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7. Games in which timing matters Consider an economy in which there is initially one firm, HealthyBreakfast, in the market for breakfast cereal. A new firm, TastyCereal, is deciding whether to enter the market, which would then change the market to a duopoly HealthyBreakfast can choose to sell its cereal to grocery stores at either a high or a low price. As a monopolist, it can earn $6.50 million by selling at a high price or $3.50 million by selling at a low price. If TastyCereal enters the market and Healthy Breakfast sells at a high price, each firm makes $1.50 million; if TastyCereal enters the market and HealthyBreakfast sells at a low price, each firm has a loss of $2.50 million. Suppose that HealthyBreakfast can't set long-term contracts with the grocery stores that sell its cereal. The following diagram shows this game: first, Tasty Cereal decides whether to enter or not, and then HealthyBreakfast decides whether to sell at a high or low price. (?) -$2.50 Milion for HealthyBreakfa Low Price -$2.50 Million for TastyCereal Enter High Price $1.50 Million for HealthyBreakfa: $1.50 Million for TastyCereal Low Price $3.50 Million for HealthyBreakfa: Don't Enter 90 Million for TastyCereal High Price 98.50 Million for HealthyBreakfa: SO Million for TastyCereal TastyCereal decides HealthyBreakfast decides Suppose HealthyBreakfast issues a press release saying that if TastyCereal enters the market, it will sell at a low price. If TastyCereal decides to enter the market despite the threat, HealthyBreakfast would earn if it chose to set a low price, and it would earn if it chose to set a high price. Therefore, HealthyBreakfast's threat credible, and TastyCereal enter the market. Now suppose that HealthyBreakfast can sign long-term contracts with grocery stores at a set price before Tasty Cereal decides whether or not to enter. The following diagram shows this game:$6.50 million $1.50 million $3.50 million SO des to sign a cont e, TastyCereal would -$2.50 million if it chose to sta if Healthy Breakfast kfast would earn$3.50 million $1.50 million car the market, and it would contract at a low -$2.50 million enter the $6.50 million real would earn if it chose to enter the my Breakfast signed a contract at a high price, Tasty CerealSO $6.50 million thyBreakfast decide ct at a low price, $1.50 million out. Therefore, if :, and HealthyBreak $3.50 million -$2.50 million other hand, if Heal des to sign a cont t, and it would earn if it chose tocen. and HealthyBreak would hand, if Hea would not would earn inter$6.50 million Tasty Cer -$2.50 million if it chose to enter t f Healthy a contract at a low price, Tasty Cereal $1.50 million $0 Cereal would earn $3.50 million stay out lthyBreakfast signed a contract at a hic uld earnce, Tasty Cereal would earn if it chose to ent if HealthyBreakfast low 3 Contract at a high price, TastyCe high ll sign a contract at a price.-$2.50 Million for HealthyBreakfa Enter $2.50 Million for TastyCereal Low Price Don't Enter $3.50 Million for HealthyBreakfa: $0 Million for TastyCereal Enter $1.50 Million for HealthyBreakfa: High Price $1.50 Million for TastyCereal Don't Enter $0.50 Million for HealthyBreakfa: $0 Million for TastyCereal Healthy Breakfast decides Tasty Cereal decides If HealthyBreakfast decides to sign a contract at a low price, TastyCereal would earn if it chose to enter the market, and it would earn if it chose to stay out. Therefore, if HealthyBreakfast signed a contract at a low price, TastyCereal enter the market, and HealthyBreakfast would earn On the other hand, if HealthyBreakfast decides to sign a contract at a high price, Tasty Cereal would earn if it chose to enter the market, and it would earn if it chose to stay out. Therefore, if HealthyBreakfast signed a contract at a high price, TastyCereal 7 enter the market, and HealthyBreakfast would earn Anticipating Tasty Cereal's response to its pricing contract, HealthyBreakfast will sign a contract at a 7 price.Id earn if it chose to set a low price, and it credible, and Tasty Cereal -$2.50 million $0 sty Cereal decides whether or not to enter $1.50 million $6.50 million $3.50 millionwould earn if it chose to set a low price, and it hyBreakfast's threat credible, and TastyCereal is not stores at 0 set price asty Cereal decides whether or not to enterIf TestyCereal decides to enter the market despite th would earn if it chose to set a h $3.50 million Now suppos 50 eakfast can sign long-t The followir this game: $1.50 million $6.50 million -$2.50 millionWIOT the mar will not that will ng diw price, TastyCereal would earn if it chose to en refore, if Healthy Breakfast signe low price, TastyCere $6.50 million $1.50 million In a contract at a high price, Tes arn those to stay out. Therefore, if H $0 igned a contract at kfast would earn -$2.50 million $3.50 million tract, HealthyBreakfast will sign price.HealthyBreakfast decides Tasty Cereal $0 -$2.50 million $3.50 million $6.50 million $1.50 million If He ecides to sign a contract at sam if it chose to stay out, market, and HealthyBreakfast would earnif it chose to enter the market, and it would it a low price, Tasty Cereal enter the would not eam would to enter the ist signed a contract at a y Cereal