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.How many gallons of water will be produced and sold 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.How many gallons of water will be produced and sold once Lisa and Mark reach a Nash equilibrium?

Quizplus · Accepted Answer

At a Nash equilibrium, Lisa and Mark will produce where their individual marginal revenue equals their marginal cost (which is zero in this case). From the table, we can see that Lisa's marginal revenue is $8 - $0.01L and Mark's marginal revenue is $6 - $0.02M. Equating each of their marginal revenue to zero gives us L = 800 and M = 500. So, Lisa and Mark will produce a total of 800 + 500 = 1,300 gallons of water, and since Lisa produces 800 gallons, Mark will produce 500 gallons.

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