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AK Growth Model Calculator

Calculates the long-run growth rate of output per capita in an AK model.

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Technology Level

Formula first

Overview

The AK growth model is a fundamental model in endogenous growth theory, explaining sustained economic growth without relying on exogenous technological progress. It posits that the aggregate production function exhibits constant returns to scale to capital, implying that capital accumulation alone can drive long-run growth. This formula determines the per capita growth rate based on the technology level, capital's productivity, and population growth.

Symbols

Variables

A = Technology Level, = Capital Share/Productivity, n = Population Growth Rate, g = Growth Rate of Output per Capita

Technology Level
dimensionless
Capital Share/Productivity
dimensionless
Population Growth Rate
% / year
Growth Rate of Output per Capita
% / year

Apply it well

When To Use

When to use: Apply this equation when analyzing long-run economic growth in models where capital accumulation does not face diminishing returns. It is particularly relevant for understanding how policy interventions affecting technology (A) or capital's productivity ($\delta$) can influence sustained growth rates, or how population growth (n) impacts per capita growth.

Why it matters: The AK model is crucial because it provides an endogenous explanation for economic growth, unlike earlier models (e.g., Solow-Swan) that relied on exogenous technological progress. It highlights the importance of human capital, R&D, and infrastructure in fostering sustained development, influencing policy debates on innovation and investment.

Avoid these traps

Common Mistakes

  • Confusing the AK model with the Solow-Swan model, especially regarding returns to capital.
  • Incorrectly interpreting 'A' as total factor productivity without considering its broader role in endogenous growth.

One free problem

Practice Problem

An economy following the AK growth model has a technology level (A) of 0.3, a capital share in production () of 0.2, and a population growth rate (n) of 0.01. Calculate the growth rate of output per capita (g).

Technology Level0.3 dimensionless
Capital Share/Productivity0.2 dimensionless
Population Growth Rate0.01 % / year

Solve for: result

Hint: Substitute the values directly into the formula g = A - n.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Economic Growth by David Romer, 4th Edition, W. W. Norton & Company
  2. Macroeconomics by N. Gregory Mankiw, 10th Edition, Worth Publishers
  3. Wikipedia: AK model
  4. Romer, David. Advanced Macroeconomics. 5th ed. McGraw-Hill, 2018.
  5. Mankiw, N. Gregory. Macroeconomics. 10th ed. Worth Publishers, 2019.
  6. Barro, Robert J. Macroeconomics: A Modern Approach. 2nd ed. South-Western Cengage Learning, 2008.
  7. Romer, D. - Advanced Macroeconomics, Chapter 2 (Endogenous Growth Theory)