Table 17-1
Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without cost so that the marginal cost of water equals zero. The town's weekly demand schedule and total revenue schedule for water is shown in the table below:
-Refer to Table 17-1. Suppose the town enacts new antitrust laws that prohibit Rochelle and Alec from operating as a monopoly. How many gallons of water will be produced and sold once Rochelle and Alec reach a Nash equilibrium?
A)600
B)700
C)800
D)900

Question

Table 17-1
Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without cost so that the marginal cost of water equals zero. The town's weekly demand schedule and total revenue schedule for water is shown in the table below: 
-Refer to Table 17-1. Suppose the town enacts new antitrust laws that prohibit Rochelle and Alec from operating as a monopoly. How many gallons of water will be produced and sold once Rochelle and Alec reach a Nash equilibrium?
A)600 
B)700 
C)800 
D)900

Quizplus · Accepted Answer

In a Nash equilibrium, each player is choosing their best strategy given the strategy of the other player. 
Looking at the table, if Rochelle produces 600 gallons, Alec would want to produce 200 gallons to maximize his profit. Rochelle's profit would be (600 x 5) = 3000, and Alec's profit would be (200 x 9) = 1800. 
However, Rochelle can also choose to produce more than 600 gallons, which means Alec must also produce more than 200 gallons to maximize his profit. Similarly, if Alec produces more than 200 gallons, Rochelle would also want to produce more than 600 gallons to maximize her profit. This creates a range of possible Nash equilibria. 
To find the Nash equilibrium, we need to find the point where neither player has an incentive to deviate from their strategy. One way is to plot the best response functions for each player and find the intersection point. In this case, that intersection point is at 800 gallons, where Rochelle and Alec each produce 400 gallons. At this point, Rochelle's profit is (400 x 4) = 1600, and Alec's profit is (400 x 4) = 1600. 
Therefore, the answer is C) 800 gallons.

Table 17-1 Imagine a Small Town in Which Only Two Residents, Rochelle