AUTHOR'S NOTE - Believe it or not, the following problem is only a slightly exaggerated version the situation, that until very recently, we saw depicted on the nightly news here in San Antonio. I thought your students might find the scenario amusing. It is a costless monopoly problem combined with a more or less standard monopolist becomes pure competitor situation and is a combination of material in both chapters eight and nine. Oh yes, they are probably too long to be put on an exam but might make a good take-home assignment.) I first write this note three editions ago and assumed that it would have been gone two editions ago - as of today June 3, 2000, the owner of the catfish farm was most recently in court two weeks ago and we are still fighting this out - and its not over yet.)
-In an area of South Texas lives the Elongated and Very Ugly Orange and Purple Spotted Salamander Salamanderis Elongatis Uglius Maximus). In addition to being ugly, it smells bad, and eats things that other animals need to survive. Because of the possibility of danger to its habitat, the water supply for the ninth largest city in the United States and the largest city in the world supplied entirely from underground water, San Antonio, has been restricted. However, because of a 14th century law about water rights, you, the owner of a catfish farm, have unrestricted use of water from the same place the city gets its water, namely the Edwards Aquifer. You and your catfish are currently using approximately 34,560,000 gallons per day; an amount equal to about 1/3 of the total water used by the rest of the 1,000,000 or so people and five or six catfish who live in San Antonio. Beyond your existing investment in equipment, this water cost you nothing. It just flows out of your two man-made artisan wells. Yes, your MC_w = 0. After your catfish are done bathing in the water, you have no use for it and are currently letting it flow into a nearby river. You have discovered that, even though you didn't pay for the water to begin with, the city of San Antonio will buy it and pay all the costs of pumping it to gathering lakes on the North side of town where it can drain back into the aquifer. That way, not only can the city use the water to keep the aquifer level high enough so that the Elongated and Very Ugly Orange and Purple Spotted Salamander's habitat will not be endangered, but, courtesy of the taxpayers of San Antonio, you get free use of the water again. Other people and businesses have also approached you about purchasing your slightly used water. Because the no-growth Neanderthals in the city have prevented the development of an alternate surface water supply, you believe that you have a costless monopoly. Given your estimate of the daily demand for water :
Q_w = 33 - .5P_w
where Q_w = acre feet of water.
a. What price would yield you the most revenue?
b. In the spring of 1997, after your operation has begun, the chairman of the Texas Water Commission decides that, because the aquifer under the city of San Antonio has fish in it blind fish I might add), the aquifer is actually a river, and therefore subject to the direct control of the state of Texas. As a result of this decision, the state of Texas takes over control of San Antonio's only source of water and begins charging you $8.00 per acre foot for your water. If demand remains as above, at what price and quantity will your slightly used water business operate if it is to maximize profit.
c. After this occurs, the San Antonio city council miraculously discovers that, since 1965, the Lower Woman Hollerin Creek Water Authority LWHCWA) has been trying to sell its surplus water to the city at very reasonable rates. This surplus water is currently being used to flood recreational areas so that they can not be used by the public, and to augment the flow of a local river that is a favorite of tubers and rafters. The LWHCWA will also sell its water to the other entities that have approached you about purchasing your water. As you qualify as a small start up business in a economically depressed area, a local CDBG federal government's Community Development Block Grant program) funded marketing consulting firm does a study of the situation and discovers that, for all intents and purposes, you and the LWHCWA operate in a purely competitive market structure. Assuming that demand and your current cost structure both remain the same, what will be your new price, output and profit.

You Believe That You Have a Costless Monopoly

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