Question 9 [3 points] A chocolate manufacturer can produce normal or gourmet chocolate bars at a per-unit coat of 'l for normal bars and 3 for gourmet bars. There are two types of chocolate consumers in the market, light consumers of chocolate is share p E {I}, l} of the population] and heavy consumers of chocolatei: l p of the population). Light consumers are willing to pay up to $4 for a normal bar, and up to $5 for a gourmet bar. Heavy consumers are willing to pay up to $5 for a normal bar, and $11 for a gourmet bar. Assume the chocolate manufacturer maximises expected per-customer prots. The manufacturer knows the valuations of normal and gourmet bars for both light consumers and heavy consumers. She also knows the value of p but she does not know which consumer is of what type. Also assume that a consumer's net utility equals 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 D. Furthermore, we assume that (i) if a consumer is indifferent between buying and not buying then she buys, and {ii} if she is indifferent between buying a gourmet bar and buying a normal bar then she buys the gourmet bar. Wherever rounding is needed, please round to 3 decimal points. For parts {a} and {b}, suppose that the chocolate manufacturer decides to choose a separating menu. {a} (ELE points] Under a separating menu, what price would he set for a normal bar? (b) {1 point] Under a separating menu, what price would he set for a gourmet bar? {c} {1.5 point} If the proportion of light chocolate consumers is less than , the chocolate manufacturer would rather choose an exclusion menu {where only heavy consumers buy] than a separating menu. Fill in the blank