Table 17-1
Imagine a small town in which only two residents,Lisa and Mark,own wells that produce safe drinking water.Each week Lisa and Mark 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 Lisa and Mark can pump as much water as they want without cost so that the marginal cost of water equals zero.The weekly town 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 Lisa and Mark from operating as a monopoly.What will be the price of water once Lisa and Mark reach a Nash equilibrium?

Question

Table 17-1
Imagine a small town in which only two residents,Lisa and Mark,own wells that produce safe drinking water.Each week Lisa and Mark 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 Lisa and Mark can pump as much water as they want without cost so that the marginal cost of water equals zero.The weekly town 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 Lisa and Mark from operating as a monopoly.What will be the price of water once Lisa and Mark reach a Nash equilibrium?

Quizplus · Accepted Answer

At the Nash equilibrium, Lisa and Mark will each choose a quantity of water that maximizes their profits given the other person’s choice. Looking at the table, we see that Lisa’s best response to Mark’s choice of 20 gallons is to choose 15 gallons, which earns her $600. Similarly, Mark’s best response to Lisa’s choice of 15 gallons is to choose 20 gallons, which earns him $800. This is a Nash equilibrium because neither player has an incentive to change their strategy given the other player’s strategy.

At this equilibrium, the total quantity of water sold is 35 gallons and the total revenue is $1400 (15 x $60 + 20 x $40). Dividing the total revenue by the total quantity gives us an equilibrium price of $40, which is choice (B).

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