Economic Growth — AP Macroeconomics Study Guide

For: AP Macroeconomics candidates sitting AP Macroeconomics.

Covers: definition of long-run economic growth, the Rule of 70, growth accounting with the Cobb-Douglas production function, crowding out/crowding in, and long-run policy effects on LRAS.

You should already know: AD-AS model fundamentals, aggregate production function basics, core fiscal and monetary policy concepts.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Macroeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Economic Growth?

Economic growth is defined as a sustained increase in an economy’s potential real output (real GDP) over time. For measuring changes in average living standards, economists use real GDP per capita growth, which adjusts total GDP growth for changes in population size. This differs from short-run "cyclical growth," which is just an increase in actual output as an economy recovers from a recession and moves toward its existing potential output. Long-run economic growth, the core concept tested in AP Macroeconomics Unit 5, represents an increase in potential output itself, which shifts the long-run aggregate supply (LRAS) curve to the right.

According to the AP Macroeconomics Course and Exam Description (CED), Unit 5 (Long-Run Consequences of Stabilization Policies) makes up 15-20% of the overall AP exam score. Economic growth concepts appear in both multiple-choice questions (MCQ) and free-response questions (FRQ): you can expect 3-5 MCQs on this topic, and it is often the core theme of a 10-point long FRQ. Standard of living comparisons and growth calculations are common MCQ topics, while policy effects on long-run growth are frequent FRQ topics.

2. The Rule of 70

The Rule of 70 is a simple approximation to calculate how long it takes a variable growing at a constant annual rate to double in value. It is most commonly used for comparing how fast different economies grow their GDP per capita, but it can also be applied to inflation, population, or any other compounding variable.

The formula for the Rule of 70 is: $$\text{Doubling Time (years)}\approx \frac{70}{g}$$ where $g$ is the annual growth rate of the variable, measured in percentage points. The approximation comes from the math of continuous compounding: to double your value, you solve $(1+\frac{g}{100}{)}^t=2$. Taking the natural log of both sides gives $t\approx \frac{0.693}{g/100}=\frac{69.3}{g}$, which rounds to 70 for simplicity. This approximation is very accurate for growth rates between 0.1% and 10%, which covers almost all cases you will see on the AP exam.

Worked Example

Country X has a real GDP per capita growing at 2.5% annually. Country Y has a real GDP per capita growing at 1.4% annually. If both start with a real GDP per capita of $15,000, what is the approximate difference in their per capita GDP after 70 years?

1. Apply the Rule of 70 to find each country's doubling time. Doubling time for X = $70/2.5=28$ years. Doubling time for Y = $70/1.4=50$ years.
2. Calculate how many times each country doubles its GDP over 70 years. X: $70/28=2.5$ doublings. Y: $70/50=1.4$ doublings.
3. Calculate final per capita GDP for each: X: $15000\ast 2^{2.5}=15000\ast 4\ast \sqrt{2}\approx 15000\ast 5.656=\$84,840$ Y: $15000\ast 2^{1.4}=15000\ast 2\ast 2^{0.4}\approx 15000\ast 2\ast 1.3195=\$39,585$
4. The difference is $84840-39585=\$45,255$, meaning X will have more than double Y's per capita GDP after 70 years.

Exam tip: Always confirm the growth rate is entered in percentage points (e.g., 2.5 for 2.5% growth), not decimal form (0.025). Entering decimals will give a doubling time 100 times too large, which is one of the most common tested mistakes.

3. Growth Accounting with the Aggregate Production Function

Growth accounting is a method to break down total economic growth into contributions from different sources: input accumulation (more labor, more capital) and productivity growth (better technology, better institutions). The standard aggregate production function used in AP Macroeconomics is the Cobb-Douglas form: $$Y=A\ast K^{\alpha }\ast L^{1-\alpha }$$ where $Y$ = total real output, $A$ = total factor productivity (TFP, which captures technology, human capital, and institutional quality), $K$ = physical capital stock, $L$ = labor input, and $\alpha$ = the share of national income that goes to owners of capital (usually 0.3 to 0.4 in most developed economies).

To get the growth accounting formula, take the percentage change of both sides, which simplifies to: $$\%\Delta Y=\%\Delta A+\alpha (\%\Delta K)+(1-\alpha )(\%\Delta L)$$ This formula lets you calculate how much of total growth comes from TFP (productivity) versus growth in capital and labor inputs, which is a common FRQ task.

Worked Example

A developing economy has a capital share of income $\alpha =0.35$. Over the last decade, total real GDP grew at 4.5% annually, the capital stock grew at 5% annually, and the labor force grew at 2% annually. What share of total annual growth comes from total factor productivity?

1. Write the growth accounting formula: $\%\Delta Y=\%\Delta A+\alpha (\%\Delta K)+(1-\alpha )(\%\Delta L)$.
2. Rearrange to isolate the unknown TFP growth: $\%\Delta A=\%\Delta Y-\alpha (\%\Delta K)-(1-\alpha )(\%\Delta L)$.
3. Plug in the given values: $\%\Delta A=4.5-(0.35\ast 5)-(0.65\ast 2)=4.5-1.75-1.3=1.45\%$.
4. TFP contributes 1.45 percentage points of the 4.5% total growth, which is roughly 32% of total annual growth.

Exam tip: On FRQs, always write out the full formula before plugging in values. Partial credit is almost always awarded for the correct formula setup even if your final calculation is wrong.

4. Long-Run Effects of Stabilization Policy on Growth

Stabilization policies (fiscal and monetary policies used to smooth short-run business cycles) have long-run consequences for economic growth, which is the core focus of this unit. The effect on growth depends on the type of policy and how it is implemented:

1. Expansionary fiscal policy: If the government runs deficits to fund stimulus, higher government borrowing raises interest rates, which crowds out private investment in physical capital. This reduces long-run capital accumulation and slows growth, shifting LRAS right less than it would otherwise. However, if the deficit funds productive public investment (infrastructure, education, R&D), this increases total factor productivity and raises the return to private investment, which crowds in private investment and accelerates long-run growth.
2. Expansionary monetary policy: Money is neutral in the long run, meaning permanent increases in the money supply only raise the price level, not potential output. But low, stable inflation from predictable monetary policy reduces uncertainty for investors, which can encourage capital accumulation and growth. Permanently high inflation reduces investment and slows growth.
3. Supply-side fiscal policy: Policies like investment tax credits, lower taxes on capital gains, and deregulation increase incentives for saving and investment, which accelerates capital accumulation and TFP growth, shifting LRAS right faster and increasing long-run growth.

Worked Example

A government responds to a recession with a $300 billion deficit-financed stimulus package: 60% of the deficit funds renewable energy infrastructure, and 40% goes to household transfer payments. How does this policy affect long-run economic growth compared to a deficit of the same size that funds only transfer payments?

1. Recall that deficit spending on public infrastructure increases public capital stock, which raises total factor productivity A in the aggregate production function. Transfer payments do not increase productive capital.
2. The productivity gain from infrastructure raises the marginal product of private capital, so private investment is more attractive than it would be in the all-transfer case. This offsets the crowding out of private investment from higher deficits.
3. A higher A and higher net capital accumulation means potential output is higher in the long run, so the LRAS curve shifts further right than it would in the all-transfer case.
4. This policy leads to faster long-run economic growth than an equal-sized deficit spent only on transfers.

Exam tip: Never assume all expansionary fiscal policy reduces long-run growth. Always check what the deficit spending is used for before concluding the effect on growth.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Using the growth rate in decimal form (e.g., 0.02 for 2%) in the Rule of 70, getting a doubling time of 350 years instead of 35. Why: Students confuse percentage growth rates with the decimal form used in compound interest formulas. Correct move: Always write the growth rate next to your calculation confirming it is in percentage points before plugging into the Rule of 70.
• Wrong move: Confusing short-run increases in real GDP (recovery from recession) with long-run economic growth. Why: Both increase measured real GDP, so students mix up the two concepts on exam questions. Correct move: Always ask "Is this movement of actual output toward existing potential output, or is potential output itself increasing?"; only the latter counts as long-run growth.
• Wrong move: Assuming all expansionary fiscal policy reduces long-run economic growth via crowding out. Why: Students learn the crowding out effect and generalize it to all deficit spending, regardless of its purpose. Correct move: Always check if the deficit is spent on productive public investment; that investment increases potential output, leading to faster not slower growth.
• Wrong move: Forgetting to weight input growth by income share in growth accounting, adding growth rates directly instead. Why: Students confuse the size of inputs with their output elasticity when calculating growth contributions. Correct move: Always multiply each input's growth rate by its share of national income before adding up, then subtract from total growth to get TFP growth.
• Wrong move: Claiming expansionary monetary policy permanently increases long-run economic growth. Why: Students see that low nominal rates increase investment in the short run, and forget the long-run neutrality of money. Correct move: State that monetary policy only affects long-run growth if it delivers low, stable inflation that encourages investment; permanently expansionary policy only raises inflation, not real growth.
• Wrong move: Using total real GDP growth to measure changes in the average standard of living. Why: Students forget that population growth erodes gains in total GDP. Correct move: If the question asks about standard of living, always subtract the population growth rate from total real GDP growth to get per capita growth.

6. Practice Questions (AP Macroeconomics Style)

Question 1 (Multiple Choice)

A country has a constant annual growth rate of real GDP per capita of 1.4%. Its population is growing at 1.1% annually. What is the approximate doubling time of the country's total real GDP? A) 28 years B) 35 years C) 50 years D) 64 years

Worked Solution: First, total real GDP growth equals the sum of real GDP per capita growth and population growth. Total growth $g=1.4\%+1.1\%=2.5\%$. Apply the Rule of 70 to get doubling time = $70/2.5=28$ years. The distractors correspond to common mistakes: 35 comes from miscalculating total growth as 2%, 50 comes from using per capita growth instead of total, 64 comes from using only population growth. The correct answer is A.

Question 2 (Free Response)

The country of Graecia has an aggregate production function given by $Y=A{K}^{0.4}{L}^{0.6}$. Over the past decade, Graecia has had 3.2% annual total real GDP growth, 3% annual growth in the capital stock, and 1% annual growth in the labor force. (a) Calculate the annual growth rate of total factor productivity (A) in Graecia. Show your work. (b) Suppose Graecia implements a permanent investment tax credit that increases annual capital stock growth by 1 percentage point, holding all other growth rates constant. What is the new annual total output growth rate? Explain. (c) Graecia's central bank is considering permanently raising the inflation target from 2% to 4% to try to increase long-run growth. Would you expect this policy to raise long-run growth? Use the concept of long-run monetary neutrality to explain.

Worked Solution: (a) The growth accounting formula for the Cobb-Douglas production function is: $$\%\Delta Y=\%\Delta A+\alpha \%\Delta K+(1-\alpha )\%\Delta L$$ We substitute the given values: $\alpha =0.4$, $\%\Delta Y=3.2$, $\%\Delta K=3$, $\%\Delta L=1$. Rearranging gives: $$\%\Delta A=3.2-(0.4)(3)-(0.6)(1)=3.2-1.2-0.6=1.4\%$$ The annual growth rate of total factor productivity is 1.4%. (b) The increase in capital growth of 1 percentage point adds $\alpha \ast 1\%=0.4\%$ to total output growth. The new total annual output growth rate is $3.2\%+0.4\%=3.6\%$. Investment tax credits increase capital accumulation, which directly adds to output growth per the growth accounting formula. (c) No, this policy will not permanently increase long-run growth. The long-run neutrality of money states that changes in the steady inflation rate only affect nominal variables like prices and wages, not real variables like potential output or long-run real growth. High inflation also increases uncertainty, which typically discourages investment and reduces long-run growth.

Question 3 (Application / Real-World Style)

In 2023, Country A has a total real GDP of $21trillion,withalong-runaverageannualgrowthrateof1.7$3.5 trillion, with an average annual growth rate of 5% over the past 20 years. Assuming both growth rates remain constant, use the Rule of 70 to approximate how many years it will take for Country B's total real GDP to equal Country A's.

Worked Solution: First, find the difference in annual growth rates: $5\%-1.7\%=3.3\%$. Country B's GDP is 1/6 of Country A's GDP, so it needs to grow by a factor of 6 to catch up. A factor of 6 equals roughly 2.58 doublings. The doubling time for the GDP gap is $70/3.3\approx 21.2$ years per doubling. Total time is $2.58\ast 21.2\approx 55$ years. If current growth rates persist, Country B will match Country A's total real GDP around 2078.

7. Quick Reference Cheatsheet

8. What's Next

This chapter builds the foundation for analyzing how short-run policy choices shape the long-run trajectory of the economy, which is the core theme of Unit 5. Next, you will apply the concepts of growth and productivity to analyze catch-up growth between developing and developed economies, and how institutional factors affect long-run growth outcomes. Without mastering how to calculate growth rates and how policies shift LRAS, you will not be able to correctly answer cross-country growth comparison questions that are common on the AP exam. This topic also connects to the broader course theme of the short-run vs long-run policy trade-off, which appears frequently on FRQs.

• Crowding Out and Crowding In
• LRAS and Potential Output Shifts
• Convergence and Catch-Up Growth