggles to explain mass unemployment.

Most economists today hold a mix: demand shocks dominate the short run, supply shocks explain stagflation, and the financial system amplifies both.

Long-run growth: moving the whole curve

The business cycle is the wave; long-run growth is the tide. Over any period longer than about a decade, the trend matters far more than the cycle, and it decides whether a country is rich.

Key termActual growth: an increase in real GDP achieved by using spare capacity, shown as a movement from inside the production possibility curve (PPC) towards it.

Key termPotential growth: an increase in the economy’s productive capacity, shown as an outward shift of the PPC.

An economy recovering from recession may grow at 5% for a couple of years just by putting idle workers and factories back to work. That is actual growth, and it stops once the output gap closes. Lasting growth needs the PPC itself to move out. The deepest driver of living standards is productivity: output per worker or per hour worked.

There are four sources of long-run growth:

Physical capital: machines, factories, roads and ports. Capital faces diminishing returns: the first tractor transforms a farm, the tenth adds little.
Human capital: education, training, skills and health. Also subject to diminishing returns, though basic education in poor countries pays off hugely.
Natural resources: land, minerals and energy. Helpful but limited, and sometimes a curse: resource-rich countries often grow more slowly, because resource money can fuel corruption and crowd out other industries. Compare Nigeria with South Korea.
Technology: the only source of unlimited growth. Ideas are non-rivalrous: your using a formula does not stop me using it. So technology escapes diminishing returns.

Key termTotal factor productivity (TFP): the part of output growth not explained by more labour or capital, capturing technology, better institutions and better organisation.

Robert Solow showed in 1957 that most US growth per worker could not be explained by extra capital. The contrast between South Korea and the Soviet Union makes the point. Both invested over 30% of output and grew fast at first. But Soviet growth came almost entirely from adding inputs, its TFP growth was close to zero, and when it ran out of workers to move into factories, growth collapsed. South Korea kept climbing the technology ladder, from textiles to steel and shipbuilding, then cars, electronics and semiconductors.

The power of compound growth

Small differences in growth rates create huge differences in living standards, because growth compounds: each year’s growth builds on the last. If your savings grow 7% a year, they double in about 10 years.

\[ \text{Years to double} \approx \frac{70}{\text{annual growth rate (\%)}} \]

At 1% a year, living standards double in about 70 years; at 2%, 35 years; at 3.5%, 20 years; at 7%, 10 years. In 1960 South Korea and Ghana had almost the same GDP per capita. By 2020, after six decades of faster Korean growth, South Korea’s was about fourteen times higher, with no single dramatic event to explain it.

Worked example

Two countries both have GDP per capita of $4,000. Country A grows at 2% a year; Country B at 7% a year. Using the rule of 70, what is each country’s GDP per capita after 70 years?

Step 1$ \text{A doubles every } \tfrac{70}{2} = 35 \text{ years}; \quad \text{B doubles every } \tfrac{70}{7} = 10 \text{ years} $

Step 2$ \text{A doubles } \tfrac{70}{35} = 2 \text{ times: } 4{,}000 \times 2^2 = \$16{,}000 $

Step 3$ \text{B doubles } \tfrac{70}{10} = 7 \text{ times: } 4{,}000 \times 2^7 = 4{,}000 \times 128 = \$512{,}000 $

A gap of 5 percentage points a year turns equal starting points into a 32-fold difference within one lifetime.

Exam tipWhen asked about a recovery, say whether growth is actual (closing a negative gap, with potential unchanged) or potential (the PPC shifting out). Recovery growth cannot last once the gap closes, so it should never be projected forward.

Should we want growth?

For: growth pays for food, sanitation, medicine and schooling. Between 1990 and 2019 the share of people in extreme poverty fell from about 36% to under 10%, driven mainly by growth in China, India and Southeast Asia. It also widens the tax base and lets every group gain without another losing. Against: growth has historically raised carbon emissions; GDP per capita is an average that can hide flat incomes for most people; using up forests or fisheries counts as income; and above a certain level, extra income adds little to reported happiness (the Easterlin paradox). A balanced answer usually concludes that growth matters most for poorer countries, while richer countries should weigh it against other goals.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. Starting from the lower turning point, list the four phases of the business cycle in order. Show worked answer

Trough → expansion → peak → contraction (recession), then back to the next trough.

EasyQ2. A country grows at 5% a year. Roughly how long will its living standards take to double? Show worked answer

$ \text{Years to double} \approx \dfrac{70}{5} = 14 \text{ years} $

MediumQ3. Potential GDP is £800 billion and actual GDP is £840 billion. Calculate the output gap and predict what happens to unemployment and inflation. Show worked answer

$ \dfrac{840 – 800}{800} \times 100 = \dfrac{40}{800} \times 100 = +5\% $
A positive gap: the economy is overheating. Unemployment will be below the natural rate and inflation will speed up, so the central bank would be expected to raise interest rates.

MediumQ4. Actual real GDP is $920 billion, potential is $1,000 billion and the natural rate of unemployment is 5%. Use Okun’s law (1 point of gap ≈ 0.5 points of unemployment) to estimate the unemployment rate. Show worked answer

Output gap $ = \dfrac{920 – 1{,}000}{1{,}000} \times 100 = -8\% $
Cyclical unemployment $ \approx 0.5 \times 8 = 4 $ percentage points
Unemployment $ \approx 5\% + 4\% = 9\% $

MediumQ5. Which of these shifts the PPC outward: (a) unemployment falls from 8% to 5%; (b) a new technology raises output per worker; (c) consumer spending rises during a recovery? Show worked answer

Only (b). New technology raises productive capacity, which is potential growth.
(a) and (c) use idle resources and move the economy towards its existing PPC. That is actual growth.

ExamQ6. Real GDP is $750bn in 2023 and $780bn in 2024. Potential output is $800bn in both years. (a) Calculate the growth rate of real GDP. (b) Calculate the output gap in each year. (c) Is this actual or potential growth? Explain. [5 marks] Show worked answer

(a) $ \dfrac{780 – 750}{750} \times 100 = \dfrac{30}{750} \times 100 = 4\% $ [1 mark]
(b) 2023: $ \dfrac{750 – 800}{800} \times 100 = -6.25\% $. 2024: $ \dfrac{780 – 800}{800} \times 100 = -2.5\% $. Both negative, but the gap has narrowed. [2 marks]
(c) Actual growth. Potential output did not change, so capacity has not grown. The 4% came from bringing idle resources back into use, moving towards the PPC. Once the gap reaches zero, further growth needs the PPC to shift out, so this rate cannot be sustained. [2 marks]

Check yourself

1. A negative output gap is associated with:

Actual output is below potential, so resources are idle and there is little pressure on prices.

2. Why is technology the only source of unlimited long-run growth?

One firm using an idea does not stop others using it, so it raises the productivity of all capital and labour.

3. Using the rule of 70, a country growing at 3.5% a year doubles its living standards in about:

70 ÷ 3.5 = 20 years.

Your score: 0 out of 3

The short version

The business cycle runs expansion → peak → contraction → trough around a rising trend (potential output).
Output gap = (actual − potential) ÷ potential × 100. Negative means recession; positive means overheating. Okun’s law: 1 point of negative gap ≈ 0.5 points of extra unemployment.
Actual growth closes the gap; potential growth shifts the PPC out. Capital, skills and resources face diminishing returns; technology (TFP) does not.
Growth compounds: doubling time ≈ 70 ÷ growth rate.
Growth cuts poverty but has environmental and distributional costs.

This guide covers the core of Chapter 22 of Economics Made Simple. For the full chapter, including the business-cycle and PPC diagrams, the South Korea and Soviet Union case study and 15 exam-style questions with a complete answer key, get the book.