Golden Rule Savings Rate Calculator
Analyze the Solow-Swan Steady State and Consumption Maximization
What is the Golden Rule Savings Rate?
In economics, specifically within the Solow-Swan Growth Model, the Golden Rule savings rate is the level of savings that maximizes steady-state consumption per capita. While saving more leads to more capital and more output, it also requires more investment to maintain that capital stock due to depreciation and population growth. The Golden Rule identifies the specific "sweet spot" where the extra output generated by additional capital is exactly offset by the cost of maintaining it.
The Core Formula
In a standard Cobb-Douglas production function environment, the Golden Rule savings rate (sgold) is elegantly simple:
Where α is the capital share of total national income. In most modern economies, α is estimated to be between 0.3 and 0.4 (or 30% to 40%).
Key Variables Explained
- Capital Share (α): The fraction of total production that goes to the owners of capital (rK/Y).
- Depreciation (δ): The rate at which physical capital wears out or becomes obsolete each year.
- Population Growth (n): The rate at which the labor force is expanding.
- Technological Progress (g): The rate at which labor efficiency improves over time.
- Effective Depreciation: The sum (n + g + δ), representing the total investment needed just to keep the capital-to-labor ratio constant.
Interpretation of Results
If your Actual Savings Rate is lower than the Golden Rule rate, your economy is "Capital Shallow." Increasing savings would lead to higher future consumption. If your Actual Savings Rate is higher than the Golden Rule rate, the economy is "Dynamically Inefficient." You are saving so much that the cost of maintaining the massive capital stock is eating into the consumption that capital should be providing; in this case, saving less would actually increase consumption both now and in the future.
Realistic Example
Assume an economy has a capital share (α) of 0.35, depreciation of 5%, population growth of 1%, and technological progress of 2%. The Golden Rule savings rate would be 35%. If the current savings rate is only 20%, the economy is under-saving relative to the consumption-maximizing peak. Moving toward a 35% savings rate would increase the steady-state capital per worker and eventually lead to higher sustainable consumption levels.