Question

Imagine a small town in which only two residents, Celia and Venya, own wells that produce safe drinking water. Each week Celia and Venya 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 Celia and Venya 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 following table Quantity Price Total Revenue and Total Profit (Gallons) (Dollars per gallon) (Dollars) 0 36 0 40 33 80 30 1,320 2,400 3,240 120 27 160 24 3.840 4,200 200 21 240 18 4.320 15 280 320 4,200 3,840 12 360 9 3,240 400 6 2,400 440 3 1,320 0 480 0 Refer to Table 17-1. Suppose the town enacts new antitrust laws that prohibit Celia and Venya from operating as a monopoly. How many gallons of water will be produced and sold once Celia and Venya reach a Nash equilibrium? 280 360 320 240

Answer 1

The demand function has a maximum price of 36 dollars and slope of 3/40. Therefore the demand function is P = 36 - 3Q/40. Marginal cost is zero

The Nash equilibrium in this case will generate Cournot outcome where each firm produces q = (maximum price minus marginal cost)/(3*slope)

= (36 - 0)/(3*3/40)

= 160

Therefore Total production will be 160 x 2 = 320 gallons

Select 320.