Price Differentiation and Menu Costs in Credit Card Payments Marcos - - PowerPoint PPT Presentation

VIII Annual Seminar on Risk, Financial Stability and Banking

São Paulo August 8, 2013

Price Differentiation and Menu Costs in Credit Card Payments

Marcos Valli Jorge

Banco Central do Brasil

W ilfredo Leiva Maldonado

Catholic University of Brasilia

Market structure

( four-party schem e) ( four party schem e) market sides

h

p

Merchant Consumer

price

f m

merchant fee consumer fee

Acquirer Issuer

a

interchange fee g

2

Credit card scheme

set rules and act as switch and router

Main reference

• Rochet&Wright (JBF 2010) : “Credit card interchange fees”

Rochet&Wright (J F 0 0) : Credit card interchange fees

– “General tendency for merchants to adhere to the setting of a single price regardless of the form of payment ” single price regardless of the form of payment. – “Part of the reason for this is the no‐surcharge rules adopted by the credit card systems.” – “If retailers were able and willing to discriminate based on the If retailers were able and willing to discriminate based on the use of store credit, they maybe able to induce consumers to use credit cards and store credit efficiently.” – “One important direction for future research: to extend our model to allow retailers to offer different prices when model to allow retailers to offer different prices when consumers make use of store credit.”

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Main aspects of R&W ’s approach Main aspects of R&W s approach

• Model the credit functionality of a credit card: much of the
• Model the credit functionality of a credit card: much of the

existing literature treats payment card as debit card;

• Consider the store credit as a competitor of the credit card (in

addition to cash);

• Cardholders can not internalize retailers’ net avoided costs from

credit card usage (merchant fee minus cost of store credit); credit card usage (merchant fee minus cost of store credit);

• Model the excessive usage of credit cards: increase interchange

fee can reduce consumers aggregated welfare;

4

Results under non surcharge rule g

Rochet&W right ( JBF 2 0 1 0 )

• Single price equilibrium;
• Interchange fee is not neutral:
• Interchange fee is not neutral:

– It affects card usage (real allocations); – There is an endogenous cap:

• The monopoly card network raise it to increase credit card

The monopoly card network raise it to increase credit card usage and maximize profit;

• If sufficiently high, merchants do not adhere to the credit

y g , card system;

• The cap value exceeds the level that maximizes consumer

The cap value exceeds the level that maximizes consumer surplus;

5

Results under non surcharge rule g

Rochet&W right ( JBF 2 0 1 0 )

• If regulators only care about consumer surplus:

– A conservative regulatory approach is to cap interchange fees A conservative regulatory approach is to cap interchange fees based on retailers’ net avoided costs from not having to provide credit themselves. – This always raises consumer surplus compared to the unregulated outcome sometimes to the point of maximizing unregulated outcome, sometimes to the point of maximizing consumer surplus.

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Consum er’s w elfare d i l i ilib i under single price equilibrium

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Methodology

• Three payment instruments: credit card, store credit and cash;
• Two types of purchases:

– ordinary purchases (deterministic, using any of the three instruments)

• rdinary purchases (deterministic, using any of the three instruments)

– extraordinary credit purchases (random, can not use cash);

• T o retailers disp te the market

here cons mers inc r in

• Two retailers dispute the market where consumers incur in

transportation costs (Hotelling competition);

• Compute:

– Consumers utilities; – Merchants market shares; – Merchants margins; – Merchants profits (margin x market share); Merchants profits (margin x market share);

• Apply first order conditions to obtain equilibrium prices;

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Model structure ith i diff ti ti w ith price differentiation

store credit costs

h

cB cS

random with c.d.f . H



product cost

pr

Merchant Consumer

x = proportion of

credit card owners

pc = pr + Δc

f = c I + π - a m = c A + a

merchant fee consumer fee

Acquirer Issuer

a

interchange fee profit margin

cI cA

credit card costs

9

Credit card Store credit

Hotelling com petition w ith transportation costs

T t ti t Transportation costs

t s .

1

t s .

2

Retailer 2 R t il 1 Consumer Retailer 2 Retailer 1

1

s

2

s

10

Distances

Store credit random cost faced by consum ers faced by consum ers ( ordinary purchases)

When credit card is not an option with a cost When credit card is an option with a benefit CB CB with a cost CB with a benefit cash credit f+Δc cash

H probability distribution

card store credit store credit f+Δc store credit 11 credit

Store credit random cost faced by consum ers faced by consum ers ( extraordinary purchases)

When credit card is not an option with a cost When credit card is an option with a benefit CB CB with a cost CB dit with a benefit credit f+Δc credit card

H probability distribution

store credit card store store credit f+Δc store credit 12 credit

I ndicators of acceptance I ndicators of acceptance

• Does the consumer use of credit cards instead of cash

at the retailers i ?

       h if ) (or card credit if 1

c i c i

f L

D th t il i dh t th dit d t ?

  cash if

i

• Does the retailer i adhere to the credit card system?

 dh if 1    

• therwise

system adhere if 1

r i

L 

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Consum er’s expected utility

) ( ) ( ) ( ) 1 (

c r r

a S L x c E c dH c p u u U        



   ) , ( . . ) ( . ) ( . ). 1 ( . 1

i i B c B B i i

a S L x c E c dH c p u u U

B

    



  

Utility of an Cost of all Benefit from credit card transactions Utility of an

• rdinary purchases.

Utilit f t di Cost of all purchases C f h Utility of extraordinary (credit) purchase with probability θ. Cost of the store credit transactions (if x=0)

 

where

 

 

            

 

B B c i

c B B c i c f B c i B c i c i

c dH c L c dH f c L a S ) ( . . ). ( ). ( : ) , ( 

14

Cost savings from substituting store credit for credit card

I ndifferent consum er and retailers’ m arket shares

  t s U .

1 1

t s U .

2 2 

1 1

2 2

Indifferent Consumer Retailer 2 Retailer 1 Consumer

s

1 s s 

1

s

1 2

1 s s  

15

Retailer’s m arket share Retailer s m arket share

  



). 1 ( .      t s U t s U

i j i i

 

 

 

 

. . 2 ) , ( . ) , ( . . ). 1 (         

i c j r j c i r i r i r j

s t t a S L a S L x p p 

                      t a S L a S L x t p p s

c j r j c i r i r i r j i

2 ) , ( . ) , ( . . 2 ). 1 ( 2 1          t t

i

. 2 . 2 2

zero when in equilibrium

16

Retailer’s expected m argin Retailer s expected m argin

   

) , ( . . . ) ( ) .( 1

c i r i S r i i

a L x c H p M           

Cost of credit card transactions Revenue net of product cost. Cost of store credit transactions (if x=0) where

 

 

 



S S c i c i c i

c H c m f H a . ) ( 1 . 1 ). 1 ( : ) , (             

where Cost of credit card transactions

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Retailers’ profits Retailers profits

M s 

i i i

M s .  

18

Equilibrium prices under price differentiation

     

       1 ) ( 1 ) (

r

c H x c H t p

       

          1 . . ) ( 1 . . ) (

S S

c H x c H t p

Use the credit card instead of cash Use store credit when instead of cash. there is no cardholders.

Subsidy to credit card users

S r c

c m p p   

c

retailers avoided cost 19

c



Rochet&W right’s single price Rochet&W right s single price

       

            1 1 . . ) ( 1 . . ) ( ) ( . . ) ( m f H x c f H H x c H t p

S S

  1

Use credit cards Abandon the store credit to use the credit card. Use store credit if there is not cardholders.

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Cross subsidies under price differentiation under price differentiation

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Mean price under price differentiation

Single price where is the proportion of credit card owners that

c r

p p p . . ) 1 (     

)] ( 1 [ : f H x   

where is the proportion of credit card owners that, under no‐surcharge rule, prefer credit cards.

)] ( 1 .[ : f H x  

But is the proportion of credit card owners that, under price differentiation, prefer credit cards.

)] ( 1 .[

c

f H x    





Then

r c

p p  



and  

 c

c r

p p p . . ) 1 (

 

    

22

mean price under price differentiation

Consum ers’ w elfare d i diff i i under price differentiation

price differentiation single price (R&W)

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Results under price differentiation p

Valli&Maldonado ( W P 2 0 1 3 )

• Unilateral movement to unique price strategy:

q p gy

Retailer 1 Retailer 1

*

p

c

p

credit cards

r

p

cash/store credit R il 2 Retailer 2

c

p

credit cards Retailer 2

c

p

r

p

p

cash/store credit

r

p

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Retailers’ profits under price differentiation

Retailers’ profits Retailer 2 Differential prices Single price Differential prices Single price Differential t/2 ; t/2 t/2 + ε/2 ; t/2 – ε.(1–ε/2t) Retailer 1 prices t/2 ; t/2 t/2 + ε.(1+ε/2t) ; t/2 – ε/2 t/2 – ε.(1–ε/2t) ; t/2 + ε/2 Single price ( ) ; t/2 ; t/2 t/2 – ε/2 ; t/2 + ε.(1+ε/2t)  



    

   

 

   ). ( ). 1 .( . 2 1 : ) (

a c c B B

A S

c dH c x a

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welfare gain of consumers and retailers from price differentiation equilibrium compared with the single price equilibrium

Margins w ith m enu costs Margins w ith m enu costs

   

) ( ) ( ) ( ) (

c c r r

 



   

) ( . ) , ( . . . ) ( ) .( 1 :

c i i c i r i S r i i

I a L x c H p M              



menu cost

           if ; 1 if ; : ) (

c i c i c i

I where

26

Equilibrium prices under price differentiation under price differentiation w ith m enu costs

         3 . 2 . 1 1

2 1 , 1

  

 r r

p p          3 . 2 . 1 1

2 1 , 2

  

 r r

p p      3 1

1

 p p      3 1

2

 p p

c r i c i

p p   

  , ,

2 1

  

3

2 1

    t 2 ) (

1

   a

Sufficient conditions:

2 1

3 2 ) (

27

Retailers’ profits under price differentiation w ith m enu costs

Retailers’profits under price differentiation and menu costs Retailer 2 DifferentialPrices Single Price and menu costs Differential Prices Single Price Differential t/2 (1 )2 t/2 (1+ )2 t/2 . (1 – α).(1 – α+β2 ) ; t/2 .(1 + α – β2)2 Retailer 1 prices t/2 .(1–α)2 ; t/2 . (1+α)2 t/2 .(1+β1 )2 ; t/2 .(1-β1)2 t/2 (1 α β )2 ; t/2 (1 + α) (1+α+β ) Single price t/2 .(1–α–β1 )2 ; t/2 .(1 + α).(1+α+β1) t/2 ; t/2 t/2 .(1–β2 ) ; t/2 .(1+β2)2

1 1 :

2 1

           1 ) ( 1 : ) (        

i i

a a   

28

1 3 . :        t 1 2 ) ( . : ) (      

i

a t a  

Conclusions Conclusions

• Without menu costs:

Without menu costs:

– Single price is not equilibrium: there are incentives to decide unilaterally to surcharge card transactions; y g – There is equilibrium with differential prices: the equilibrium surcharge, or spread, is equal to the merchant fee minus the cost surcharge, or spread, is equal to the merchant fee minus the cost

• f the store credit (“retailer’s net avoided cost”: m – cS);

– The interchange fee becomes neutral: does not affect card usage; – The interchange fee becomes neutral: does not affect card usage; – Merchants are indifferent with respect the non‐surcharge rule: same profit with or without differentiation same profit with or without differentiation; – Consumers obtain maximum welfare: the welfare under d ff l h l d differentiation is equal to the maximum utility under non‐ surcharge, independently of the interchange rate (neutral) ;

29

Conclusions Conclusions

• With menu costs:
• With menu costs:

– Interchange fee is not neutral anymore:

• If low: single price equilibrium;

If low: single price equilibrium;

• If high: differential prices equilibrium;
• Endogenous cap: a high interchange fee can deviate merchants from the single

i li iti th k t f th dit d t (“ i ” f price, limiting the market power of the credit card system (“excessive” usage of credit cards);

– Retailer with the highest (smallest) menu cost have a smaller g ( ) (higher) profit than under no‐surcharge single price equilibrium; – Card system has a smaller profit, because the volume of transactions decrease; – Consumers increase welfare compared with non‐surcharge single price equilibrium, despite the menu costs.

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THE END

Thank you!! Thank you!! Email: marcos.valli@bcb.gov.br

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