Price taking consumers’ receive a benefit from consuming electricity Q, according to the following function:

B(Q)= -Q^2+2500Q.

A single vertically integrated utility (VIU) has a cost function given by:

C(Q)= 0.4Q^2+50Q+306250.

The VIU has convinced the public utility commission (PUC) that it is a natural monopoly and thus it has been granted an exclusive franchise to produce electricity.

At the most recent rate-hearing, the PUC established a target price based on rate of return regulation. During the hearing, the VIU claimed that its rate-base was $4,875,000 and that the market rate of return it should be allowed should be 10%. It provided receipts to the PUC showing expenses of $262,500. Suppose the PUC has complete knowledge of market demand.

What is the competitive equilibrium in the absence of rate of return regulation?

What is the monopoly equilibrium in the absence of rate of return regulation?

What is the target price set as a result of the regulatory hearing? Use the quantity from part a to calculate.

What is the monopoly equilibrium under the rate of return regulation?

What is the change in consumer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

What is the change in producer surplus from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

What is the change in total welfare from the rate of return regulation relative to the competitive equilibrium? Relative to the no regulation monopoly equilibrium?

The government provided the monopoly franchise under the assumption that the VIU was a natural monopoly. Was their assessment correct? Did society gain or lose because of the government’s decision? How much did they gain or lose? Please provide detailed reasoning for all three answers.