Practice Problems on Price Discrimination MBA814 Professor Conlin

Transcription

1 Practice Problems on Price Discrimination MBA814 Professor Conlin 1. (7 points) Matt Ritter is responsible for the 2 nd Annual MBA Mustache Competition Benefitting CureSearch. As part of this fund raiser, faculty and MBA students can nominate other faculty and students. This nomination requires the faculty or student to grow a mustache unless the nominated individual chooses to buyout. A buyout requires the nominated faculty and student to pay a certain amount to relieve him/her of the obligation of growing a mustache. Matt set the buyout price at $3 this year. Assume that Matt had paid attention when he took MBA814 last year and decided to use 3 rd degree price discrimination for these buyouts basically, set the price of the buyout for faculty different than the price for an MBA students. Also, assume Matt knew that the demand for MBA student buyouts (D S ) and the demand for faculty buyouts (D F ) are as depicted below. MBA Student Demand Faculty Demand DS DF a) If Matt wanted to maximize the amount raised for CureSearch, what price should he set for a faculty buyout (p F ) and what price should he set for a student buyout (p s )? At these prices, how much would be raised for CureSearch? Show calculations. b) Based on the prices in part a), what is the own price elasticity of demand for the faculty and what is the own price elasticity of demand for the students? Show calculations. c) Consider the own price elasticities in part b). Are they what you expected? Explain.

2 4. (6 points) The Demmer Center, located at Michigan State University, contains an indoor archery range which is deciding on a 2-part pricing scheme. This 2-part pricing scheme involves a monthly fixed fee as well as a price to use the bow and arrow during each visit (i.e., variable fee paid on each visit). The Demmer Center s costs include a constant marginal cost of $1 (for each rental) and monthly fixed costs of $1,. The market demand for the Demmer Center archery rentals is based on demand from 5 Type A individuals and 3 Type B individuals. The monthly demand curve for each Type A individual (D A ) is depicted below, along with the monthly demand curve for each Type B individual (D B ). (The quantities on the x-axis correspond to number of visits in the month.) TYPE A (5) TYPE B (3) DA 5 4 DB a) Suppose the Demmer Center selects a rental price (variable fee) of $2 per visit. If the Demmer Center cannot distinguish between Type A and Type B individuals, what monthly fixed fee will be selected to maximize profits? What will be the monthly profits? SHOW ALL CALCULATIONS. b) Now suppose the Demmer Center knows that Type A individuals are economic faculty at MSU and Type B individuals are MSU finance faculty. Suppose the Demmer Center can charge finance faculty a given 2-part pricing scheme and the economic faculty a different 2-part pricing scheme. In this case, what would be these 2-part pricing schemes and the corresponding profits? (You should specify a variable/rental fee and a monthly fixed fee for the finance faculty as well as a variable/rental fee and a monthly fee for the economic faculty. The variable fee need not be the one specified in part a).) Show Calculations.

3 1. (1 points) Below is an excerpt of an article entitled Bon Appetit that appeared in the Wall Street Journal. Apparently, hotels will do anything to get out of cooking. First, midrange hotels started closing their fullservice restaurants, replacing them with fast food kiosks and take-out service. Now, even the higher-end hotels are leasing their restaurants to people in the food business. David Ruggerio, chef of the upscale restaurant Le Chantilly in New York, plans to open Pastis, a French Restaurant, at the Parker Meridien in November. Hoteliers hope mane-brand chefs will attract more than just hotel guests to the restaurant, and turn an unprofitable operation into a money maker. It s a very different experience in Europe, where many of the best restaurants are in hotels, says Mark Lomanno of Smith Travel Research, in Hendersonville, Tenn. That very rarely happens in the U.S.. How many times have you gone out to dinner in a hotel? Suppose you own the Parker Meridien hotel and are deciding whether to pay David Ruggerio to open a restaurant (Pastis) in your hotel. Currently, you do not contract with an individual to operate a restaurant in your hotel. Instead, you operate your own restaurant. The current daily demand for your hotel and the current daily demands for lunch and dinner at your restaurant are depicted on the graphs below. The demand for your restaurant during lunch is denoted by D L and the demand during dinner is D D. The hotel has daily total fixed costs of $3, a constant marginal cost of $8, and 6 rooms. The restaurant has daily total fixed costs of $5 and 6 seats. The marginal cost associated with preparing a lunch or a dinner is constant at $2. Assume you cannot price discriminate for hotel rooms and you charge a single price for dinner and a single price for lunch. HOTEL RESTAURANT D DL DD

4 Suppose you sign a contract with David Ruggerio for him to operate the Pastis restaurant in your hotel. The contract specifies that David Ruggerio is entirely responsible for the operations of Pastis. He is responsible for paying all labor and material expenses (i.e. all variable costs) and keeps all revenue generated by the restaurant. If Pastis does open in your hotel, it increases the demand for your hotel rooms. Suppose the demand for your hotel if Pastis opens is as depicted on the graph below (and you still cannot price discriminate). If you allow Ruggerio to operate the restaurant, assume the hotel s fixed costs remain the same but the hotel s marginal cost increases from $8 to $12. What is the minimum you are willing to accept per day or the maximum you are willing per day to pay Ruggerio (for him to open the restaurant in your hotel)? SHOW YOUR CALCULATIONS AND EXPLAIN D

5 2. (7 points) Matt Ritter is responsible for the 2 nd Annual MBA Mustache Competition Benefitting CureSearch. As part of this fund raiser, faculty and MBA students can nominate other faculty and students. This nomination requires the faculty or student to grow a mustache unless the nominated individual chooses to buyout. A buyout requires the nominated faculty and student to pay a certain amount to relieve him/her of the obligation of growing a mustache. Matt set the buyout price at $3 this year. Assume that Matt had paid attention when he took MBA814 last year and decided to use 3 rd degree price discrimination for these buyouts basically, set the price of the buyout for faculty different than the price for an MBA students. Also, assume Matt knew that the demand for MBA student buyouts (D S ) and the demand for faculty buyouts (D F ) are as depicted below. 6 MBA Student Demand 2 Faculty Demand MR DS MC d) If Matt wanted to maximize the amount raised for CureSearch, what price should he set for a faculty buyout (p F ) and what price should he set for a student buyout (p s )? At these prices, how much would be raised for CureSearch? Show calculations. Set a price of 3 for students and a price of 1 for faculty. The amount raised would then be 3*15+1*5= e) Based on the prices in part a), what is the own price elasticity of demand for the faculty and what is the own price elasticity of demand for the students? Show calculations. Own price elasticity for faculty = (1/slope)(P/Q)=(1/-2)(1/5) = -1 Own price elasticity for students = (1/slope)(P/Q)=(1/-2)(3/15) = -1 f) Consider the own price elasticities in part b). Are they what you expected? Explain MR Because the marginal cost is zero, the quantities and prices are selected to maximize revenue and revenue is maximized when own price elasticity equals -1. DF MC

6 5. (6 points) The Demmer Center, located at Michigan State University, contains an indoor archery range which is deciding on a 2-part pricing scheme. This 2-part pricing scheme involves a monthly fixed fee as well as a price to use the bow and arrow during each visit (i.e., variable fee paid on each visit). The Demmer Center s costs include a constant marginal cost of $1 (for each rental) and monthly fixed costs of $1,. The market demand for the Demmer Center archery rentals is based on demand from 5 Type A individuals and 3 Type B individuals. The monthly demand curve for each Type A individual (D A ) is depicted below, along with the monthly demand curve for each Type B individual (D B ). (The quantities on the x-axis correspond to number of visits in the month.) TYPE A (5) TYPE B (3) DA 5 4 DB c) Suppose the Demmer Center selects a rental price (variable fee) of $2 per visit. If the Demmer Center cannot distinguish between Type A and Type B individuals, what monthly fixed fee will be selected to maximize profits? What will be the monthly profits? SHOW ALL CALCULATIONS. Type A is willing to pay a maximum monthly fixed fee of.5(5-2)(6)=9. Type B is willing to pay a maximum monthly fixed fee of.5(1-2)(8)=32. Profits if fixed fee is 9 8*9+5*6*2-5*6*1+3*8*2-3*8*1-1=26 Profits if fixed fee is 32 3*32+3*8*2-3*8*1-1=2 Set fixed fee at 9 and obtain profits of 26. d) Now suppose the Demmer Center knows that Type A individuals are economic faculty at MSU and Type B individuals are MSU finance faculty. Suppose the Demmer Center can charge finance faculty a given 2-part pricing scheme and the economic faculty a different 2-part pricing scheme. In this case, what would be these 2-part pricing schemes and the corresponding profits? (You should specify a variable/rental fee and a monthly fixed fee for the finance faculty as well as a variable/rental fee and a monthly fee for the economic faculty. The variable fee need not be the one specified in part a).) Show Calculations. The key to this part is recognizing that you can perfectly price discriminate. That being the case, you should set the rental price equal to the $1 marginal cost. Then the fixed fee for Type A individuals would be.5*(5-1)*8=16 and fixed fee for Type B individuals would be.5*(1-1)*9= (1 points) Below is an excerpt of an article entitled Bon Appetit that appeared in the Wall Street Journal. Apparently, hotels will do anything to get out of cooking. First, midrange hotels started closing their fullservice restaurants, replacing them with fast food kiosks and take-out service. Now, even the higher-end hotels are

7 leasing their restaurants to people in the food business. David Ruggerio, chef of the upscale restaurant Le Chantilly in New York, plans to open Pastis, a French Restaurant, at the Parker Meridien in November. Hoteliers hope mane-brand chefs will attract more than just hotel guests to the restaurant, and turn an unprofitable operation into a money maker. It s a very different experience in Europe, where many of the best restaurants are in hotels, says Mark Lomanno of Smith Travel Research, in Hendersonville, Tenn. That very rarely happens in the U.S.. How many times have you gone out to dinner in a hotel? Suppose you own the Parker Meridien hotel and are deciding whether to pay David Ruggerio to open a restaurant (Pastis) in your hotel. Currently, you do not contract with an individual to operate a restaurant in your hotel. Instead, you operate your own restaurant. The current daily demand for your hotel and the current daily demands for lunch and dinner at your restaurant are depicted on the graphs below. The demand for your restaurant during lunch is denoted by D L and the demand during dinner is D D. The hotel has daily total fixed costs of $3, a constant marginal cost of $8, and 6 rooms. The restaurant has daily total fixed costs of $5 and 6 seats. The marginal cost associated with preparing a lunch or a dinner is constant at $2. Assume you cannot price discriminate for hotel rooms and you charge a single price for dinner and a single price for lunch. HOTEL RESTAURANT D DL DD MR MR L MR D Profits if don t contract with David Ruggerio 24*4-8* *4-2*4+8*6-2*6-5=8,1

8 Suppose you sign a contract with David Ruggerio for him to operate the Pastis restaurant in your hotel. The contract specifies that David Ruggerio is entirely responsible for the operations of Pastis. He is responsible for paying all labor and material expenses (i.e. all variable costs) and keeps all revenue generated by the restaurant. If Pastis does open in your hotel, it increases the demand for your hotel rooms. Suppose the demand for your hotel if Pastis opens is as depicted on the graph below (and you still cannot price discriminate). If you allow Ruggerio to operate the restaurant, assume the hotel s fixed costs remain the same but the hotel s marginal cost increases from $8 to $12. What is the minimum you are willing to accept per day or the maximum you are willing per day to pay Ruggerio (for him to open the restaurant in your hotel)? SHOW YOUR CALCULATIONS AND EXPLAIN D MR Profits if contract with David Ruggerio where he pays price p: 36*4-12* p=6,1+p So the minimum you are willing to accept per day is 81-61=2