Suppose that a regulated firm wishes to maximize its profit:
where is the revenue function, is the firm's capital stock, is the firm's labor stock, is the wage rate, and is the cost of capital. The firm's profit is constrained such that:
where is the allowable rate of return. Assume that . We may then form a functional to find the firm's optimal action:
where is the Lagrange multiplier (also known as the shadow price). 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.[4]