The golden rule of savings, in the context of economic growth models, states that the optimal savings rate is the one that maximizes steady-state consumption per capita. This occurs when the marginal product of capital equals the rate of population growth.
In simpler terms, the golden rule helps determine how much a society should save and invest versus consume today to achieve the highest possible level of consumption in the long run. It's not about maximizing output, but maximizing the well-being of the population through consumption.
Here's a breakdown:
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Steady-State: This refers to a long-run equilibrium where key economic variables like capital per capita and output per capita are constant.
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Consumption per Capita: This is the amount of goods and services available for each person in the economy. The golden rule aims to maximize this.
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Marginal Product of Capital (MPK): This represents the additional output generated by adding one more unit of capital.
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Rate of Population Growth (n): This is the percentage increase in the population size.
The Golden Rule Condition:
The golden rule condition is:
MPK = n
This equation means that the marginal product of capital should be equal to the rate of population growth. When this condition holds, the economy is saving and investing at the golden rule rate.
What happens if the saving rate is too low or too high?
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Dynamically Inefficient (Saving rate too low): If the saving rate is below the golden rule level, the economy is consuming too much today at the expense of future consumption. Increasing the saving rate will initially lower consumption, but in the long run, it will lead to a higher steady-state capital stock and higher consumption per capita.
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Dynamically Efficient (Saving rate too high): If the saving rate is above the golden rule level, the economy is consuming too little today. Decreasing the saving rate will increase consumption both today and in the long run.
Example:
Imagine an economy where adding one more machine (capital) increases output by 5%. If the population is growing at 2%, then the marginal product of capital (5%) is greater than the population growth rate (2%). This means the economy is saving too little, and it could increase long-run consumption per capita by saving more.
In Summary:
The golden rule of savings provides a benchmark for evaluating whether an economy is saving enough or too much. By adhering to this rule, a society can achieve the highest possible level of long-run consumption per capita and improve the overall well-being of its citizens. The condition r = n (real interest rate equals the rate of population growth) is met, where the real interest rate reflects the marginal product of capital in a competitive economy. Saving per capita also equals profit per capita under this rule.
