The Woebegone Water Company, a small water utility serving rural customers in Minnesota, is currently engaged in

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Question:

The Woebegone Water Company, a small water utility serving rural customers in Minnesota, is currently engaged in a rate case with the regulatory commission under whose jurisdiction it operates. At issue is the monthly rate that the company will charge for unmetered sewer and water service. The demand curve for monthly service is P = $40 – $0.01Q. This implies annual demand and marginal revenue curves of:

P = $480 – $0.12Q
MR = ∆TR/∆Q = $480 – $0.24Q

where P is service price in dollars and Q is the number of customers served. Total and mar- ginal costs per year (before investment return) are described by the following function:

TC = $70,000 + $80Q + $0.005Q2

MC = ∆TC/∆Q = $80 + $0.01Q

The company has assets of $2 million and the utility commission has authorized an 11.5% return on investment.

a) Calculate Woebegone’s profit-maximizing price (monthly and annually), output, and rate- of-return levels.

b) Woebegone has requested a monthly price of $22. Calculate Woebegone’s output and total return on investment if the request were to be granted. Why are these values different from those calculated in part A?

c) What monthly price should the commission grant to limit Woebegone to an 11.5% rate of return?