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Instructions: Complete all questions. Show working for all parts. Answers do not have to be integers: assume all variables (goods, prices) are infinitely divisible. Submit answers in PDF format. 1. 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