Question

To reduce reliance on their local water company, the city of St. Augustine has decided to build their own municipal water supply. They must now decide what price to charge consumers. After some careful research, you estimate the following demand curve and marginal revenue curve for water per month:

P = 76 – 3Q

MR = 76 – 6Q

where Q represents the quantity of water used per month in 1,000 gallons. The marginal costs of water purification and delivery are a flat $4 per 1,000 gallons. The fixed costs of running the water treatment plant come to $200 per month.

a) Because the municipal power plant is the only source of water for local residents, the city can act like a monopolist provider of water. Councilman Alexander argues that acting as a monopolist and maximizing profits from the power plant will bring in needed revenue to the city. Find the amount of water purchased per month, along with the price per month, if the city maximizes profits as a monopolist.

b) How much profit does the city make if it acts as a monopoly? (Hint: Profit = TR – TC = TR – TVC – TFC)

c) Draw a graph using the information from part (a) and show the deadweight loss from this pricing strategy. You do not need to calculate the values for these areas, but simply show where they are represented on the graph.

d) Councilwoman Eliza believes that the city is providing a vital public service, and so should provide water without any deadweight loss. To completely eliminate the deadweight loss, what should the price of water be? How much water will citizens purchase at that price? Will the city make money, break even, or lose money at that price? Explain.

Answer 1

For a monopolist, Quantity is where MC = MR.

76 - 6Q = 4 or Q = 12

He will equate this quantity with demand curve in order to calculate price

P = 76 - 3Q or P = 76 - 3*12 So, P = 40

So, quantity will be 12,000 gallons price will be $40

b) Profit = TR - FC - VC

TR = price * quantity = 40 * 12,000 = 480,000

So, profit = 480,000 - 200 - 48,000 (VC = MC * quantity = 4*12 = 48)

Therefore, profit = $431,800

c) Graph:

  

The blue triangle is the deadweight loss.

d) If they were to completely eliminate the deadweight loss, quantity would be: 24,000 gallons.

Calculation:

76 - 3Q = 4 or Q = 72/ 3 = 24

price would be P = 76 - 3Q = 76 - 3*24 = 4

Quantity = 24,000 gallons. Price would be $4.

Profit = TR - FC - VC

= (4*24,000) - 200 - (4*24,000)

= 96,000 - 96,200 = -200

They would incur a loss of $200 per month. They would recover cost of production (TVC) and incur a loss of $200.