Transcript Price Customization by Quantity - Faculty Directory | Berkeley-Haas

Class Concepts – Advanced Pricing
 Advanced Pricing
- Use price customization to sell the same good at different prices per unit
- Ideally, we would like to sell each unit at exactly the maximum willingness to pay
(WTP) of each customer. Since we don’t have enough information to do this, we
use the following types of customization:
 Types of Price Customization
- Price Customization by Group
- Two-Part Tariff
- Versioning
- Price Customization by Quantity
- Bundling
Class Concepts – Versioning
 Versioning
- Sell two versions of the same products (usually high and low quality) to customers with
different preferences for the product versions.
 How to use Versioning
- 1) Price the low type product at the low type customer willingness to pay
- 2) Price the high type product at the high type customer’s willingness to pay less the
consumer surplus he/she receives from buying the low type product
- 3) Compare the profit of selling to the high and low type customer with selling to just
the high type customer. Choose the strategy that produces the highest profits.
 Requirements for using Versioning
- This pricing method works best when there are two distinct customer groups and
everyone agrees which product version is better than the other.
- Arbitrage?: No, you are charging one price for each product version.
- Better than simple pricing?: Depends on how expensive it is to create two versions
Class Concepts – Versioning
 Knowledge Check
- You are working for Wrigley, trying to determine how to price your new Five gum as
compared to your Doublemint product. You have identified two types of customers:
trendsetting, gum fanatics and ordinary people. Trendsetters are willing to pay $1.50 for
a pack of premium Five gum and $1.25 for Doublemint. Ordinary types are willing to
pay $0.95 for Five gum and $0.85 for Doublemint. You believe the two customer types
are equally numerous and the marginal cost of producing the products is the same,
$0.10, for both products. How should you price the two products?
 Solution
- Sell to both types
- Price the Doublemint at the Ordinary Type’s willingness to pay: $0.85
- Price the Five at the Trendsetter’s willingness to pay, less their consumer surplus from
buying Doublemint: $1.50 – ($1.25-$0.85) = $1.50 - $0.40 = $1.10
- Profit = ($0.85 + $1.10) – 2($0.10) = $1.95 - $0.20 = $1.75
- Selling just to the high type at $1.50
- Profit = $1.50 - $0.10 = $1.40
- So, sell to both types!
Class Concepts – Price Customization by Quantity
 Price Customization by Quantity
- Sell your product in a small package and a large package to customers with different
volume preferences
 How to use Price Customization by Quantity
- Choose the size of the Large Package: For the volume preferring group, find the
highest volume for which the consumer Marginal Benefit (MB) is higher than MC
- Try all possible smaller sizes for the Small Package.
- Set the price of the Small Package equal to the low volume preferring group WTP
- Set the price of the Large Package equal to the high volume preferring group WTP
less the consumer surplus for purchasing the Small Package (or the consumer surplus
for purchasing multiple Small Packages).
- Calculate the profit when combining each possible Small Package with the chosen
large package and choose the Small Package that maximizes profit
- Check the profitability of only the Large Package to the volume preferring group,
and choose the more profitable option.
 Other Considerations
- Arbitrage?: There are definite arbitrage opportunities. Be sure to consider whether
they are a problem.
- Better than simple pricing?: Not necessarily. Check to be sure!
Class Concepts – Price Customization by Quantity
 Knowledge Check
- You are working for a magical candy company selling Bertie Bott’s Every Flavor Beans
to Wizards and Muggles. Wizards are willing to pay $7 for half a pound of jelly beans,
and $4 for the second. Muggles will pay only $5 for the first half pound, and $3 for
the second. It costs you $3 to produce each pound of jelly beans. How should you
package and sell Bertie Bott’s? (Wizards & Muggles are equal in number)
1st Half Pound
Muggle
Wizard
$5
$7
2nd Half Pound
$3
$4
Class Concepts – Price Customization by Quantity
1st Half Pound
Muggle
Wizard
2nd Half Pound
$5
$3
$7
$4
 Solution
- Determine the size of the large package:
- MC = $1.50 so the size of the large package is 1 pound
- Try every possible small package size
- The only smaller possible size is half a pound. WTP for the first half pound by
Muggles is $5, so this is the price of the smaller package.
- The larger package is priced at the willingness to pay of the Wizards less the consumer
surplus they receive from purchasing the smaller package. $11 - $2 = $9
- Profit = ($9 + $5) – 3 x $1.50 = $14 - $4.50 = $9.50
- Check Selling just to Wizards: Profit = $11 - $3 = $8.00
- Check Simple Pricing
- Sell only half pound: Profit = 2 x $5 – 2 x $1.50 = $10 - $3 = $7
- Sell only one pound: Profit = 2 x $8 – 4 x $1.50 = $16 - $6 = $10
- So, the optimal pricing is to sell a one pound package using simple pricing for $8
Class Concepts – Price Customization by Quantity
 Knowledge Check
- You are selling hot dogs at the “Haas for Students” stand before the Oregon State
game (on October 13). You are serving two customer types: Families and Singles.
Families are willing to pay $4 for the first hot dog and $0.90 less for each subsequent
hot dog. Singles are willing to pay $3 for the first and second hot dogs, $2 for the
third, and $1 for the fourth. Your marginal cost for each hot dog is $1. How should
you price the hot dogs?
Class Concepts – Price Customization by Quantity
 Solution
- Use Price Discrimination by Quantity
- Determine the size of the Large Package. Marginal Benefit ≥ MC
Hot Dog
Family Marginal Benefit
1st
2nd
$4.00
3rd
$3.10
4th
$2.20
5th
$1.30
$0.40
- The Large Package size is 4 hot dogs for Marginal Benefit of $10.60
- Try All Possible Small Package Sizes
Hot Dog
1st
2nd
3rd
4th
5th
Singles Marginal Benefit
$3.00
$3.00
$2.00
$1.00
$0.00
- Small Package – Quantity 1: $3  Large Package – Quantity 4: $9.50
-
If
If
If
If
Family buys 1 Small Package, their Marginal Benefit is $1
Family buys 2 Small Packages, their Marginal Benefit is $1.10
Family buys 3 Small Packages, their Marginal Benefit is $0.30
Family buys 4 Small Packages, their Marginal Benefit is -$1.40
- Small Package – Quantity 2: $6  Large Package – Quantity 4: $9.50
- If Family buys 1 Small Package, their Marginal Benefit is $1.10
- If Family buys 2 Small Packages, their Marginal Benefit is -$1.40
- Small Package – Quantity 3: $8  Large Package – Quantity 4: $9.30
- If Family buys 1 Small Package, their Marginal Benefit is $1.30
Class Concepts – Price Customization by Quantity
Hot Dog
Family Marginal Benefit
1st
2nd
$4.00
3rd
$3.10
4th
$2.20
5th
$1.30
$0.40
Hot Dog
1st
2nd
3rd
4th
5th
Singles Marginal Benefit
$3.00
$3.00
$2.00
$1.00
$0.00
 Solution
- Try All Possible Small Package Sizes
- Small Package – Quantity 1: $3  Large Package – Quantity 4: $9.50
- Profit = ($3 x 2 hot dogs) + $9.50 – ($1 x 6 hot dogs) = $6 + $9.50 - 6 = $9.50
- (This is because the Single customer will by two hot dogs at a $3 price)
- Small Package – Quantity 2: $6  Large Package – Quantity 4: $9.50
- Profit = $6 + $9.50 – ($1 x 6 hot dogs) = $15.50 - $6 = $9.50
- Small Package – Quantity 3: $8  Large Package – Quantity 4: $9.30
- Profit = $8 + $9.30 – ($1 x 7 hot dogs) = $17.30 - $7 = $10.30
- Try Just Selling to the Volume Preferring Group
- Large Package – Quantity 4: $10.60
- Profit = $10.60 – ($1 x 4 hot dogs) = $10.60 - $4 = $6.60
- So, the most profitable option is to sell a small package with 3 hot dogs for $8, and a large
package with 4 hot dogs for $9.30
Class Concepts – Bundling
 Bundling
- Two or more products that can be consumed separately, packaged together and sold at
one price
 How to use Bundling
- Try Simple Pricing
- Price each product at the profit maximizing point
- Try Pure Bundling
- Price the bundle so that it appeals to all consumers and determine profits
- Try Mixed Bundling
- Create smaller bundles and offer (some) individual products, and calculate profits
- Compare profits of each strategy
 Requirements for using Bundling
- This pricing method works best when there are two or more customer groups with
strong willingness to pay for one product and weaker willingness to pay for the other.
- Arbitrage?: Yes, think about how to prevent consumers from unbundling & reselling.
- Better than simple pricing?: Depends on how correlated demand is among customers
Class Concepts – Bundling
 Knowledge Check
- You are in charge of pricing Stanford football tickets for the 2007 season. Since
your football team is less than stellar, your alumni have limited demand for the
regular season tickets and almost no demand for tickets to the Big Game (as it will
likely be an embarrassing game). Cal alums, on the other hand, have no need for
tickets to your regular season games, and (since you’ve just downsized your stadium
and issued far fewer tickets to opposing teams) enormous demand for Stanford
issued Big Game tickets. If your marginal cost is negligible and fans from both sides
are equally numerous, how can you price your tickets if the willingness to pay of the
alumni are as follows?
Cal Alumni
Stanford Alumni
Regular Season Tickets (5 games)
$0
$100
Big Game Tickets
$120
$30
Class Concepts – Bundling
 Solution
- Simple Pricing
- Sell Regular Season tickets to Stanford Fans for $100
- Sell Big Game tickets to Cal Fans for $120
- Profits = $100 + $120 = $220
- Pure Bundling
- Since Cal Fans value the bundle at $120, and Stanford Fans value the bundle at $130,
price the bundle at $120
- Profits = $120 x 2 = $240
- Mixed Bundling
- Since Cal Fans value the Big Game tickets at $120, sell Big Game tickets individually
for $120, and sell the bundle for $130.
- Profits = $120 + $130 = $250
- So, Mixed Bundling is the most profitable Strategy!
Class Concepts – Advanced Pricing Recap
 Price Customization by Group
- One product, different prices for different types of consumers
 Two-Part Tariff
- One product sold at a fixed fee prices and a unit price
 Versioning
- Two versions of a product (low and high quality) sold to multiple consumer types
 Price Customization by Quantity
- One product sold in a small and large packages
 Bundling
- Two products that can be consumed separately, packaged and sold together
Class Concepts – Practice Problems
 Knowledge Check
- You have recently decided to start a line of pasta sauces. The first line will compete with
Ragu and be known as Everyday. The other will compete with the Classico brand and be
known as Authentic Italian. Assuming you can match these two brands, $0.50 marginal
cost, and the willingness to pay of Gourmet and Regular customers for a 26 oz jar is as
follows, what prices should you charge?
Classico
Regular
Gourmet
Ragu
$1.75
$3.00
$1.50
$2.00
Class Concepts – Practice Problems
 Solution
Classico
Regular
Gourmet
Ragu
$1.75
$3.00
$1.50
$2.00
- Use Versioning to price to two pasta sauce types
- Sell Both Types
- Set the price of the low type equal to the willingness to pay of the low type: $1.50
- Set the price of the high type equal to the willingness to pay of the high type less the
consumer surplus from purchasing the low type product:
- $3 – ($2 - $1.50) = $3 - $0.50 = $2.50
- Profit = $1.50 + $2.50 – (2 x $0.50) = $4 - $1 = $3
- Sell to Just the High Type
- Profit = $3 - $0.50 = $2.50
- So, sell to both types
Class Concepts – Practice Problems
 Knowledge Check
- You are starting up a golf country club, and are trying to determine what your annual
membership fees and 18-hole greens fees should be. You have done some market
research and determined that there are two types of customers: avid golfers and
business golfers. Avid golfers have annual demand of: Q = 300 – 2P. Business golfers
have annual demand of: Q = 200 – 3P. Where Q is the number of rounds played in a
year, and P is the price of a round of golf. It costs you $40 for each round of golf
played. How much should you charge if you are only trying to attract the avid golfers?
- What approach would you take to set up choosing a membership fee for both Avid
Golfers and Business Golfers?
Class Concepts – Practice Problems
 Solution – Two-Part Tariff
- MC = $40, Unit price for each round of golf is $40
- Inverse Demand for Golfers: P = 150 – 0.5Q
- Membership Fee = Golfers’ Consumer Surplus
- Membership Fee = ½ x (150 – 40) x 220 = ½ x 110 x 220
- Membership Fee = $12,100
 For Two Demand Curves
- Determine the number of Business Golfers and Avid Golfers.
- Generalize the number of rounds of golf consumed by both types of golfers (in terms of
Price).
- Calculate the Unit Revenue (in terms of Price).
- Find the Consumer Surplus of the Business Golfers, generalized for a single price.
- Calculate the Fixed Fee Revenue from both types (in terms of Price)
- Calculate the Costs for the quantity consumed
- Set MR = MC (with respect to P) and solve for P
- The solve for the Fixed Fee
Class Concepts – Practice Problems
 Knowledge Check
- Now that you’ve selected the membership and greens fee, you would like to set prices
for the driving range. Avid Golfers and Business Golfers have different preferences for
purchasing buckets of balls at the driving range. Those preferences are as follows
Bucket Size
Avid Golfers
Business Golfers
25
$3.00
$2.00
- Your cost for each 25 balls is $1.00
50
$5.25
$3.30
75
$6.75
$4.50
100
$8.00
$5.25
125
$8.50
$5.75
Class Concepts – Practice Problems
Bucket Size
Avid Golfers
Business Golfers
25
$3.00
$2.00
50
$5.25
$3.30
75
$6.75
$4.50
100
$8.00
$5.25
125
$8.50
$5.75
 Solution
- Translate the table into willingness to pay for each additional 25 balls
Bucket Size
Avid Golfers
Business Golfers
25
$3.00
$2.00
50
$2.25
$1.30
75
$1.50
$1.20
100
$1.25
$0.75
125
$0.50
$0.50
- The Large Bucket size will be 100 balls, since the marginal willingness to pay by the avid
golfers is $1.25 for the 76th to 100th balls, and only $0.50 for the 101st to 125th balls.
- The total benefit to the avid golfer of 100 balls is $8.00
- So, possible Small Bucket Sizes are: 25 balls, 50 balls, or 75 balls
Class Concepts – Practice Problems
Bucket Size
Avid Golfers
Business Golfers
25
$3.00
$2.00
50
$2.25
$1.30
75
$1.50
$1.20
100
$1.25
$0.75
125
$0.50
$0.50
 Solution
- The Large Bucket size will be 100 balls
- Possible Small Bucket Sizes are: 25 balls, 50 balls, or 75 balls
- Pricing for Small and Large Buckets
- 25 Ball Small Bucket: P = $2  Large Bucket, P = $8 – ($3 - $2) = $8 – 1 = $7
- Profit = $2 + $7 – ($1 x 5) = $9 - $5 = $4
- 50 Ball Small Bucket: P = $3.30  Large Bucket, P = $8 – ($5.25 - $3.3) = $8 – 1.95 = $6.05
- Profit = $3.50 + $6.05 – ($1 x 6) = $9.55 - $6 = $3.55
- 75 Ball Small Bucket: P = $4.50  Large Bucket, P = $8 – ($6.75 - $4.50) = $8 - $2.25 = $5.75
- Profit = $4.50 + $5.75 – ($1 x 7) = $10.25 - $7 = $3.25
- Sell Only Large Buckets to Avid Golfers for $8
- Profit = $8 – ($1 x 4) = $8 - $4 = $4
- So, the following two options are equally profitable:
- Small Bucket of 25 balls for $2, Large Bucket of 100 balls for $7
- Large Bucket of 100 balls ONLY for $8
Class Concepts – Practice Problems
Bucket Size
Avid Golfers
Business Golfers
25
$3.00
$2.00
50
$5.25
$3.30
75
$6.75
$4.50
100
$8.00
$5.25
125
$8.50
$5.75
 Solution
- Check Simple Pricing
- Sell 25 bucket to Avid for $3 or to Both for $2
- Profit (Selling to Avid) = ($3 x 1) – ($1 x 1) = $3 - $1 = $2
- Profit (Selling to Both) = ($2 x 2) – ($1 x 2) = $4 - $2 = $2
- Sell 50 bucket to Avid for $5.25 or Both for $3.30
- Profit (Selling to Avid) = ($5.25 x 1) – ($1 x 2) = $5.25 - $2 = $3.25
- Profit (Selling to Both) = ($3.30 x 2) – ($1 x 4) = $6.60 - $4 = $2.60
- Sell 75 bucket to Avid for $6.75 or Both for $4.50
- Profit (Selling to Avid) = ($6.75 x 1) – ($1 x 3) = $6.75 - $3 = $3.75
- Profit (Selling to Both) = ($4.50 x 2) – ($1 x 6) = $9 - $6 = $3
- Sell 100 bucket to Avid for $8 or to Both for $5.75
- Profit (Selling to Avid) = ($8.00 x 1) – ($1 x 4) = $8 - $4 = $4
- The above is the same as ‘Sell Only Large Buckets to Avid Golfers from prev. slide
- Profit (Selling to Both) = ($5.75 x 2) – ($1 x 8) = $11.50 - $8 = $3.50
- So, the options from the previous slide hold. These two options are most profitable:
- Selling a Small Bucket of 25 balls for $2 and a Large Bucket of 100 balls for $7 OR
- Selling a Large Bucket of 100 balls ONLY for $8