Transparency and
Credible Commitment:
Most-Favored-Customer Price Differentiation
James Stodder and Houman Younessi
Lally School of Management, Dept. of Engineering & Science
Rensselaer Polytechnic Institute at Hartford
Hartford, Connecticut, USA
7/12/2016
1
Recent Stock History
http://www.lse.co.uk/funds/exchange-traded-funds/KFG0dow_jones_us_pharmaceuticals_index/performance/?sc=
7/12/2016
2
Pharma Futures Report, 2007 (www.pharmafutures.org):
Challenge 7: To Respond Appropriately to Demands for
More Equitable and Extensive Access to Medicines
• As emerging markets become more commercially interesting they pose a
two-pronged challenge to the industry, which requires a significantly
different management skill set from those needed in industrialised
markets.
• The first prong requires industry to develop a pricing policy that captures
not only the premium markets but permits an extension of volume sales to
a wider customer base. And this must be achieved while simultaneously
preventing negative impacts – such as reference pricing or inappropriate
parallel trade – in established markets.
• The second prong is to respond to demand for access to medicines in
these markets (and in countries that are less commercially promising) in such
a way as to defend the industry’s commercial interests while at the same time
persuading key decision makers that the response is sufficient to overcome
mistrust, minimize criticism and extend licence to operate.
7/12/2016
3
Separable Markets:
3rd Degree Price Discrimination
Domestic Examples
• Airline Tickets
• Starbucks Prices, Different Cities
• Student, Senior Discounts for Movies
• Dry Cleaning for Men and Women
• College Scholarships
• Pharmaceuticals*
(1)
(2)
www.merck.com/merckhelps/ ,
www.pfizerhelpfulanswers.com/pages/Find/findall.aspx
7/12/2016
4
International Price Discrimination
Examples:
• Starbucks Coffee
• Automobiles
• Software, Movies, Textbooks!
• Consumer Electronics
• Pharmaceuticals*
(1) www.merck.com/cr/enabling_access/developing_world/
7/12/2016
5
For Successful Price Discrimination,
One Needs:



Price-Setting Power
Differing Price Sensitivities
Barriers to Resale, can be
• Practical (hard to re-sell your senior
discount meal), or
• Legal (Big Pharma attempts to prohibit
‘re-importation,’ a.k.a, ‘parallel trade’)
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6
“Mail-in Rebates” Combat Reselling:




Sell to the broad public at Single (High) Price,
but then…
Give targeted customers Personalized and
“Lump-sum” Rebate; i.e., one that cannot be
changed by the amount purchased (e.g., based
on the customer’s past income).
Personalized means the company can ask for
evidence of direct consumption, and refuse refills
to those shown to have resold.
Lump-sum (or equivalently, limited quantities)
means that any new units of the good must be
bought at the regular price, and so are not
vulnerable to discounted reselling.
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7
However, in solving One Problem,
the Lump-Sum Rebate gives
Rise to Another Problem:


Larger Customers will now try to
Re-Negotiate Larger Rebates;
e.g., ‘reference pricing’.
How can a Company defend against
such pressures?
7/12/2016
8
Patricia Danzon (Wharton) idea on
How to Prevent Re-negotiation:


Keep Lump-sum Rebates Secret
But how good are Governments
at keeping other secrets?
7/12/2016
9
Consider a common device to defend
a single (monopolistic) price:
A Most-Favored-Customer (MFC) Clause:


Any Discount given to one customer must
be given to All MFCs.
A MFC Clause makes highly credible the
seller’s promise to not renegotiate prices –
since to do so would be very expensive.
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10
Most-Favored-Customer (MFC)
+Price Differentiation (PD) = MFCPD



Our idea is that the non-negotiable credibility
of MFC can add transparency to PD to create
MFCPD.
Customers are most-favored in the sense that
they see no one gets a better formula for
their income-based rebate – even though they
have different incomes.
Giving a better formula to anyone would mean
giving that same formula to all – with a big
impact on profits.
7/12/2016
11
Derivation: Linear Demand Function
Demand for quantity Qi from segment i:
Qi = Popi{α – βPi + γYi }
where Popi is Population, Pi is Price,
Yi is income to group i, and
α, β, γ > 0 are Market Parameters
to be Estimated.
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12
Profit Maximizing Price for group i:
If Marginal Cost = μ, then Comapany Profits from
group i:
π i = (Pi – μ)Q i
= (Pi – μ)Popi{α + γYi – βPi}
 First Order Condition for Profit Max =
Published Formula for Price After Rebate:
P*i = (α + γYi +
+ μβ)/2β
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13
Full Incentive Compatibility


A MFCPD clause is fully incentive compatible –
i.e., will stop the Company from allowing a pricecut with group i (which costs it ∆πi , even though it
avoids threatened ∆ ~i )
when the resulting decrease in profits from other
groups ∑ j≠i ∆πj is so large that (in absolute values):
|∆πi + ∑ j≠i ∆πj | > | ∆~i |
from asked-for
lower price by i
7/12/2016
from lower price from threat of curtailed
impact on all j ≠ i
purchases by i
14
To overcome Incentive Compatibility
(so inequality reverses),
Group i would need a Very Large
Threat Multiplier (τi)
~

∆πj| < |∆ i |
|∆πi| + |∑ j≠i
then, dividing by |∆πi|, we have
0 < 1 + (∑ j≠i ∆πj) /∆πi < ∆~i /∆πi ≡ τi
Effective Threat Multiplier
7/12/2016
15
Size of the Threat Multiplier


Even for the largest economy (US), τi is very
substantial.
In our simulation price discrimination by
country, even the US accounts for only 38% of
all Company profits.
1 + (∑ j≠i ∆πj)/∆πi < ~i /∆πi ≡ τi
~
1 + (62% / 38%) = 2.66 <  i /∆πi ≡ τi
7/12/2016
16
THEOREM on “Fineness” of Price Discrimination:
Finer Price Disc =>
Fewer “corner solutions” =>
More Stable Threat Multiplier
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17
Summary of Simulation Results:
Single World Monopoly Price vs. Two Levels of Discriminating Prices *
(Average)
Total Producer Consumer
Total
Price
Quantity Surplus
Surplus Surplus
$4.72
3,506
$16,181
$15,807 $31,988
1 Price for Whole World
$1.68
6,609
$18,943
$15,787 $34,730
1 Price for Each Country
$1.56
7,016
$22,938
$11,469 $34,408
1 Price for Each Quintile
within each Country
* All Figures except Price in units of one million
7/12/2016
18
Size of Threat Multiplier matters because:
Any Threat to Company’s Profits Implies a
Proportional Threat to
Group i’s Own Surplus

If group i’s demand is linear, we show that its
hoped-for gain in consumer surplus, ∆θi, if
backed up by threat multiplier τi
– poses a proportional threat to its own surplus:
~
~
|  i | > τi |∆πi | => | i | > τi ∆θi
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19
No-Negotiation is Sub-Game Perfect
(∆θi , ∆πi + ∑ j≠i ∆πj )
Grants
Price Cut
The Company
Threatens
Curtailment
Imposes ( - τ∆θi , τ∆πi )
Curtailment
Refuses
Price Cut
Country i
Country i
(0, 0)
Accepts
Original Price
7/12/2016
(-ε, 0)
Accepts
Original Price
20
No-Negotiation is Sub-Game Perfect
(∆θi , ∆πi + ∑ j≠i ∆πj )
Grants
Price Cut
The Company
Threatens
Curtailment
Imposes ( - τ∆θi , τ∆πi )
Curtailment
Refuses
Price Cut
Country i
Country i
(0, 0)
Accepts
Original Price
7/12/2016
(-ε, 0)
Accepts
Original Price
21
No-Negotiation is Sub-Game Perfect
(∆θi , ∆πi + ∑ j≠i ∆πj )
Grants
Price Cut
The Company
Threatens
Curtailment
Imposes ( - τ∆θi , τ∆πi )
Curtailment
Refuses
Price Cut
Country i
Country i
(0, 0)
Accepts
Original Price
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(-ε, 0)
Accepts
Original Price
22
No-Negotiation is Sub-Game Perfect
(∆θi , ∆πi + ∑ j≠i ∆πj )
Grants
Price Cut
The Company
Threatens
Curtailment
Imposes ( - τ∆θi , τ∆πi )
Curtailment
Refuses
Price Cut
Country i
Country i
(0, 0)
Accepts
Original Price
7/12/2016
(-ε, 0)
Accepts
Original Price
23
No-Negotiation is Sub-Game Perfect
(∆θi , ∆πi + ∑ j≠i ∆πj )
Grants
Price Cut
The Company
Threatens
Curtailment
Imposes ( - τ∆θi , τ∆πi )
Curtailment
Refuses
Price Cut
Country i
Country i
(0, 0)
Accepts
Original Price
7/12/2016
(-ε, 0)
Accepts
Original Price
24
What about Imperfect Knowledge?
Sub-Game Perf. Eq. does not apply.
Call pi group i’s subjective probability of the Company’s
acceding to its threat. Then a risk-neutral i should make threat
if and only if the hoped-for gain in surplus is positive:
pi ∆θi + (1- pi) τi (-∆θi) > 0
=> pi > (1- pi) τi, and τi > 2.66
=> pi /(1- pi) > τi > 2.66
=>
7/12/2016
pi > 72.7%
25
Summary of Simulation Results:
Single World Monopoly Price vs. Two Levels of Discriminating Prices *
(Average)
Total Producer Consumer
Total
Price
Quantity Surplus
Surplus Surplus
$4.72
3,506
$16,181
$15,807 $31,988
1 Price for Whole World
$1.68
6,609
$18,943
$15,787 $34,730
1 Price for Each Country
$1.56
7,016
$22,938
$11,469 $34,408
1 Price for Each Quintile
within each Country
* All Figures except Price in units of one million
7/12/2016
26
World Monopoly Price –
Few Countries Can Purchase
Table 2: Thirty-two Countries that Can Purchase Good at Monopoly World Price:
Number of Countries (Number of Quintiles) That Can Purchase
5 (All 5) GDPpc
Denmark $47,984
Japan $35,757
Luxembourg $80,288
Norway $64,193
Switzerland $50,532
Avg GDPpc $55,751
5 (Top 3) GDPpc
Hong Kong $25,493
Italy $30,200
New Zealand $26,464
Singapore $26,836
Spain $27,226
Avg GDPpc $27,244
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12 (Top 4) GDPpc
(Top 4, cont.) GDPpc
Australia $34,740
Germany $33,854
Austria $37,117
Ireland $48,604
Belgium $35,712
Netherlands $38,618
Canada $35,133
Sweden $39,694
Finland $37,504 United Kingdom $37,023
France $33,918
United States $42,000
Avg GDPpc $35,687
5 (Top 2) GDPpc
5 (Top 1) GDPpc
Greece $20,327
Chile $ 7,124
Israel $19,248 Czech Republic $12,152
Korea $16,308
Estonia $ 9,727
Portugal $17,456
Hungary $10,814
Slovenia $16,986
Mexico $ 7,298
Avg GDPpc $18,065
Avg GDPpc $ 9,423
27
Single World Monopoly Price, Distributional Effect on Three Countries*
Country_i
One-fifth of GDPpc_i
Population
P*i
Q*i Producer Consumer
Total
Surplus
Surplus Surplus
Canada1
6.45
$12,657
$4.72
0
$0
$0
$0
Canada2
"__"
$22,354
"__"
5
$22
$2
$24
Canada3
"__"
$30,180
"__"
15
$69
$17
$86
Canada4
"__"
$40,322
"__"
28
$129
$61
$190
Canada5
"__"
$70,155
"__"
66
$307
$343
$650
Canadian GDPpc:
$35,133
Totals:
114
$528
$423
$951
Mexico1
21.06
$1,571
$4.72
0
$0
$0
$0
Mexico2
"___"
$3,025
"___"
0
$0
$0
$0
Mexico3
"___"
$4,612
"___"
0
$0
$0
$0
Mexico4
"___"
$7,186
"___"
0
$0
$0
$0
Mexico5
"___"
$20,094
"___"
6
$30
$1
$30
Mexican GDPpc:
$7,298
Totals:
6
$30
$1
$31
United States1
59.31
$11,416
$4.72
-
$0
$0
$0
United States2
"___"
$22,432
"___"
46
$211
$18
$229
United States3
"___"
$32,887
"___"
170
$784
$243
$1,026
United States4
"___"
$47,053
"___"
338
$1,559
$962
$2,521
United States5
"___"
$96,214
"___"
921
$4,251
$7,150
$11,401
United States GDPpc:
$42,000
Totals:
1,474
$6,804
$8,373
$15,177
* All figures except Price and GDP per-capita in units of one million.
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28
Price Discrimination by Country, Distributional Effect on 3 Countries*
One-fifth of
Population
Canada
6.45
6.45
6.45
6.45
6.45
Canadian_GDPpc
GDPpc_i
P*i
Q*i
Producer
Surplus
Consumer
Surplus
Total
Surplus
$
$
$
$
$
$
12,657
22,354
30,180
40,322
70,155
35,133
$
4.63
$
4.63
$
4.63
$
4.63
$
4.63
Totals:
5
16
29
67
117
$0
$25
$70
$129
$304
$528
$0
$2
$19
$64
$349
$434
$0
$27
$89
$193
$653
$962
$
$
$
$
$
$
1,571
3,025
4,612
7,186
20,094
7,298
$
1.28
$
1.28
$
1.28
$
1.28
$
1.28
Totals:
1
7
14
24
79
124
$1
$8
$16
$29
$93
$147
$0
$1
$4
$14
$147
$167
$1
$9
$20
$43
$240
$313
$
$
$
$
$
$
11,416
22,432
32,887
47,053
96,214
42,000
$
6.42
$
6.42
$
6.42
$
6.42
$
6.42
Totals:
69
237
820
1,125
$0
$0
$433
$1,496
$5,182
$7,111
$0
$0
$40
$472
$5,665
$6,176
$0
$0
$473
$1,968
$10,847
$13,288
Mexico
21.06
21.06
21.06
21.06
21.06
Mexican_GDPpc
United States
59.31
59.31
59.31
59.31
59.31
United States_GDPpc
* All figures except Price and GDP per-capita in units of one million.
7/12/2016
29
One Price for Each Quintile, Distributional Effect within Three Countries*
One-fifth of
Country_i Population
Canada1
6.45
Canada2
"__"
Canada3
"__"
Canada4
"__"
Canada5
"__"
Canadian GDPpc:
Mexico1
21.06
Mexico2
"___"
Mexico3
"___"
Mexico4
"___"
Mexico5
"___"
Mexican GDPpc:
United States1
59.31
United States2
"___"
United States3
"___"
United States4
"___"
United States5
"___"
United States GDPpc:
GDPpc_i
$12,657
$22,354
$30,180
$40,322
$70,155
$35,133
$1,571
$3,025
$4,612
$7,186
$20,094
$7,298
$11,416
$22,432
$32,887
$47,053
$96,214
$42,000
P*i
$1.82
$2.79
$3.57
$4.58
$7.57
Totals:
$0.71
$0.85
$1.01
$1.27
$2.56
Totals:
$ 1.69
$ 2.79
$ 3.84
$ 5.26
$10.17
Totals:
Q*i
11
17
22
29
48
128
13
16
19
25
52
124
94
160
222
306
597
1,379
Producer
Surplus
$19
$46
$78
$130
$359
$632
$8
$12
$17
$29
$127
$193
$150
$430
$829
$1,576
$6,016
$9,002
Consumer
Surplus
$9
$23
$39
$65
$180
$316
$4
$6
$9
$14
$64
$97
$75
$215
$415
$788
$3,008
$4,501
Total
Surplus
$28
$70
$116
$194
$539
$948
$12
$18
$26
$43
$191
$290
$225
$645
$1,244
$2,365
$9,025
$13,503
* All Figures except Price and GDP per-capita in units of one million
7/12/2016
30
Percentage Changes in Producer Surplus (PS), Consumer Surplus (CS) and
Total Surplus (TS) for Moves in Pricing Schemes
7/12/2016
Moves from Single to
Country-Based Pricing
∆ PS
∆ CS
∆ TS
0%
0%
0%
10%
25%
11%
2%
8%
3%
0%
4%
1%
-1%
2%
0%
0%
2%
1%
Canada1
Canada2
Canada3
Canada4
Canada5
Total Canada:
Mexico1
Mexico2
Mexico3
Mexico4
Mexico5
Total Mexico:
United States1
United States2
United States3
United States4
United States5
Total U.S.:
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
215%
396%
0%
-100%
-45%
-4%
22%
5%
15,054%
17,070%
0%
-100%
-84%
-51%
-21%
-26%
687%
928%
0%
-100%
-54%
-22%
-5%
-12%
Total, All 3 Countries:
6%
-23%
-10%
Moves from Country to
Quintile-Based Pricing
∆ PS
∆ CS
∆ TS
∞
∞
∞
88%
10%
0%
18%
20%
806%
48%
10%
0%
37%
32%
909%
107%
2%
-49%
-27%
30,888%
436%
101%
2%
-57%
-42%
159%
31%
1%
-17%
-1%
1,239%
95%
29%
1%
-20%
-7%
∞
∞
∞
∞
∞
∞
91%
5%
16%
27%
947%
67%
-47%
-27%
163%
20%
-17%
2%
26%
-27%
1%
31
Consumer Surplus Comparisons of Pricing Schemes, by All Countries’ Quintile
Single World Monopoly Price
First
Second
Third
Fourth
Fifth
TOTAL,
Quintiles Quintiles Quintiles Quintiles Quintiles all Quintiles
$3
$91
$573
$2,007 $13,133
$15,807
OneSingle
PriceMonopoly
for Each Country
Price
$79
$195
$581
$1,893
$13,040
$15,787
One Price for Each Quintile
$418
$813
$1,304
$2,174
$6,760
$11,468
2,292%
114%
1%
-6%
-1%
0%
432%
316%
124%
15%
-48%
-27%
12,639%
791%
127%
8%
-49%
-27%
∆ from World to Country Prices
∆ from Country to Quintile Prices
∆ from World to Quintile Prices
* All Dollar Figures are in units of one million
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32
Figure 3: Countries with Improvement by Move from
World to Country-based Pricing
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33
Figure 5: Countries with Improvement by Move from
Country to Quintile-Based Prices, Lowest 3 or 4 Quintiles
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34
Fig. 2: World Consumer Surplus, by Quintile
$14,000
Single World Price
One Price Each Country
One Price Each Quintile
$12,000
Millions of $
$10,000
$8,000
$6,000
$4,000
$2,000
$0
1st Quintile
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2nd Quintile
3rd Quintile
4th Quintile
5th Quintile
35