Question

1. The demand curve for the Magic 8-Ball toy is P = 15 – 0.5Q. Frances currently has a patent on the concept of predictive billiards accessories, and is thus the only person able to sell Magic 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 lower production costs because of his mob connections, so C(QS) = QS. However, Frances is able to produce the latest batch of Magic 8-Balls before Simon can make his, so she sets her quantity first (this is now Stackelberg competition). What quantity (QF) will she produce since she is going first? What quantity (QS) will Simon produce in response? Also calculate the market price and each firm’s profits. You don’t have to do this problem in alphabetical order: you learned how to do Cournot in part (d) first.  

c. Someone who barely paid attention in their Business Econ class suggests that Frances’s goal should be to use her market power to drive Simon out of business. If Simon is “out of business,” that means QS = 0. Use your reaction function to determine the quantity (QF) Frances would have to produce so that Simon chooses QS = 0. Calculate market price and Frances’s profit. Compare her profit now that she has kept Simon out of the industry to her profit in part (b). Should her goal be to put Simon out of business?  

d. What if Frances didn’t get to “go first” and she and Simon were 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 under Cournot competition.  

e. Frances notices that her profit now that she has competition is less than half of the profit when she was a monopoly (part (a)). She “happens to run into” Simon at an alligator farm and suggests that they would make more profit by colluding. She proposes that instead of competing against each other, they each produce half of the monopoly quantity (she suggests that each firm produce half of the the QF you found in part (a).) If Frances were producing this new quantity, use Simon’s reaction function to find the QS Simon will produce. Calculate the market price and Simon’s new profit and compare it to his profits in part (c) and (d).

f. What if it were Bertrand competition instead of Cournot/Stackelberg? Calculate the equilibrium price Simon would charge for Magic 8-Balls if it were Bertrand competition. Estimate his quantity produced (QS) and his profit. Use the same costs as before. Note: I said “estimate” instead of “calculate” for quantity. You should still do math, but you should also use your intuition: there is a very reasonable assumption you can use to make the math a little simpler.

g. A new producer (Erin) enters. Her costs are the same as Simon’s: C(QE) = QE. What is the new market price if these 3 producers are engaged in Bertrand competition? Tell me the profit for each of the 3 firms (Frances, Simon, and Erin.)

Answer 1