Question

1) Table 17-30 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 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

Discuss the difference between the monopoly outcome and the Nash equilibrium.

2)

Table 17-32
Suppose that Angelina and Brad own the only two professional photography stores in town. Each must choose between a low price and a high price for senior photo packages. The annual economic profit from each strategy is indicated in the table below:

Angelina
Low price High price

Brad	Low price	Angelina’s profit = $20,000 Brad’s profit = $20,000	Angelina’s profit = $4,000 Brad’s profit = $23,000
	High price	Angelina’s profit = $25,000 Brad’s profit = $5,000	Angelina’s profit = $22,000 Brad’s profit = $22,000

Refer to Table 17-32. Is there a Nash equilibrium? If so, describe it.

Answer 1

1)

Monopoly Case

Abby and Brad has a monopoly in the production of water it will be better for them to produce only the amount of water that maximises their total profits.

From Table, we can see that The maximum profit level is at $6 price where the quantity demanded is 6 gallons. The total profits at this level are the highest at $36. each of them will get $18 each.

The monopoly outcome occurs at the highest total profit level of Q=6, P=$6, and profit=$36.

Nash Equilibrium Case

If each duopolist pursues his/her self-interests, each will produce Q=4 for a total Q=8, P=$4, and each duopolist’s profit will be half of $32 or $16. Because neither duopolist can do better by producing an output level different from 4, they reach a Nash equilibrium. This problem illustrates the tension between cooperation and self-interest

Difference between monopoly outcome and Nash equilibrium -

Particulars	Monopoly	Nash equilibrium
No of sellers	1	2
Market equilibrium Conditions	Marginal Revenue = Marginal Cost            Or                                                              Total Profit is Maximum	Under Nash equilibrium, 2 sellers have a decision to make from 2 given choices. Each seller will decide the level of outcome at which he can not increase his total profit any further

2)

Particulars		Angelina
		Low Price	High Price
Brad	Low Price	Angelina’s profit = $20,000 Brad’s profit = $20,000	Angelina’s profit = $4,000 Brad’s profit = $23,000
	High Price	Angelina’s profit = $25,000 Brad’s profit = $5,000	Angelina’s profit = $22,000 Brad’s profit = $22,000

From part (1) We know that the equilibrium will be at the level when none of them is able to increase the profits any further.

yes, equilibrium does exist, regardless of Brad’s strategy, Angelina should choose the low pricing strategy. If Brad chooses the low pricing strategy, his profit will be $20,000 > $5,000 higher from the high price strategy. hence equilibrium will occur where both Brad and Angelina choose the low price strategy.

In case they decide to come together to form a monopoly their combined profits will be higher at $44000 >$40000 in case of Nash equilibrium by choosing high pricing strategy.