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To be more specific, the steady state level of capital solves the following equation: k = k(1 − δ) + sAf(k). At the steady state, the amount of capital lost by depreciation is exactly offset by saving.
The Solow growth model focuses on long-run economic growth. A key component of economic growth is saving and investment. An increase in saving and investment raises the capital stock and thus raises the full-employment national income and product.
Steady state represents the equilibrium of the economy in the long term. Equilibrium occurs exactly when the investment equals the break-even investment. As a result, capital stock does not change.
The key assumption of the Solow–Swan growth model is that capital is subject to diminishing returns in a closed economy. Given a fixed stock of labor, the impact on output of the last unit of capital accumulated will always be less than the one before.
The overall change in the capital stock is equal to new investment minus depreciation: change in capital stock = new investment − depreciation rate × capital stock.
For the change in the capital stock per worker, as opposed to the rate of change, multiply each side by k, or K/L, as convenient: ∆k = (I/K - δK/K)K/L – nk = I/L - δK/L – nk, this simplifies to: ∆k = i – (δ + n)k.
Capital Accumulation g K = i K / Y − δ . The growth rate of the capital stock depends positively on the investment rate and negatively on the depreciation rate. It also depends negatively on the current capital-output ratio.