The derivatives of this functional are:Taken together, this implies that:The ratio of the marginal product of capital and the marginal product of labor is:Since this new cost of capital is perceived to be less than the market cost of capital, the firm will tend to overinvest in capital.
The derivatives of this functional describe a relationship between capital and labor, indicating that their marginal products have a constant ratio. This ratio is also equivalent to the inverse of the ratio of the firm's new capital expenses to its market capital expenses. As a result, if the company perceives its new capital expenses as being lower than those on the market, it will likely overinvest in capital.