1. Microsoft Research 2013
4/26/2018 9:12 AM
Cross Validation, Freemium, Transfer Pricing, Intertemporal Substitution
Jacob LaRiviere
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

2. Validation set methodology
4/26/2018 9:12 AM
Validation set methodology
Train the model with a subset of the data
Test the model on the remaining data (the validation set)
What data to choose for training vs. test?
In a time-series dimension, it is natural to hold out the last year (or time period) of the data, to simulate predicting the future based on all past data. In most settings, however, we’ll randomly select our training/test sets.
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

3. 4/26/2018 9:12 AM
Cross-validation
A class of methods to do many training/test splits and average over all the runs
Here is a simple example of 5-fold cross validation. Gives 5 test sets  5 estimates of MSE.
The 5-fold CV estimate is obtained by averaging these values.
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

4. K-fold cross-validation
4/26/2018 9:12 AM
K-fold cross-validation
Split the data up into K “folds”. Iteratively leave fold k out of the training data and use it to test.
The more folds, the smaller each testing set is (more training data), but the more times we need to run the estimation procedure. Using rules of thumb like 5—10 folds is often utilized in practice. This can be done with a simple for loop in R
For generalized linear models, the cv.glm() function can be used to perform k-fold cross validation. For example, this code loops over 10 possible polynomial orders and computes the 10-fold cross-validated error in each step
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

5. Ridge and Lasso in R We will use the cv.glmnet package
4/26/2018 9:12 AM
Ridge and Lasso in R
We will use the cv.glmnet package
cv.glmnet() works for generalized linear models (OLS, Logit, etc.)
Lots of good tools for learning cross validation at Hastie’s website:
Look at example cross validation code on the website…
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

6. Now… Back to trees to verify intuition
4/26/2018 9:12 AM
Now… Back to trees to verify intuition
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

7. Freemium and transfer pricing
4/26/2018 9:12 AM
Freemium and transfer pricing
© 2013 Microsoft Corporation. All rights reserved. Microsoft, Windows, and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

8. Is freemium new?
Search query: “freemium”

9. Goals
Understand how the different forms of freemium are situated within a broader context of business models
Understand the core logic of pricing strategies grouped under the freemium umbrella
Understand supply and demand conditions that may make some form of freemium an attractive option

10. Differentiating via restrictions
Features
Capacity/usage
Time
Features
Pricing Tier
Basic
Free
+ Premium 1
Good
+ Premium 2
Better
+ Premium 3
Best
You know you’ve spoken too long

11. Examples in the market Features Capacity/usage Time
Free: 12 Months small VM
Premium: Pay-as-you-go IaaS
Free: Fed EZ
Premium: State, Higher income tax needs
Free: 10 articles per month
Premium: Unlimited
You know you’ve spoken too long
Free: 1 month
Premium: $10 per month
Free: 5GB
Premium:
Pay for storage packages GB >5
Free: Read
Premium: Edit

12. The business model landscape
Free
100%
I. Free
FB, Google, Yahoo
Free users determine value. Supplemental Biz Model Required
LinkedIn, OKCupid, Evernote
Zynga, NYTimes, Skype, Adobe
Free users add value to platform, supplemental biz models typically necessary
II. “Hard” Freemium
Free
(80-99%)
Pay
(1-20%)
Match.com, NetFlix,
TurboTax, WSJ
Product is free to attract users, ultimate goal is to get most users to pay
III. “Soft” Freemium
Free
~(<20%)
Pay
~(>80%)
Required for high marginal cost products/services
IV. Traditional
Pay
100%
Most stuff

13. Successful implementations
I. Free
All Users pay
nothing
Successful implementations
Failed or at risk
Free version “available forever”
No premium versions avail
Social networks
Search
Low-cost web publishing
Network television
Travel booking
Any offering that did not achieve sufficient scale
Many smartphone apps
GroupOn
High-cost web publishing
Companies pay
for User Access, Data or User Control
User Access (Advertising)
User Data (Analytics)
User Control (Administration)
Conditions to Success
Very low marginal costs, fixed costs recovered with scale
Massive scale (typically 100s of Millions+)
High user retention rates
Strong network effects and/or Two-sided markets creating lock-in
No Direct
Revenue
All
Revenue

14. Successful implementations
II. Hard Freemium
Users pay for
premium version(s) ONLY
Successful implementations
Failed or at risk
Power features
High capacity or usage
Free version “available forever”
Dating sites
Social networks
Communications
Adobe PDF
Job search
Undifferentiated apps/software
Online version of traditional newspapers
Zynga?
Spotify (unprofitable with 75M users, 20M paid)?
Dropbox?
Companies pay
for User Access, Data or User Control
User Access (Advertising)
User Data (Analytics)
User Control (Administration)
Conditions to Success
Similar to free conditions
Frictionless Path to Premium + Product Differentiation => Conversions
Some
Revenue
Some
Revenue

15. Successful implementations
III. Soft Freemium
Most users eventually pay
Successful implementations
Failed or at risk
Free version available is limited by time (and/or capacity, features, or usage)
Most users will convert to premium once they “understand” the value
Free trials in many contexts
Cloud computing
Software (e.g. TurboTax, Office)
Undifferentiated products that people abandon when the free period expires
Premium version does not offer enough value vs. the free alternatives
Product differentiation can further segment users
Paths to conversion free to first tier and then to more specialized offerings
Conversion is “within the product”
Conditions to Success
Learning and discovery (product-specific skills and comfort level)
Other product specific investments (e.g. engineering, stored files)
“Take a hostage”  create switching costs and dampen competition for the high version(s) of the product
All
Revenue
More
Revenue

16. Successful implementations
IV. Traditional
All users pay
Successful implementations
Failed or at risk
Licenses and traditional goods: have lifetime usage rights
Subscription/DRM limits to usage on time dimension
Traditional economic output
Goods with free substitutes (e.g. newspapers vs. free websites, most paid apps have very few downloads)
Stuff people don’t want
Product differentiation can further segment users
Segmentation usually happens at time of purchase
Conditions to Success
You make a good product (and/or have a great strategy)
Limited competition from free alternatives
Consumers accustomed to paying for the good/service
Traditional cost structures (e.g. marginal cost not close to zero)
All
Revenue
More
Revenue

17. Traditional businesses and freemium
Tension between profitable legacy biz and maintaining dominant user base ?
Free
Pay
Competitive/disruptive pressure of free offerings in the space v1
Good
Soft freemium to attract more customers v2
Better v3
Best
Desire to take advantage of benefits of freemium v1
Most firms start in the traditional model
Good v2
Better v3
Best

18. Freemium requires within-product conversion paths
Goal is to minimize frictions by engineering discoverable features to convert users to more profitable versions of the product w/ minimal hassle
Frictions to convert
1) entering payment information
2) paid features hard to find
3) higher tier versions cannot be “unlocked” from within the product
Free
Free
Pay v1 v2 v3 v1 v2 v3

19. Opening paths via targeted offers and “unlocking”
Un-targeted offers provide a freebie to “everyone”
Paying users have to support a larger base of freebies
Offer restrictions, such as free trials that have eligibility triggers based on platform usage can greatly limit costs, with minimal damage to conversion rates
“Unlockable features” that can are surfaced within the “low version” can be powerful drivers of conversions. Usage credits can be used to allow free unlocking for limited time

20. The “growing up rich” problem
Traditional, profitable products generally had versions, e.g. good-better-best, that are chosen at time of purchase. Little/zero effort to upsell users from within the product
“Grow up rich” because the “low version” is profitable
In freemium, low version loses money! Have be very tactical about within product upsell.
Products that make freemium work efficiently eke out every last conversion (targeted offers, unlocking features, frictionless upgrades) as part of the core UX in the product

21. Key Takeaways Free & Hard Freemium success stories
Requirements: massive scale, low marginal costs
Good to have: strong networks effects, two-sided markets
Supplemental monetization models required
Know where you are and where you are going
Legacy businesses are being pressured towards free, pushed “up the board”
New businesses push for a larger fraction of paying user, trying to move “down the board”
Maximize your current position
Engineer the product to convert users to higher versions with identified segments in mind
Minimize frictions along conversion paths
“Freemium” is not a single strategy: different variations have fundamentally different requirements for success

22. A simple freemium model: Goals
Introduce a formal framework to evaluate and monitor freemium pricing strategies. This framework extends the material we laid out in the Introduction to Freemium.
Set out the key parameters in this model that drive KPIs and discuss how to estimate these relationships.
Discuss methods that help freemium implementations succeed in practice

23. Model description
Model captures simplified instances of the business models in our landscape.
We assume there are at most two “versions” of the product, high 𝒉 (paid version) and low (𝒍).
𝑵 potential consumers. Product attributes denoted 𝑎 ℎ , 𝑎 𝑙 .
The price of the high version is given by 𝑝 ℎ The low version has price 𝑝 𝑙 (=0 for freemium), firm earns 𝑚 𝑙 per user of the low version ( 𝑝 𝑙 plus advertising and related channels).
Customers can directly buy the paid version first or start with the free version and “convert” up, in the case when 𝑝 𝑙 =0
1. direct buy rate 𝒃 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉
2. low version acquisition rate 𝒂 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉
3. conversion rate 𝒄 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉

24. Model dynamics 1. direct buy rate 𝒃 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉
2. low version acquisition rate 𝒂 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉
3. conversion rate 𝒄 𝒂 𝒍 , 𝒂 𝒉 ,𝒑 𝒍 , 𝒑 𝒉
Impact to:
Introduce low version
High price drops
Low Version
Attributes Improve
High Version
Acquisition Rate é
(maybe é)
Conversation Rate
new ê
Direct buy rate
 Offsetting
Dynamics
Offsetting

25. KPIs in the simple model
User base: 𝑵×(𝑎+𝑏) (if only paid version, 𝑎=0, free trial 𝑏=0)
Revenue at any point in time
: 𝑵×𝑎×(1−𝑐) × 𝑚 𝑙 + 𝑵×𝑎×𝑐 +(𝑵×𝑏) × 𝑝 ℎ
Costs: 𝐹𝑖𝑥𝑒𝑑+𝑚𝑐×[𝑁× 𝑎+𝑏 ]
# of low users
# of paid users who convert from low
# of paid users buy direct

26. KPIs in the simple model
User base: 𝑵×(𝑎+𝑏) (if only paid version, 𝑎=0)
Revenue: 𝑵×𝑎×(1−𝑐) × 𝑚 𝑙 + 𝑵×𝑎×𝑐 +(𝑵×𝑏) × 𝑝 ℎ
𝑑𝑎 𝑑 𝑝 𝑙 “change in acquisition rate based on change in price of low”. When 𝑑𝑎 𝑑 𝑝 𝑙 is very high at low prices then freemium may be attractive.
If 𝑐≫𝑏, this means very few people buy the high version without experiencing the low version  freemium may be attractive
In a fancier model: network effects, learning, referrals
# of low users
# of paid users who convert from low
# of paid users buy direct

27. Free trial example: “Netflix”
Low version: free 1 month trial, high version: subscription $10 per month. Assume customers stay on for average of 12 months. Marginal cost is $5 per month. Assume w/ free version:
𝑎=0.3, 𝑐=0.7, 𝑚 ℎ =0, 𝑏=0
Conversion rate is 70%, but is soft freemium optimal?
Profit w/ soft freemium: 𝑁∗.3∗.7∗ 11∗ 10−5 −𝑁∗.3∗5−FC=12.15𝑁−𝐹𝐶
Profit w/ paid only: 𝑁∗𝑏∗ 120−60 −𝐹𝐶=𝑁∗𝑏∗60−𝐹𝐶
Freemium optimal if: 12.15𝑁>60∗𝑁∗𝑏 → 𝟎.𝟏𝟔𝟕>𝒃
With freemium 21% of people eventually pay. w/o freemium you get b.
if b<16.7%  do freemium.
Marginal profits from users who convert
Marginal costs of free month of service

28. Ex. continued Costs of offering freemium:
Users who would have paid for the first month get it free.
Users who don’t convert get a free month
Note: unrealistic for 𝒃>𝟎.𝟐𝟏 (market share with freemium) since this would imply more users buy the paid directly than w/ free trial
If we assume customer duration of 4 years, the threshold becomes 19.9%  only in a narrow band of % would we not do the free trial.
As customer lifetime value increases, incentive to give a free trial does so as well. the buy rate threshold for offering freemium increases (the window where is not optimal gets smaller)

29. Varying customer lifetime
X-axis: varies the assumed average lifetime of the customer
The threshold converges to 0.21
No free trial
Do free trial

30. Varying marginal costs
X-axis: varies the marginal cost from 10% to 93% of the purchase price assuming customer lifetime of 24 months
As marginal costs increase, freemium window shrinks. At high marginal costs, “direct buy rate” has to be incredibly low to rationalize a freemium strategy

31. Summary
Freemium can be attractive when a certain set of demand and supply characteristics hold
Segments. Ideally freemium strategy turns “low types” into “high types”
Relatively low marginal cost of provision
Low version encourages adoption but is insufficient for high-value types. High feature set encourages conversion for these types.
High returns from a large user base.
We gave formal model that can be used to evaluate scenarios, determine if a freemium strategy is optimal and monitor progress.
We discussed extensions of this model that more accurately capture consumer preferences

32. Transfer Pricing & more
Jacob LaRiviere & Justin Rao
April 20, 2016
Econ 404, Spring 2016

33. organization Transfer Pricing Interpretation versus Prediction
Monopolistic Competition

34. Transfer Pricing: Fact- Firms often have many vertical levels
Transfer Pricing: Fact- Firms often have many vertical levels. Ex 1: MSFT makes the Windows operating system and the Surface device. Ex 2: Amazon sells goods on website (amazon.com) and sells remote computing (AWS) As a result, firms often sell products to themselves. Question: How should they go about setting internal prices or “transfer prices”; setting prices within a firm! Assumptions 1) We’ll model this as a two stage game. 2) For simplicity, assume the firm is a monopolist in the retail market. 3) Model each “level” of the firm as an independent agent maximizing own profit. 4) We’ll extend to other cases soon; this model offers powerful insights.

35. Monopolists, like all firms, should price to maximize profits.
As a result, the demand curve and costs matter
Monopolist doesn’t have to worry about competitors -> set Q such that MC = MR

36. Monopolist’s math max 𝑞 𝜋 𝑞 =𝑃 𝑞 𝑞 −𝑇𝐶(𝑞)
f.o.c.: 𝑃 ′ 𝑞 𝑞+𝑃 𝑞 −𝑇 𝐶 ′ 𝑞 =0
Maximizes profits (TR – TC) by setting a quantity and charging needed price to have market clear
e.g., price is a function on quantity: P(q) and note the TR = P(q)*q
𝑃 ′ 𝑞 𝑞+𝑃 𝑞 −𝑀𝐶 𝑞 =0
𝑃 ′ 𝑞 𝑞+𝑃 𝑞 𝑀𝑅(𝑞) =𝑀𝐶 𝑞
NOTE: P’(q) < 0 since demand slopes downward
𝑃 ′ 𝑞 𝑞
Intensive margin loss as q increases
𝑃 𝑞
Extensive margin gain as q increases

37. Upstream Monopolist’s math
Previously this is the point we introduced Lerner equation. Now lets consider an upstream monopolist selling to a downstream monopolist.
Can happen
within a single firm (Amazon/MSFT)
across firms (Content & Content Providers)

38. Upstream Monopolist’s math
Previously this is the point we introduced Lerner equation. Now lets consider an upstream monopolist selling to a downstream monopolist.
Can happen
within a single firm (Amazon/MSFT)
across firms (Content & Content Providers)
Rather than a competitive up and downstream market lets just focus on the problem in market 1
U1 is upstream firm
D1 is downstream firm
Firm 2 Monopoly
Firm 1 Monopoly

39. D1’s problem: Same as before
D1 will take whatever the costs they pay to U1 as given then price to maximize profits.
max 𝑞 𝜋 𝑞 =𝑃 𝑞 𝑞 −𝑇𝐶(𝑞)
f.o.c.: 𝑃 ′ 𝑞 𝑞+𝑃 𝑞 −𝑇 𝐶 ′ 𝑞 =0
𝑃 ′ 𝑞 𝑞+𝑃 𝑞 −𝑀𝐶 𝑞 =0
𝑃 ′ 𝑞 𝑞+𝑃 𝑞 𝑀𝑅(𝑞) = 𝐶 𝑈1 = 𝑃 𝑈1
NOTE: Irrespective of the upstream/downstream problem, this is bad for welfare [W(q)].
Extra term (− 𝑃 ′ 𝑞𝑚 𝑞𝑚) represents the welfare gains to increasing output by an additional unit; creates deadweight loss.
Social Optimum → W q =u q −c q → W ′ q∗ = u ′ q∗ − c ′ q∗ =MB q∗ −𝑀𝐶 q∗ =𝑃 𝑞∗ −𝑐=0
Monopoly equilibrium →𝑃 𝑞𝑚 −𝑐=− 𝑃 ′ 𝑞𝑚 𝑞𝑚

40. U1’s problem: Novel max 𝑞𝐷1 𝜋 𝑞𝐷1 =𝑃 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
U1 understands the D1 will price as a monopolist.
As a result, their effective demand curve is the MR curve of D1.
max 𝑞𝐷1 𝜋 𝑞𝐷1 =𝑃 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
𝜋 𝑞𝐷1 =𝑀𝑅 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
𝜋 𝑞𝐷1 =[ 𝑃 ′ 𝑞∗(𝑐) 𝑞∗+𝑃 𝑞∗ ]𝑞𝐷1 𝑀𝑅(𝑞) −𝑇𝐶 𝑞𝐷1

41. U1’s problem: Novel max 𝑞𝐷1 𝜋 𝑞𝐷1 =𝑃 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
U1 understands the D1 will price as a monopolist.
As a result, their effective demand curve is the MR curve of D1.
max 𝑞𝐷1 𝜋 𝑞𝐷1 =𝑃 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
𝜋 𝑞𝐷1 =𝑀𝑅 𝑞𝐷1 𝑞𝐷1−𝑇𝐶 𝑞𝐷1
𝜋 𝑞𝐷1 =[ 𝑃 ′ 𝑞∗ 𝑐 𝑞∗+𝑃 𝑞∗ ]𝑞𝐷1 𝑀𝑅 𝑞 −𝑇𝐶 𝑞𝐷1
𝜋 ′ 𝑞𝐷1 =𝑀 𝑅 ′ 𝑞𝐷1 𝑞𝐷1+𝑀 𝑅 ′ 𝑞𝐷1 −𝑀𝐶 𝑞𝐷1 =0
MRDM

42. Double Marginalization Analysis
Retail
Price
Retail Demand 12
Quantity 12

43. Double Marginalization Problem
Retail
Price 12
Marginal Revenue
Quantity 12

44. Double Marginalization Problem
Retail
Price 12 4
Marginal Cost
QC = 8
Quantity 12

45. Double Marginalization Problem
Retail
Price 12
Marginal Cost QC
QC = 8
Quantity
QM = 4 12

46. Double Marginalization Problem
Retail
Price
Wholesale profits 12
Wholesale Price 8
Wholesale
Margin 4
Marginal Cost
QC = 8
Quantity 12
QM = 4
QDM =2

47. Double Marginalization Problem
Retail
Price
Retail profits 12
Retail
Margin 10
Wholesale Price 8 4
Marginal Cost
QC = 8
Quantity 12
QM = 4
QDM = 2

48. Consumers Are Worse Off Too
Retail
Price
Surplus Under double marginalization 12
Wholesale Price
Marginal Cost QC
Quantity
QDM 12 QM

49. Consumers Are Worse Off Too
Retail
Price
Surplus Under monopoly 12
Wholesale Price
Marginal Cost QC
Quantity
QDM 12 QM

50. Contractual Solutions
Using “two-part tariffs” can overcome the double marginalization problem.
Recipe for Two-Part Tariffs
Part 1: Maximize value created
Part 2: Use the fixed fee to capture value

51. Two-Part Tariffs in Action
Part 1: Maximize Value Created
The wholesaler can set the wholesale price at marginal cost
This maximizes the size of industry profits
Part 2: Capture Downstream firm’s Value
It can then use the fixed fee to capture the bulk of the surplus of downstream firm.
Rent extraction may induce downstream firm to underprovide support and costly services such as advertising – leads us to agency issues

52. Consumers get back to first best; wealth transfer to upstream firm
Retail
Price
Consumer Surplus Under monopoly 12
Wholesale Price
Fixed fee
Marginal Cost QC
Quantity
QDM 12 QM

53. Double Agency Solution Take away
Ex: Simple linear profit share (approximates MC) plus fixed fee contract
Works well but need to observe profits X…..
Hollywood Video Case: When Video Market started to decline Hollywood Video started “off the books” rentals
Thus avoiding the profit sharing – caught and sued
How easy is this to detect? If difficult then a franchise contract will not work

54. Case study: Video (VCR era) Distribution
Hollywood studios have monopoly content
Priced tapes high $60~$100 for sale to rental stores
About 20,000 local rental stores but each one has some local market power due to travel costs
Double marginalization issue: stores buy too few copies
Introduction Rentrack system: share revenues on rentals
New contract $20 plus 45% rental revenues go to studio
Increased sales and rentals both sides profits go up 10%
(Mortimer 2008)

55. Transfer Pricing
So, what should MSFT and Amazon do when selling products within the firm?
Always have upstream firm price at MC when selling within firm.
If there is an implicit subsidy (e.g., Amazon.com helps AWS sales) then that can be handled with a side payment between different parts of the company.
NOTE: opposite could occur where AWS could power some sales engines which compete with amazon.com. In this case there is a negative side payment.

56. Intertemporal Substitution We saw that the price today can affect demand tomorrow for a durable good This is also true of non-durable goods which are storable. e.g., Costco/buying in bulk. Question: How does this fit in to our larger pricing framework?

57. A Simple Model of Consumers
𝐸𝑡 𝑈 =𝑈 𝑐𝑡 +𝛿𝑈 𝑐𝑡
Where is how much future utility is discounted.
NOTE: with respect to NPV
𝛿=1/(1+𝑟)
Vector of ones, vector of inverse elasticities
𝑉𝑡 1+𝑟 = 𝑉 𝑡+1 → 𝑉 𝑡 = 𝑉 𝑡+1 /(1+r)

58. A Simple Model of Consumers
Think about implications for consumers which maximize NPV of utility
𝑈=𝑣−𝑝 if purchases (e.g., 𝑈=𝜃𝑠−𝑝)
=0 if no purchase
Durable good: Buy at t=1 or wait until t=2?
𝑣−𝑝1+𝛿𝑣 ~ 0+𝛿(𝑣−𝑝2)
Vector of ones, vector of inverse elasticities

59. A Simple Model of Consumers
Trade off between impatience (r) and relative price differences.
Firms know this and so do consumers.
Common knowledge trade-offs
Durable goods case: buy when it first comes out or wait
p1 versus p2 conditional on v and r
Vector of ones, vector of inverse elasticities

60. A Simple Model of Consumers
Trade off between impatience (r) and relative price differences.
Firms know this and so do consumers.
Common knowledge trade-offs
Durable goods case: buy when it first comes out or wait
p1 versus p2 conditional on v and r
Non-Durable goods case: cost of storage versus savings
p1 versus p2 conditional storage costs (a form of transportation costs t)
Vector of ones, vector of inverse elasticities

61. A Simple Model of Consumers
Think about implications for consumers which maximize NPV of utility
𝑈=𝑣−𝑝 if purchases (e.g., 𝑈=𝜃𝑠−𝑝)
=0 if no purchase
Durable good: Buy at t=1 or wait until t=2?
𝑣−𝑝1+𝛿𝑣 ~ 0+𝛿(𝑣−𝑝2)
Vector of ones, vector of inverse elasticities
Non-Durable good: Buy once and hold or buy in each period?
𝑣−2𝑝1 −𝑡+𝛿𝑣 ~𝑣−𝑝1+𝛿(𝑣−𝑝2)

62. A Simple Model of Consumers
We’ve done this before…
Think of the same product in two separate periods as two unique products.
What was i and j we can call 1 and 2
Vector of ones, vector of inverse elasticities