Question

The graph below shows the demand for nectar in Gardenia. Price 0 40 80 120 160 200 240 280 320 360 400 Quantity per period Suppose that there are only two firms, Ace and Pace, producing nectar, and they decide to act as a cartel (monopoly) and share the market equally. a. What price and output will maximize their joint total revenue, and what amount is that? Price: $0 Output:O Total joint revenue: $ b. In the payoff matrix in table below. show in cell A the amount of total revenue each will receive if they stick to the agreement. Keep agreement 1 Ace Keep agreement Break agreement Cell A Cell B Ace: Ace: Pace: Pace: Cell D Ace: Pace Break agreement Ace: Pace: Pace: c. Suppose that Ace believes that Pace will honour the agreement by maintaining his present output. However, Ace decides to cheat and increase his output by one-third. What will be Ace's and Pace's total revenues? Show Ace's and Pace's results in cell B. d. Now, assume that the positions are reversed and that Pace decides to cheat while assuming that Ace will stick to the agreement. Show Ace's and Pace's resulting revenues in cell C. e. Finally, in cell D show the total revenue of Ace and Pace that would result if they both cheat.

Answer 1

A) joint Revenue is maximized when MR = 0

Price 0 40 80 120 160 200 240 280 320 360 400 Quantity per period

So Q = 180, P = 18

Joint Revenue = 180*18 = 3240

b) both stick ,

each gets = 3240/2 = 1620

each produce = Q/2 = 90

Pace / Ace	Keep	break
Keep	1620 1620	1800 1350
Break	1350 1800	1440 1440

C) ace output = 90+(1/3)*90 = 90+30

= 120

Total Q = 120+90 = 210

P = 15,

π ace , cheater = 15*120 = 1800

π pace = 15*90 = 1350

D) π pace = 1800

π ace = 1350

E) both cheat

Q = 120+120 = 240

P = 12

π = 12*120 = 1440