1. The demand curve for the Magic 8-Ball toy is P = 15 – 0.5Q.Frances currently has a patent on the concept of predictivebilliards accessories, and is thus the only person able to sellMagic 8-Balls. For now, Frances is a monopoly. Her costs are C(QF)= 2QF a. Calculate the (monopoly) market price, quantity produced,and Frances’s profit.  
b. Frances’s patent is about to expire, and another producer(Simon) is planning on entering the market. Simon has lowerproduction costs because of his mob connections, so C(QS) = QS.However, Frances is able to produce the latest batch of Magic8-Balls before Simon can make his, so she sets her quantity first(this is now Stackelberg competition). What quantity (QF) will sheproduce since she is going first? What quantity (QS) will Simonproduce in response? Also calculate the market price and eachfirm’s profits. You don’t have to do this problem in alphabeticalorder: you learned how to do Cournot in part (d) first.  
c. Someone who barely paid attention in their Business Econclass suggests that Frances’s goal should be to use her marketpower to drive Simon out of business. If Simon is “out ofbusiness,†that means QS = 0. Use your reaction function todetermine the quantity (QF) Frances would have to produce so thatSimon chooses QS = 0. Calculate market price and Frances’s profit.Compare her profit now that she has kept Simon out of the industryto her profit in part (b). Should her goal be to put Simon out ofbusiness?  
d. What if Frances didn’t get to “go first†and she and Simonwere in Cournot competition? Remember: demand for 8-Balls is P = 15– 0.5Q, Frances has costs C(QF) = 2QF , and Simon has costs C(QS) =QS. Calculate QF, QS, market price, and each firm’s profit underCournot competition.  
e. Frances notices that her profit now that she has competitionis less than half of the profit when she was a monopoly (part (a)).She “happens to run into†Simon at an alligator farm and suggeststhat they would make more profit by colluding. She proposes thatinstead of competing against each other, they each produce half ofthe monopoly quantity (she suggests that each firm produce half ofthe the QF you found in part (a).) If Frances were producing thisnew quantity, use Simon’s reaction function to find the QS Simonwill produce. Calculate the market price and Simon’s new profit andcompare it to his profits in part (c) and (d).
f. What if it were Bertrand competition instead ofCournot/Stackelberg? Calculate the equilibrium price Simon wouldcharge for Magic 8-Balls if it were Bertrand competition. Estimatehis quantity produced (QS) and his profit. Use the same costs asbefore. Note: I said “estimate†instead of “calculate†forquantity. You should still do math, but you should also use yourintuition: there is a very reasonable assumption you can use tomake the math a little simpler.
g. A new producer (Erin) enters. Her costs are the same asSimon’s: C(QE) = QE. What is the new market price if these 3producers are engaged in Bertrand competition? Tell me the profitfor each of the 3 firms (Frances, Simon, and Erin.)
