Quantitative Question 2 of 3:

A firm is regulated by the government as a natural monopoly.

The firm's fixed costs are F.

The firm's marginal costs are 10.

The firm sells to two customers.

Customer A has an inverse demand curve given by P = 50 - Q.

Customer B has an inverse demand curve given by P = 90 - Q.

(a) (5 points) Suppose the lowest linear price the government can set while providing the firm at least zero economic profit is P = 20.What does this imply about firm's fixed costs, F?

(b) (4 points) The regulator is considering a switch to a welfare maximizing two-part tariff that splits the burden of the fixed costs equally between the two customers.What is the optimal two part tariff?

(c) (4 points) How much would welfare increase if the government used the optimal two-part tariff relative to the linear price in part (a)?

(d) (5 points) Your friend states "Since both customers are able to purchase at a lower per-unit price under the optimal two-part tariff, they both prefer the two-part tariff to the linear price from part (a)."Briefly explain whether your friend's statement is correct or incorrect.

(e) (4 points) Based on your answers to questions (a) - (d) above, is there a reason why we might expect the government to prefer the linear prices in part (a), despite the fact that the two-part tariff in (b) leads to higher welfare?