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9. Equilibrium with asymmetric information 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's costs of production are either high or low; if HealthyBreakfast has low costs, then it will be able to charge a lower price than TastyCereal, and TastyCereal will earn negative profit from entry. If HealthyBreakfast has high costs, however, then TastyCereal will be able to compete, earning profits of $6 million and reducing HealthyBreakfast's profits to $2 million. The payoffs (in millions) from the four possible outcomes are given in the following diagram (HealthyBreakfast's Payoff, TastyCereal's Payoff). The diagram shows this game: First, luck and past investments (or "nature") determine whether HealthyBreakfast has high or low costs; then. Tasty Cereal decides whether to enter the market (without being able to observe HealthyBreakfast's costs). (?) Nature O HealthyBreakfast with High Costs Healthy Breakfast with Low Costs TastyCereal A TastyCereal No Entry Entry No Entry Entry 50. -$2 If TastyCereal knows that the probability of HealthyBreakfast having high costs is 0.5, then the expected profit from entering is |$ million. Suppose HealthyBreakfast has high costs but wants to signal to Tasty Cereal that it has low costs. To do so, it lowers its prices, thereby reducing its profits. This strategy is advantageous to HealthyBreakfast only as long as it reduces its profits by less than * million and TastyCereal responds to the signal and does not enter.is 0.5, then the expected pr $2 entering is 56 at it has low costs. To do 50, its prices, thereby r duces its profits by less than million and Tasty Cereal