An important equilibrium condition that is not of the supply-must-equal-demand form is the equilibrium condition for balanced growth, which plays a big part in the study of long-run economic growth. This equilibrium condition relates the following economic variables and parameters:
- The net share of total net income in the economy that is saved and invested, written s.
- The proportional rate of growth of the labor force, written n.
- The proportional rate of growth of the efficiency of the labor force, written g.
- The economy's stock of produced means of production—of capital, written K.
- The economy's level of production and output, written Y.
- The ratio of the capital stock to the rate at which output is produced, written κ.
- The particular value of that capital-output ratio κ* at which it is neither rising nor falling over time.
Growth will be balanced if, and only if, the ratio of the economy’s stock of capital K to its level of output Y is constant. This equilibrium condition holds if, and only if, the capital-to-output ratio K/Y is equal to:
The capital-output ratio must be equal to the economy’s net savings rate s divided by the sum of the population growth rate n and the labor efficiency growth rate g.
If the capital-output ratio is lower than this value, it will grow because net investment will be high relative to the capital stock. If the capital-output ratio is higher than this value, it will shrink because net investment will be low relative to the capital stock. In either case, the capital-output ratio will converge to its balanced-growth equilibrium level over time.
Thus this balanced-growth capital-output-ratio equation satisfies the two requirements for being an equilibrium condition. If the economy does not satisfy the equilibrium condition, it will be heading toward it. If the economy satisfies the equilibrium condition, it will remain in the same place.
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