Price Discrimination (when there is no strategic interaction)

Profit Maximization when setting a Single Price CONSUMER SURPLUS Profits are maximized at Q=4 and P=6. Profits=TR-TC= 6*4-4.5*4= 24-18=6 Or Profits=P*Q-ATC*Q =(P-ATC)*Q =(6-4.5)*4=6 Consumer Surplus -the value consumers get from a good but do not have to pay for. PROFITS Q MR

Definition of Price Discrimination The practice of charging different prices to consumers for the same good or service (and the price differences do not reflect cost differences)

Three Conditions Required for Price Discrimination to Occur Seller must exercise some “price control” (i.e. face a downward sloping demand) Seller must be able to distinguish among customers who are willing to pay different prices. It must be impossible or too costly for one buyer to resell the good to other buyers (i.e., buyers cannot arbitrage).

Strategic Behavior By Firms What actions do firms take to prevent resale or make resale more “costly”? Warranty becomes invalid if item is resold. Software firms do not provide support services if software is resold. Software firms’ programs prevent downloading multiple times. Any others you can think of?

Types of Price Discrimination First-Degree (Perfect) Price Discrimination - Occurs when the seller charges the highest price each consumer would be willing to pay for the product (consumer's reservation values) rather than go without it. Universities, Car Dealers, Contractors, Flea Market (at least they all try) Third-Degree Price Discrimination - Occurs when the seller charges different prices in different markets, or charges a different price to different segments of the buying population. Movies, Soda, Computers, prescription drugs, textbooks, safety gates, airlines, dry cleaning, haircuts, …

Types of Price Discrimination Second-Degree Price Discrimination - Occurs when the seller charges a uniform price per unit for one specific quantity, a lower price for an additional quantity, and so on. QUANTITY DISCOUNTS (2-part Pricing is a type of quantity discount) Electric Utilities, Country Clubs, Michigan Athletic Club, Disneyland (in old days), Grocery Stores, Espresso Royale, … Peak Load Pricing – the practice of charging higher prices during “peak hours” (i.e. high demand times) than during off-peak hours. Hotels, Ski Resorts, Airlines, Stadiums, Restaurants, Toll roads, Bridges, …

Types of Price Discrimination Bundling – the practice of bundling several different products together and selling them at a single “bundle price”. Happy Meals, Restaurants, Stereos, Cars with Options, Celebrity Endorsements, Movies (years ago),… Screening- the practice of requiring consumers to “jump over a hurdle” to obtain a lower price. Coupons, Warranties, Rebates, Outlet malls, Saturday Night Stayovers for airlines,….

No Price Discrimination Profits are maximized at Q=20 and P=30. Profits=TR-TC =P*Q-ATC*Q =30*20-14*20=320 MR

First-Degree (Perfect) Price Discrimination Definition: Occurs when the seller charges the highest price each consumer would be willing to pay for the product (consumer's reservation values) rather than go without it. Universities, Car Dealers, Contractors, Flea Market (at least they all try)

1st-Degree Price Discrimination Charge Every Consumer the maximum he/she is willing to pay. The demand curve is based on what consumers are willing to pay.

Market Demand is Obtained from Adding Individual Demand Curves

Suppose Market Demand is Obtained from Individual Demands Below

1st-Degree Price Discrimination What output would the firm produce to maximize profits if it could 1st-degree price discriminate? Q=30 What would be the firm’s total revenue? TR=.5*(50-20)*30+20*30 =1050 What would be the firm’s TC at an output of 30? TC=ATC*Q=15*30=450 Profits=1050-450=600 TR TC Marginal Revenue is the Demand Curve

1st Degree Price Discrimination MaxQ Profits = MaxQ TR(Q)-TC(Q) = MaxQ -TC(Q) So, =P(Q)-MC=0 and P(Q)=MC Fundamental Theorem of Calculus MR

Price Discrimination on the Internet Online Pricing: Economist, June 2012

Reckonings; What Price Fairness? The New York Times, October 4, 2000

Amazon's Pricing Strategy Makes Life Miserable For The Competition (Forbes Retail 10-20-2014) During the Christmas shopping season we will see Amazon change prices on as many as 80 million products during a single day. That is amazing since companies like Walmart, Best Buy and Toys “R” Us have already announced that they will not be undersold and will match any competitors’ prices in a printed flyer or website. That is going to create a competitive environment that will make shopping more challenging for savvy customers.

Expensive Lesson: Colleges Manipulate Financial Aid Offers The Wall Street Journal, April 4, 1996

Certain Degrees Now Cost More at Universities The New York Times, July 29, 2007

Third-Degree Price Discrimination Definition: Occurs when the seller charges different prices in different markets, or charges a different price to different segments of the buying population. Movies, Soda, Computers, prescription drugs, textbooks, safety gates, airlines, …

Movie Theater with 300 seats that price discriminates based on age by offering different prices to senior citizens and non-senior citizens. Assume (Daily) Fixed Costs of $1,000 and constant Marginal Cost of $2. Senior Citizen Non-Senior Citizen Ds Dns MRs MRns

Movie Theater with 300 seats that price discriminates based on age by offering different prices to senior citizens and non-senior citizens. Assume (Daily) Fixed Costs of $1,000 and constant Marginal Cost of $2. Senior Citizen Non-Senior Citizen Ds Dns MC MC MRs MRns Set a price of $6 for Senior Citizens and have 160 buy tickets. Set a price of $11 for Non-Senior Citizens and have 90 buy tickets. Daily Profits would then be 6*160+11*90-2*160-2*90-1000 = 450.

3rd Degree Price Discrimination MaxQ1,Q2 TR1(Q1)+TR2(Q2)-TC(Q1+Q2) So, = MR1-MC=0 so MR1=MC So, = MR2-MC=0 so MR2=MC

3rd Degree Price Discrimination MaxQs,Qns (10-.025Qs)Qs +(20-.1Qns)Qns-2(Qs+Qns)-1000 So, =10-.05Qs -2=0 so Qs=160 So, =20-.2Qns-2=0 so Qns=90 Profits=(10-.025(160))(160) +(20-.1(90))(90)-2(160+90)-1000=450

CBS News goes undercover to reveal gender price discrimination CBS NEWS / January 25, 2016 CBS News went undercover with one female producer and one male producer visiting a handful of dry cleaners in New York City. They brought nearly-identical, 100 percent cotton button down shirts in comparable sizes and requested the same service. Our female producer was charged at least twice as much in more than half the businesses visited. In one, she was charged $7.50 while her male counterpart just $2.85. At another, she paid $3 dollars more. At one of the dry cleaners, the female producer asked the employee why the pricing was different for men's and women's shirts. "The machines and how we press it, that's the difference," the employee said.The employee was referring to pressers used after clothing is dry cleaned. They aredesigned for men, but owner of Next Cleaners Kam Saifi said it's not a justification. "Having a shirt laundered and machine pressed does not exist for women's tops," Saifi said. It exists only for men, he said.

A Funeral May Cost You Thousands Less Just By Crossing The Street NPR News Investigations February 7, 2017 Ellen Bethea sat alongside her husband's hospital bed after doctors told her that Archie, the man she had been married to for almost five decades, wouldn't make it. Bethea had never planned a funeral before, but knew of only one in town — Hardage-Giddens Funeral Home of Jacksonville. She and her family went there the next day. After meeting with a staff member, they walked out with a bill of over $7,000. The cost of Archie's cremation — $3,295 — was more than twice the amount charged elsewhere in Jacksonville by the company that owns Hardage-Giddens. The cremations are done in the same place and in the same way. In a months-long investigation into pricing and marketing in the funeral business, also known as the death care industry, NPR spoke with funeral directors, consumers and regulators. We collected price information from around the country and visited providers. We found a confusing, unhelpful system that seems designed to be impenetrable by average consumers, who must make costly decisions at a time of grief and financial stress. Funeral homes often aren't forthcoming about how much things cost, or embed the information in elaborate package deals that can drive up the price of saying goodbye to loved ones. While most funeral businesses have websites, most omit prices from the sites, making it more difficult for families to compare prices or shop around. NPR reporters also found it difficult to get prices from many funeral homes, and federal regulators routinely find the homes violating a law that requires price disclosures.

A Funeral May Cost You Thousands Less Just By Crossing The Street NPR News Investigations February 7, 2017 In Jacksonville, Hardage-Giddens and several other businesses in and around Jacksonville are part of a large, corporate-owned portfolio of about 1,500 funeral homes and several hundred cemeteries. The owner and operator is Service Corporation International (SCI), a multibillion-dollar company traded on the New York Stock Exchange. The Houston-based firm claims 16 percent of the $19 billion North American death care market, which includes the U.S. and Canada. Company documents say it has 24,000 employees and is the largest owner of funeral homes and cemeteries in the world. In Jacksonville, SCI sells cremations under the Hardage-Giddens/Dignity Memorial brand at large, luxurious funeral homes. The company also sells them for lower prices at strip-mall storefront outlets under other brands such as Neptune Society and National Cremation Society.

Second-Degree Price Discrimination Definition: Second-Degree Price Discrimination - Occurs when the seller charges a uniform price per unit for one specific quantity, a lower price for an additional quantity, and so on. QUANTITY DISCOUNTS (2-part Pricing is a type of quantity discount). Electric Utilities, Country Clubs, Michigan Athletic Club, Disneyland (in old days), Espresso Royale, … http://www.seasonticketrights.com/TeamSeats.aspx?lid=21

2-Part Pricing Suppose the graph to the right depicts the demand and cost curves for a country club where quantity (Q) represents the number of rounds of golf. Q

Suppose the country club sets the price per round of golf at $20 Suppose the country club sets the price per round of golf at $20. What membership fee (fixed fee) should the country club set? Individual A If the price per round is $20 and the membership fee isn’t too high, how many rounds of golf will Individual A play? 3 What is the maximum membership fee Individual A will pay given the price per round is $20? .5*(50-20)*3=45 Maximum membership fee Individual A is willing to pay.

Suppose the country club sets the price per round of golf at $20 Suppose the country club sets the price per round of golf at $20. What membership fee (fixed fee) should the country club set? Individual B If the price per round is $20 and the membership fee isn’t too high, how many rounds of golf will Individual B play? 6 What is the maximum membership fee Individual B will pay given the price per round is $20? .5*(50-20)*6=90 Maximum membership fee Individual B is willing to pay.

Suppose the country club sets the price per round of golf at $20 Suppose the country club sets the price per round of golf at $20. What membership fee (fixed fee) should the country club set? Given the cost of each round is $20, the country club should charge a membership fee of either $45 or $90. Profits if membership fee is $45 Both types of individuals join with Type A golfing 3 rounds each and Type B golfing 6 rounds. 45*9+20*(8*3+1*6)-15*30= 555 Profits if membership fee is $90 Only Type B joins and Type B golfs 6 rounds. 90*1+20*(1*6)-35*6= 0 SET MEMBERSHIP FEE AT $45

2-Part Pricing If membership fee is $45, total number of rounds golfed is 8*3+1*6=30. At Q=30, ATC=15 so TC=ATC*Q=15*30=450. If membership fee is $90, total number of rounds golfed is 1*6=60. At Q=6, ATC=35 so TC=ATC*Q=35*6=210. Q

Peak Load Pricing Definition The practice of charging higher prices during “peak hours” (i.e. high demand times) than during off-peak hours. Hotels, Ski Resorts, Airlines, Stadiums, Restaurants, … http://panynj.info/bridges-tunnels/tolls.html

Demands at a Restaurant for Lunch and Dinner

TR-TC=TR-TVC-TFC= 35*15+60*40-20*(15+40)-1800= 25 Suppose Restaurant’s Capacity is 45 seats, Fixed Costs are $1800 per day and Marginal Cost of a meal is constant at $20 What prices will the Restaurant charge for lunch and dinner? PL=$35 and PD=$60 What are the Restaurant’s daily profits? TR-TC=TR-TVC-TFC= 35*15+60*40-20*(15+40)-1800= 25 PD= PL= MC=AVC

Peak Load Profit Maximization MaxQL,QD (50-QL)QL+ (100-QD)QD -20(QL+QD) -1800 s.t. QL< 45 , QD< 45 So, = 50-2QL -20=0 so QL=15 So, = 100-2Qb-20=0 so QD=40 Profits=(50-15)15+ (100-40)40 -20(15+40) -1800=25

TR-TC=TR-TVC-TFC= 35*15+70*30-20*(15+30)-1200= 525 Suppose Restaurant’s Capacity is 30 seats, Fixed Costs are $1200 per day and Marginal Cost of a meal is constant at $20 What prices will the Restaurant charge for lunch and dinner? PL=$35 and PD=$70 What are the Restaurant’s daily profits? TR-TC=TR-TVC-TFC= 35*15+70*30-20*(15+30)-1200= 525 PD= PL= MC=AVC

Bundling Definition The practice of bundling several different products together and selling them at a single “bundle price”. Happy Meals, Restaurants, Stereos, Cars with Options, Celebrity Endorsements, Movies (years ago),… What are possible explanations as to why firms do this?

Quote from Lebron James (article in November 28, 2007 Fortune) So in 2006, James founded LRMR Marketing, so named for the initials of the four buddies: Lebron, Randy Mims, Maverick Carter, and Richard Paul. While James is LRMR's core business, the goal is to diversify by representing other athletes. Right now they have only one other client. In August the company signed a contract with Ted Ginn Jr., the Ohio State star and a rookie wide receiver on the Miami Dolphins. … "He should be looking at multiyear deals with a vested interest," says Doug Shabelman, the president of Burns Entertainment & Sports Marketing. "He'll probably be in a position to take some ownership stakes." Shabelman added that if LRMR develops a stable of athletes, it could package them in deals for marketers. In other words, if you want LeBron, you gotta take the others.

Bundling – Example 1 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15

Bundling – Example 1 Willingness to Pay Type I Type II Appetizer 10 8 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=8, PE=12 Profits= 8*20+12*20=400 Bundling PAE=22 Profits = 22*20 = 440 Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15

Bundling – Example 1 Willingness to Pay Type I Type II Appetizer 10 8 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=8, PE=12 Profits= 8*20+12*20=400 Bundling PAE=22 Profits = 22*20 = 440 Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15 For Both 22 23

Bundling – Example 2 Willingness to Pay Type I Type II Appetizer 8 10 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=8, PE=12 Profits= 8*20+12*20=400 Bundling PAE=20 Profits = 20*20 = 400 Willingness to Pay Type I Type II Appetizer 8 10 Entrée 12 15

Bundling – Example 2 Willingness to Pay Type I Type II Appetizer 8 10 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=8, PE=12 Profits= 8*20+12*20=400 Bundling PAE=20 Profits = 20*20 = 400 Willingness to Pay Type I Type II Appetizer 8 10 Entrée 12 15 For Both 20 25

Bundling – Example 3 Willingness to Pay Type I Type II Appetizer 10 2 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=10, PE=12 Profits= 10*10+12*20=340 Bundling PAE=17 Profits = 17*20 = 340 Willingness to Pay Type I Type II Appetizer 10 2 Entrée 12 15

Bundling – Example 3 Willingness to Pay Type I Type II Appetizer 10 2 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=10, PE=12 Profits= 10*10+12*20=340 Bundling PAE=17 Profits = 17*20 = 340 Mixed Bundling PE=15, PAE=22 Profits= 15*10+22*10=370 Willingness to Pay Type I Type II Appetizer 10 2 Entrée 12 15 For Both 22 17

Bundling – Example 4 Willingness to Pay Type I Type II Appetizer 2 10 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=10, PE=12 Profits= 10*10+12*20=340 Bundling PAE=14 Profits = 14*20 = 280 Willingness to Pay Type I Type II Appetizer 2 10 Entrée 12 15

WRONG BECAUSE TYPE II WILL BUY ONLY ENTRÉE Bundling – Example 4 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=10, PE=12 Profits= 10*10+12*20=340 Bundling PAE=14 Profits = 14*20 = 280 Mixed Bundling PE=12, PAE=25 ? WRONG BECAUSE TYPE II WILL BUY ONLY ENTRÉE Willingness to Pay Type I Type II Appetizer 2 10 Entrée 12 15 For Both 14 25

Bundling – Example 4 Willingness to Pay Type I Type II Appetizer 2 10 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. For simplicity, assume costs are zero. No Bundling PA=10, PE=12 Profits= 10*10+12*20=340 Bundling PAE=14 Profits = 14*20 = 280 Mixed Bundling PE=12, PAE=22 Profits= 12*10+22*10=340 Willingness to Pay Type I Type II Appetizer 2 10 Entrée 12 15 For Both 14 25 Assume that Type II buys bundle even though indifferent between buying bundle and just entrée. If you don’t like this assumption, just set PAE=21.99.

Bundling – Example 5 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. Assume marginal cost of an appetizer is $5 and marginal cost of an entrée is $10 . Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15

Bundling – Example 5 Willingness to Pay Type I Type II Appetizer 10 8 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. Assume marginal cost of an appetizer is $5 and marginal cost of an entrée is $10 . No Bundling PA=8, PE=15 Profits= (8-5)*20+(15-10)*10=110 Bundling PAE=22 Profits = (22-15)*20 = 140 Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15

Bundling – Example 5 Willingness to Pay Type I Type II Appetizer 10 8 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. Assume marginal cost of an appetizer is $5 and marginal cost of an entrée is $10 . No Bundling PA=8, PE=15 Profits= (8-5)*20+(15-10)*10=110 Bundling PAE=22 Profits = (22-15)*20 = 140 Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15 For Both 22 23

Bundling – Example 5 Willingness to Pay Type I Type II Appetizer 10 8 Assume there are 10 Type I individuals and 10 Type II individuals and that each individual only demands one appetizer and one entrée. Assume marginal cost of an appetizer is $5 and marginal cost of an entrée is $10 . No Bundling PA=8, PE=15 Profits= 110 Bundling PAE=22 Profits = 140 Mixed Bundling PA=10, PAE=23 Profits= (10-5)10+(23-15)10=130 OR PE=14, PAE=22 Profits= (14-10)10+(22-15)10=110 Willingness to Pay Type I Type II Appetizer 10 8 Entrée 12 15 For Both 22 23

Screening The practice of requiring consumers to “jump over a hurdle” to obtain a lower price. Coupons, Warranties, Rebates, Outlet malls, Saturday Night Stayovers for airlines,…. http://maps.google.com/maps?ie=UTF-8&oe=UTF-8&q=car+wash&near=Okemos,+MI&fb=1&cid=42682926,-84430200,9316045653265795993&li=lmd&z=14&t=m

Coupon for Box of Cereal – Assume MC of a box is constant at $ Coupon for Box of Cereal – Assume MC of a box is constant at $.50 and TFC=15

Suppose Don’t Issue a Coupon Set Price at $2 or $3 to maximize profits. If Set Price=$2 Profits = 30*2-30*.5-15= 30 If Set Price=$3 Profits = 10*3-10*.5-15= 10

Suppose the opportunity cost of cutting a coupon is $0 for Type A individuals and $1.50 for Type B individuals. What Price and Coupon Value Maximizes Profits? Price=$3 and Coupon Value=$1 Type A cuts coupon and Type B does not. TR=3*10+(3-1)*20 = 70 TC=.5*30+15=30 Profits= 70-30=40

Suppose the opportunity cost of cutting a coupon is $0 Suppose the opportunity cost of cutting a coupon is $0.25 for Type A individuals and $1.50 for Type B individuals. What Price and Coupon Value Maximizes Profits? Price=$3 and Coupon Value=$1.25 Type A cuts coupon and Type B does not. TR=3*10+(3-1.25)*20 = 65 TC=.5*30+15=30 Profits= 65-30=35

Suppose the opportunity cost of cutting a coupon is $0 Suppose the opportunity cost of cutting a coupon is $0.75 for Type A individuals and $1.50 for Type B individuals. What Price and Coupon Value Maximizes Profits? Price=$2.75 and Coupon Value=$1.50 Type A cuts coupon and Type B does not. TR=2.75*10+(2.75-1.50)*20 = 52.50 TC=.5*30+15=30 Profits= 52.50 -30=22.50 Better off just charging a price of $2 and not using coupon.

Suppose the opportunity cost of cutting a coupon is $0 Suppose the opportunity cost of cutting a coupon is $0.75 for Type A individuals and $1.50 for Type B individuals. What Price and Coupon Value Maximizes Profits? Price=$2.75 and Coupon Value=$1.50 TR=2.75*10+(2.75-1.50)*20 = 52.50 TC=.5*30+15=30 Profits= 52.50 -30=22.50 You could make Price=$2.74 and Coupon Value=$1.49 if you want to make Type B strictly prefer to not cut the coupon.

Intuition There are two types of consumers. One with a high willingness to pay and one with a low willingness to pay. The cost of “jumping over the hurdle” is greater for the high willingness to pay type. You want the low willingness to pay type to jump over the hurdle and then pay the maximum he/she is willing to pay. You then want to charge the high willingness to pay the maximum possible without providing him/her the incentive to “jump over the hurdle” or to not buy.

“Shopper Alert: Price May Drop for You Alone”, New York Times 2012

iPhone Buyer Sues The Times (London), October 3, 2007