A numerical example can be used to show the changes of the A-J input bias and social welfare when a rate-of-return regulated monopolist moves from linear price to perfect price discrimination.
Significantly, unlike the case with no regulation, where perfect price discrimation (without considered equity) always outperforms profit-maximized linear price in terms of given higher social welfare (the sum of the firm's profits and the consumer's surplus), the rate-of-return regulated perfect price discrimination (at least in this example) always produces smaller social welfare because of deadweight loss.
The second example assumes that a rate-of-return regulated monopolist is allowed to move from linear price to uniform two-part tariffs, i.e., the customers must pay a uniform fixed entrance fee T for the right to buy a product at a unit price P.
This paper showed that when a rate-of-return regulated monopolist moves from linear to nonlinear prices, the A-J input bias will decrease (increase) if the marginal revenue product of capital increases (decreases).
also use numerical examples to show the changes of social welfare under rate-of-return regulated linear price.