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FRE 460 Duel April 20, 2020 Some restaurants are unique and have no substitutes. Assume uniqueness is an experience attribute: once you have dined at a unique restaurant, you know exactly Whether it is unique or not. To keep the math clean, we assume "uniqueness cannot be determined by word of mouth and does not require verification by a third party. As mentioned, a unique restaurant has no substitutes. This means a unique restaurant doesn't have to worry about losing customers to competitors and can act like a monopolist. Assume the marginal private benefit to consumer i from consuming meals at restaurant ; is MPB, = 20 - if the restaurant is unique. If, however, restaurant is non-unique, consumer i receives exactly the same amount of additional use value from consuming a meal ati as she would get if she instead dined at any of its equally non-unique competitors. Assume the marginal cost of providing a meal at a non-unique restaurant is n = 7 as so the equilibrium price of unambiguously non-unique restaurants is $7. anume mc of unique restaurant is constant and equal to 115 a non-unique real is assum constant a comestor's and equal MPB from eating to d7 weal -me non-unique restaurant is Grey Late assignments are accepted upon prior agreement with the instructor, but may delay calculation/reporting of a student's course grade. 1. Show that pu, the price that maximizes the revenue a unique restaurant carns from one of its customers, is pli - 17,5 Calculate how many times a individual will dine at a unique restaurant that charges p if the consumer knows the restaurant is unique. Denote this as q". Also calculate the consumer and producer surplus associated with each consumer who becomes a customer at a unique restaurant. For all parts, show your work Proof (10 points): miB = mc 2 0-9/ 15 20-9-150 96 P= 70-3 00 - 17.00 mPB=mc20-9 = 15 # 20-g-15- 0 9 =20-15 (5 points) q = 0 0 0 0 = Corromer surplus is sum of mpo or each of I vint CG- (0-% -17.)+(20-% -110 + (2018-01-30-9-175) (30-56-110) (5 points) CS* = a +15+ 0.1 + 0 unt the Pu - Astol pridur supply of Wigut pelaput for Dumt w (5 points) PS" = 5 (176-15) 12.5 2. (10 points) Explain why/whether a non-unique restaurant would like to signal that is it "unique" if such signaling was inexpensive. (Hint: compare the firm's profit from a consumer who pays for her first and any subsequent) meal at the restaurant versus the restaurant's profits if it is upfront about its non-uniqueness and charges only $7 per meal.) FRE 460 Duel April 20, 2020 Some restaurants are unique and have no substitutes. Assume uniqueness is an experience attribute: once you have dined at a unique restaurant, you know exactly Whether it is unique or not. To keep the math clean, we assume "uniqueness cannot be determined by word of mouth and does not require verification by a third party. As mentioned, a unique restaurant has no substitutes. This means a unique restaurant doesn't have to worry about losing customers to competitors and can act like a monopolist. Assume the marginal private benefit to consumer i from consuming meals at restaurant ; is MPB, = 20 - if the restaurant is unique. If, however, restaurant is non-unique, consumer i receives exactly the same amount of additional use value from consuming a meal ati as she would get if she instead dined at any of its equally non-unique competitors. Assume the marginal cost of providing a meal at a non-unique restaurant is n = 7 as so the equilibrium price of unambiguously non-unique restaurants is $7. anume mc of unique restaurant is constant and equal to 115 a non-unique real is assum constant a comestor's and equal MPB from eating to d7 weal -me non-unique restaurant is Grey Late assignments are accepted upon prior agreement with the instructor, but may delay calculation/reporting of a student's course grade. 1. Show that pu, the price that maximizes the revenue a unique restaurant carns from one of its customers, is pli - 17,5 Calculate how many times a individual will dine at a unique restaurant that charges p if the consumer knows the restaurant is unique. Denote this as q". Also calculate the consumer and producer surplus associated with each consumer who becomes a customer at a unique restaurant. For all parts, show your work Proof (10 points): miB = mc 2 0-9/ 15 20-9-150 96 P= 70-3 00 - 17.00 mPB=mc20-9 = 15 # 20-g-15- 0 9 =20-15 (5 points) q = 0 0 0 0 = Corromer surplus is sum of mpo or each of I vint CG- (0-% -17.)+(20-% -110 + (2018-01-30-9-175) (30-56-110) (5 points) CS* = a +15+ 0.1 + 0 unt the Pu - Astol pridur supply of Wigut pelaput for Dumt w (5 points) PS" = 5 (176-15) 12.5 2. (10 points) Explain why/whether a non-unique restaurant would like to signal that is it "unique" if such signaling was inexpensive. (Hint: compare the firm's profit from a consumer who pays for her first and any subsequent) meal at the restaurant versus the restaurant's profits if it is upfront about its non-uniqueness and charges only $7 per meal.)