Use the Jack and Jill duopoly example we did in class to answer the following question. As a reminder, the demand schedule for water is given below. Suppose that Jack and Jill are the duopolys Nash Equilibrium (40 gallons each; 80 gallons total produced) when a third person, John discovers a water source and joins the market as a third producer (he also has a zero marginal cost of production).

Quantity (gallons)	Price	Total Revenue (and Profit)
0	120	0
10	110	1,100
20	100	2,000
30	90	2,700
40	80	3,200
50	70	3,500
60	60	3,600
70	50	3,500
80	40	3,200
90	30	2,700
100	20	2,000
110	10	1,100
120	0	0

Jack and Jill propose that the three of them continue to produce a total of 80 gallons, splitting the market three ways. If John agrees to this, how much profit will he make?

After agreeing to the proposed deal, John is considering increasing his production by 10 gallons? If he does, and Jack and Jill stick to the agreement, how much profit will John make? What does this tell you about the proposed agreement?

What is the Nash equilibrium for this market with three producers? How does it compare to the Nash equilibrium with two producers? Show your work.