<P> The marginal product of capital (MP) is the additional output resulting, ceteris paribus, 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) (\ displaystyle Q = f (K, L)), then </P> <Dl> <Dd> M P K = change in Q change in K = ∂ f (K, L) ∂ K (\ displaystyle MP_ (K) = (\ frac ((\ text (change in)) Q) ((\ text (change in)) K)) = (\ frac (\ partial f (K, L)) (\ partial K))) </Dd> </Dl> <Dd> M P K = change in Q change in K = ∂ f (K, L) ∂ K (\ displaystyle MP_ (K) = (\ frac ((\ text (change in)) Q) ((\ text (change in)) K)) = (\ frac (\ partial f (K, L)) (\ partial K))) </Dd> <P> 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 </P>

Marginal product of capital vs marginal productivity of capital