A chocolate manufacturer can produce normal or gourmet chocolate bars at the same cost (for simplicity, assume this cost is 0). There are two types of chocolate consumers in the market, light consumers of chocolate (half the population ) and heavy consumers of chocolate (half the population). Light consumers are willing to pay up to $2 for a normal bar, and up to $3 for a gourmet bar. Heavy consumers are willing to pay up to $2.50 for a normal bar, and $7 for a gourmet bar. Assume the chocolate manufacturer can price discriminate. Also assume that consumer payoffs equal willingness to pay minus price paid, that a consumer buys at most one chocolate bar, and that a consumer who does not buy any chocolate gets a payoff of 0. (a ) If the manufacturer sold only normal bars, what price of a normal bar p,, would he choose? If the manufacturer sold only gourmet bars, what price of a gourmet bar p, would he choose? (b) Write down the constraints that must hold for a separating menu under asym- metric information. (c) Find the prices charged under the optimal separating menu under asymmetric information.