9. Equilibrium with asymmetric information Consider an economy in which there is initially one firm, Healthy Breakfast, in the market for breakfast cereal. A new firm, Tasty Cereal, 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 Tasty Cereal, and Tasty Cereal will earn negative profit from entry. If Healthy Breakfast has high costs, however, then Tasty Cereal will be able to compete, earning profits of $9 million and reducing Healthy Breakfast's profits to $3 million. The payoffs (in millions) from the four possible outcomes are given in the following diagram (Healthy Breakfast's Payoff, Tasty Cereal's Payoff). The diagram shows this game: First, luck and past investments (or "nature") determine whether Healthy Breakfast has high or low costs; then, Tasty Cereal decides whether to enter the market (without being able to observe Healthy Breakfast's costs). Nature Healthy Breakfast with High Costs Healthy Breakfast with Low Costs Tasty Cereal A A Tasty Cereal No Entry Entry No Entry Entry $12. $0 $3, $9 $18, $0 $9,-$3 If Tasty Cereal knows that the probability of Healthy Breakfast 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 Tasty Cereal responds to the signal and does not enter