Marginal product of capital

The marginal product of capital (MP_K) is the additional output resulting, ceteris paribus ^{("all things being equal")}, from the use of an additional unit of physical capital. It equals the reciprocal of the incremental capital-output ratio. Mathematically, it is the partial derivative of the production function with respect to capital. If production output $Q=f(K,L)$ , then

MP_{K}={\frac {{\text{change in }}Q}{{\text{change in }}K}}={\frac {\partial f(K,L)}{\partial K}}

One of the key assumptions in economics is diminishing returns, that is the marginal product of capital is positive but decreasing in the level of capital stock, or mathematically

{\frac {\partial }{\partial K}}MP_{K}={\frac {\partial ^{2}f(K,L)}{\partial K^{2}}}<0

In a perfectly competitive market, the marginal product of capital is equal to the rental rate of capital.

References

Nicholson, Walter (1978). Microeconomic Theory: Basic Principles and Extensions (2nd ed.). Hinsdale: Dryden Press. pp. 182–188. ISBN 0-03-020831-9.
Robinson, R. Clark. "Marginal product of labor and capital" (PDF). Northwestern University Class Handout. Archived from the original (PDF) on September 9, 2006.

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Marginal product of capital

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References