Imagine a small town in which only two residents, Abby and Brad, own wells that
ID: 1174403 • Letter: I
Question
Imagine a small town in which only two residents, Abby and Brad, own wells that produce safe drinking water. Each week Abby and Brad work together to decide how many gallons of water to pump. They bring water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Abby and Brad can pump as much water as they want without cost so that the marginal cost is zero. The weekly town demand schedule and total revenue schedule for water is shown in the table above.
(A) Suppose that Abby and Brad work together to operate as a profit-maximizing monopolist.
I) What price will they charge for water?
II) How many gallons of water will be produced and sold?
(B) If this market for water were perfectly competitive instead of monopolistic.
(I) What would be the price for water?
(II) How many gallons of water would be produced and sold?
(C) Suppose the town enacts new antitrust laws that prohibit Abby and Brad from
operating as a monopoly.
(I) What will be the price of water once Abby and Brad reach a Nash equilibrium?
(II) How much profit will Abby and Brad each earn once they reach a Nash equilibrium?
Explanation / Answer
A. (1) Suppose Abby and Brad work together as profit-maximising monopolist, then condition is MR=MC. Therefore, the price they charge for water = $6 per gallon. Because when they charge $5 per gallon ,then MR<MC.
(2) At thi price , they will produce total 6 gallons implies 3 gallons produced by each.
B (1) If this market were perfectly competitive instead of monopolistic. Then , the condition = P=MC. So, price for water = $0 per gallon.
(2) At this price , total 12 gallons would be produced and sold.
C (1) Suppose the town enacts new antitrust laws that prohibit Abby and Brad from operating as a monopoly. The price would fall to $4 because each would try to earn more profit by producing one more item i.e earlier the total quanitity is 6 gallons , now, they would produce 8 gallons (by producing one more by each).
(2). At this , total profit is $32 , this implies tthat Abby and Brad each earn $16 in profit.
Quantity (in gallons) Price ($) Total revenue (TR) Marginal revenue (MR) 0 12 0 - 1 11 11 11 2 10 20 9 3 9 27 7 4 8 32 5 5 7 35 3 6 6 36 1 7 5 35 -1 8 4 32 -3 9 3 27 -5 10 2 20 -7 11 1 11 -9 12 0 0 -11