Question

Imagine a small town in which only two residents, Abby and Brad, own wells that produce...

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 the 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 below:

Quantity
(in gallons)

Price

Total Revenue
(and Total Profit)

0

$12

$0

1

$11

$11

2

$10

$20

3

$9

$27

4

$8

$32

5

$7

$35

6

$6

$36

7

$5

$35

8

$4

$32

9

$3

$27

10

$2

$20

11

$1

$11

12

$0

$0

  1. Where is the profit highest?
  1. Given this, if Abby and Brad decide to collude (and cooperate), how much would each person pump? What would be their individual profit?
  1. What if Abby decides to renege and pump one more unit of water? What is the total production of water? What is Abby’s profit compared to her profit where she colludes? Has Brad’s profit changed?

  1. Suppose Brad also reneges. Now they both reneges. What is the total production of water? What is Abby’s profit now? What is Brad’s profit?

  1. Why does each duopoly earn a smaller profit at the Nash Equilibrium than if they cooperate?
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Homework Answers

Answer #1

a) The profit highest at the quantity of 6 gallon ans charges $6 per gallon.

b) If Abby and Brad decide to collude, each will pump 3 gallons of water (i.e., 6 / 2). The individual profit is $18 (i.e., $36 / 2).

c) If Abby decides to renege and pump one more unit of water, the total production will be 7 gallons of water (i.e., 4 + 3). Now the price charged is $5.

Abby’s profit compared to her profit where she colludes = $5 * 4 = $20

Brad’s profit = $5 * 3 = $15

d) When Brad reneges, the total production = 4 + 4 = 8 gallons of water. Now the price charged is $4.

Abby’s profit = $4 * 4 = $16

Brad’s profit = $4 * 4 = $16

e) If both the firm they cooperate, thery will act as a monopoly and charge a higher price and earm more profit than the Nash Equilibrium where both firms compete.

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