Price Discrimination. 1. The graph below depicts the demand curve and cost curves for a particular medical procedure from the Sparrow Medical Clinic.

Transcription

1 Economics EC Professor Mike Conlin Price Discrimination. The graph below depicts the demand curve and cost curves for a particular medical procedure from the Sparrow Medical Clinic. MC ATC AVC D Calculate the clinic s maximum profits if the medical clinic can perfectly price discriminate (i.e. first degree price discriminate). Show your calculations.

2 . The following graph depicts a firm's cost curves and the demand curve the firm faces. MC ATC AVC Q a) What is the firm's marginal revenue (MR) associated with the th unit of output if the firm sets a single price? b) What are the maximum profits if the firm sets a single price? Show calculations. c) What is the firm's marginal revenue (MR) associated with the th unit of output if the firm can st degree price discriminate? d) What are the firm s profits (approximately) if the firm can st degree price discriminate? e) What is the maximum revenue the firm can obtain if it st degree price discriminates? (The firm can select any output it would like.)

3 . The demand curve for students who have applied for early admissions to John Hopkins University this year is given on the graph to the left. The demand curve for students who have applied to John Hopkins University this year, but not for early admissions, is given on the graph to the right. (Assume these are all the students who have the qualifications to be accepted into the program and that these qualifications are the same.) EARLY ADMISSIONS NO EARLY ADMISSIONS De Dne Suppose tuition at John Hopkins University is set at $, and the marginal cost is constant at $,. (Marginal cost is just the increase in total cost associated with increasing the number of students by one.) If John Hopkins is to maximize profits, how much financial aid (i.e., scholarships) should be offered to students who apply for early admissions and how much to students who do not apply for early admissions? Explain. Assume that John Hopkins must provide the same financial aid to all those who apply early and the same financial aid to all those who do not apply early. However, John Hopkins can provide different amounts of financial aid to those who apply early and those who do not apply early.

4 . The graphs below represent the demands for the Love Boat cruise from senior citizens and non-senior citizens. Senior Citizens DS Non-Senior Citizens DNS Let the Love Boat s total capacity be passengers. Suppose total fixed costs (TFC) are $, and marginal cost (at quantities less than and equal to capacity) is constant at $. (The marginal cost is extremely high when quantity is more than capacity.) What are the Love Boat s maximum profits if they are able to third degree price discriminate (i.e., charge senior citizens a different price than non-senior citizens)? SHOW CALCULATIONS.

5 . Suppose the demand for local telephone service in East Lansing is from two types of individuals. There are type A individuals and type B individuals. Each type s individual demand curve is depicted on the graphs below (where q is the number of local phone calls per month). The telephone company cannot distinguish between type A and type B individuals. The marginal cost of a local phone call is constant at $. and the telephone company s monthly fixed costs are $. Suppose the telephone company charges $. per call and a monthly fixed fee that maximizes their profits. Type A Type B.... DA DB What are the telephone company s profits from this -part pricing scheme? SHOW CALCULATIONS.. The first graph on the next page depicts a monopolist s cost curves and the market demand curve the monopolist faces. The market demand curve is based on demand from Type A individuals and Type B individuals. The demand curve for each Type A individual is depicted on the next page, along with the demand curve for each Type B individual. Suppose the monopolist decides on a two-part pricing scheme where the monopolist charges a fixed fee (often called membership or entry fee) and variable fee (often called a per unit fee). Assume the monopolist charges a variable fee of $ per unit. a) If the monopolist cannot distinguish between type A and type B individuals, what fixed fee will the monopolist select to maximize profits? SHOW ALL CALCULATIONS. b) Now suppose that the monopolist can hire Mike Conlin who can distinguish a Type A individual from a Type B individual. Therefore, if the monopolist hires Mike Conlin, the monopolist can offer Type A individuals a different pricing scheme than Type B individuals. What is the maximum amount the monopolist is willing to pay Mike Conlin? SHOW CALCULATIONS.

6 TYPE A TYPE B D AVC ATC MC DA DB

7 . You own an Italian restaurant that serves only a fettuccine alfredo meal. The graphs below depicts the demand for your fettuccine alfredo meal during dinner (D D ) and during lunch (D L ). Suppose your marginal cost for each meal is $ during dinner and $ during lunch. (The difference in the marginal cost is because you serve larger portions at dinner and labor is more expensive during dinner time.) Also assume that you have a capacity of seats in your restaurant and your fixed costs per day are $. What are your daily profits? Show Calculations DL DD. Suppose the graph below depicts the hourly demand curves for the Lincoln Tunnel during peak hours, D P, and during non-peak hours D NP. Q P and Q NP indicate the number of cars per hour during peak hours and non-peak hours, respectively. Assume there are peak hours in a day (-am and -pm) and non-peak hours. Let the marginal cost of a car passing through the Lincoln Tunnel be zero. Dp Dnp Qp, Qnp Suppose the Port Authority of New York and New Jersey sets one price per car during peak hours and another price per car during non-peak hours. What are the Lincoln Tunnel s daily profits if the short-run capacity of cars per hour is,? Assume that the daily fixed costs are $,. Show your calculations and use above graph.

8 . This question is based on my experience when I visited Amazon.com. Amazon.com sells two tapes for one and two year olds. They are entitled Celebration of Song I and Celebration of Song II. Suppose two types of customers visit Amazon.com: Type A and Type B. There are Type A customers and Type B customers. Type A customers are willing to pay $ for Celebration of Song I and $ for Celebration of Song II. Type B customers are willing to pay $ for Celebration of Song I and $ for Celebration of Song II. Assume Amazon.com s marginal costs for Celebration of Song I and Celebration of Song II are constant at $ (for each) and Amazon.com has zero fixed costs. a) Suppose Amazon.com does not bundle. By not bundling, I mean that Amazon.com charges a certain price for Celebration of Song I (p I ) and charges a certain price for Celebration of Song II (p II ). If Amazon.com does not bundle, what prices does Amazon.com select (p I and p II ) and what are their profits? SHOW CALCULATIONS. b) Now suppose Amazon.com does bundle. By bundling, I mean that Amazon.com charges a single price for both Celebration of Song I and Celebration of Song II (p III ). If Amazon.com does bundle, what price does Amazon.com select and what are their profits? SHOW CALCULATIONS. c) Now suppose Amazon.com does mixed bundling. If Amazon.com does mixed bundling, what prices are selected and what are Amazon.com profits? SHOW CALCULATIONS.. You operate a travel company in Los Angeles that makes vacation plans for people. One of your offerings is a trip to East Lansing, MI. You are deciding how to price the vacation. You can either set one price for the transportation to East Lansing (p T ) and a separate price for the accommodations/entertainment at East Lansing (p AE ) and/or set a single price for the transportation and accommodations/entertainment (P TAE ). If you set separate prices, a person can choose to use your travel company for transportation, for accommodations/entertainment, or for both. Your clientele consists of two types of customers. Type I customers value the transportation at $ and the accommodations/entertainment at $,. Type II customers value the transportation at $ and the accommodations/entertainment at $,. There are Type I customers and Type II customers. Your costs are $ for every person you provide transportation and $ for every person you provide accommodations/entertainment. You have no fixed costs. a) What are your maximum profits from not bundling? Show calculations. b) What are your maximum profits from bundling? Show calculations. c) What are your maximum profits from mixed bundling? Show calculations

9 . This question is based on my experience when I visited TC Timber. TC Timber is a company located in Skaneateles, New York that manufactures wooden train sets (similar to those produced by Brio). Suppose TC Timber has two types of customers: grandparents and parents. Assume that TC Timber cannot distinguish grandparents from parents. The grandparents are willing to pay a maximum of $ for a wooden train set and parents are willing to pay a maximum of $ for a wooden train set (assuming they do not have to wait in line in order to purchase the train set). There are grandparents and parents. Every year TC Timber has a sale the first weekend in December where they sell the wooden train set for a sale price. During this weekend, people buying a train set must wait hours in line (there are no lines other than this sale weekend). Suppose the opportunity cost associated with waiting the hours is $ for grandparents and $ for parents. Assume that TC Timber s marginal cost of a wooden train set is constant at $. What price should TC Timber charge for the train set and what should be the sale price? SHOW CALCULATIONS.. Sony has an outlet store in Aurora Illinois. On Black Friday, the day after Thanksgiving, the Sony outlet store opened at : am. Sony usually opens the store at : am. Sony s outlet store sells the Bravia Flat-Panel High Definition Television. Suppose Sony has two types of customers for their Bravia Flat-Panel High Definition Television (Type A and Type B). Assume that Sony cannot distinguish between the types. Type A s are willing to pay a maximum of $ for a television and Type B s are willing to pay a maximum of $ (assuming they do not have to wait in line in order to purchase the television). There are Type A s and Type B s. On Black Friday the Sony outlet store decided to offer a sales price for the television if the person purchased the television between : and : am. Assume that customers did not have to wait at all if they purchased the television after am but the sales price was not offered at this time. Therefore, customers purchasing the television would have to pay the regular price after am. Between : and : am, Sony only had two cashiers working so customers had to wait an hour in line in order to purchase the television. Suppose the opportunity cost per hour associated with waiting in line is $ for Type A s and $ for Type B s. Assume that Sony s marginal cost of a Bravia Flat-Panel High Definition Television is constant at $ and their fixed costs are zero. For simplicity, assume each consumer only demands a single television. a) What price should Sony charge for the television after : am (i.e., the regular price) and what price should Sony charge for the television between : and : am (i.e., the sales price)? SHOW CALCULATIONS AND EXPLAIN. b) Now suppose that Sony can choose to have more cashiers (increasing the number of cashiers from to ) work from : to : am. This would decrease the waiting time in line (i.e., to check out) from hour to half an hour. What is the maximum Sony should be willing to pay these two cashiers in order for them to work from : to : am? (Note that Sony can change the sales and regular prices calculated for part a) if they increase the number of cashiers from to.) SHOW CALCULATIONS AND EXPLAIN.