Pricing Online Banking amidst Network Effects

Pricing Online Banking amidst Network Effects

Baba PrasadAssistant Professor

Carlson School of ManagementUniversity of Minnesota, Minneapolis, MN 55455

bprasad@csom.umn.edu

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Network Effects

When the value of a product is affected by how many people buy/adopt it

Example: Phone System

Types of Network EffectsDirectIndirectPost-purchase

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Direct Network EffectsThe number of users directly impacts the value of the systemBased on interaction between members of a network

E.g. Telephone service

Metcalfe’s Law: Network of size N has value O(N2)

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Indirect Network Effects

Do not directly affect the value of the productIndirect influenceCredit cards:

More adopters of the card more merchants accept it higher value for the card

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Post-Purchase Network Effects

Mostly support relatedExamples

Software user groups (LINUX Users Group)Consumer networks

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The Model

Value of a product in a market with network effects is given by:

Zt is the size of the network at time t, α represents the value without network effectsγ represents value from network effects.

tZV γα +=

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Pricing with Network Effects

Value ascribed to system by customer: Willingness to Pay (WTP)

Most optimal policy: price at WTPDifficulty: How to determine WTP?

High collective switching costsLeads to default standards (e.g. QWERTY; VHS, Java…)

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Monopoly pricing

What happens to Coase conjecture?Coase (1937): prices drop to marginal costs over a long period of time even in monopolistic settings

tZV γα +=

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Standard Assumptions

Product purchase decision

Positive network effects

Constant parameter to represent network effect

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Services and Network Effects

Assumptions in product purchase model are not valid

Not a one-time purchasing decisionPossibility of reneging and resubscribing: Market is not depleting over time

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Services and Network Effects (contd.)

Network effects can be negativeService systems have fixed capacitiesFixed capacities deterioration in service User notices negative network effects:

Random sampling; or word-of-mouth

Number of users

value

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Are network effects constant?

Previous discussion implies time-dependencyThus, not really constant, but random (how many users are already on the system, when an additional user enters?)Thus, stochastic network effects

E-Banking and Network Effects

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Network Externalities in Retail Banking

Checking facility and exchange of checksE-Checks (Kezan 1995, Stavins 1997, Ouren et al 1998)Critical mass theory and Internet-banking users

Credit cards and indirect network effectsIntroduced in 1930s, “re-introduced” in the 60s, did not take off till the mid-80s

Econometric StudiesGowrisankaran and Stavins (1999) find strong evidence of network effects in electronic payments (ACH)Kauffman et al have observed network effects in ATM networks

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Why Electronic Banking?

Tremendous reduction in transaction costs

Coordination of Delivery Supply Chain

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Cost of Transactions Across Delivery Channels

$0.01Internet$0.27ATM$1.09Teller

Cost of TransactionDelivery Channel

Source: Jupiter Communications 1997 Home Banking Report

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Coordination of Delivery Supply Chain

Electronic transactions facilitate :

Exchange of information with other banks through Electronic Clearing Houses (ECH)

Flow of information within the firmWorkflow management; process control

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Banking Some Online Banking Options and Prices (March 2002)

Bank

Free with checking account(Checking account balance > $1500)

Wells Fargo

Free first 3 months, then $4.95/monthHuntington

PriceBank

Free first 3 months, then $5.95/monthWachovia

$5.00/month (Free if average account balance > $5000)

Chase

$4.95/monthBank One

$5.95/monthNations Bank

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Bank ProblemChoose a price vector (P) over the two periods at the outset

Choose the optimal price vector assuming that the customer will switch in such a way as to optimize value over the two periods

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Reservation PricesEach customer indexed by h ∈ [0, 1]Customer strategies

(0, 0): Do not choose online banking in either period(0, 1): Choose online banking only in period 2(1, 0): Choose online banking in period 1 and renege in

period 2(1, 1): Choose online banking in both periods

Let h00 (= 0), h01, h10, and h11 denote the minimal reservation prices that will allow each of these strategies

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Some propositionsh11 ≥ h10 ≥ h01 ≥ 0

There exists threshold network effects γu and γl such that

when γ > γu, consumers who choose online banking in period 1, do not renege in period 2, and when γ < γl , consumers who do not choose in period 1 will not do so in period 2 also.

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Consumer Surplus EquationsFirst period

V1(h, p1) = h – p1, for online banking= 0, for non-online banking

Second Period

V1(h, p2, qi-1) = δ(h – p2+ γ qi-1) for online banking= -δCjk, for non-online

bankingδ is the one-period discount factor (0 < δ < 1)

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Demand EquationsD1 = 1 – h10 and D2 = 1 – h01

Using indifference equations between choices in the 2 periods, we arrive at:

D1 = {1 – δ – p1 + δp2 + δ(C01 – C10)}(1 – δ + δγ)

D2 = {(1– δ + δγ) (1– p2) – γp1 + δp2(1+ γ) + δγ(C01 – C10) – δC01 – δγ2}(1–δ+ δγ)}

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Optimal Pricing Problem

Π = max p1D1 + δp2D2(p1, p2)

s.t. 0 ≤ h01 ≤ h10 ≤ h11≤ 1

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Optimal Prices

p1*

= {(1 – δ) (2 – δγ + δ2 +2δγC10 + 2δC01) – 6δ}{(δ –2)2 + δ2γ(γ-2)}

p2*

= {(2p1* + δ(C10 +C01) – (1 – δ)}

{δ (1 – γ)}

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Price behaviorNote that as γ → 1, p2* → ∞

Increased network effects cause higher second period benefit.Contrast with Coase conjecture; common with other studies with positive network effects

Note also that as γ increases, p1* decreases

Increased network effect leads to low introductory pricing

If δ = 0, p1* = ½ and p2* → ∞

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Optimal Prices over 2 Periods

-0.6 -0.4 -0.2

0 0.2 0.4 0.6 0.8

γ 0.2 0.4 0.6 0.8 1

p1

p2

γ--->

C01 = 0.4; C10 = 0.2; δ = 0.6

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Demands at Optimal Prices

Figure 1.2. Demands at Optimal Prices in the Two Periods

0 0.2 0.4 0.6 0.8

1 1.2

0 0.3 0.5 0.7 0.9

γ ------>

Demand --

D1 D2

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Intermediate Conclusions

Should banks have chosen low introductory pricing to promote online banking?Positive switching costs lead to initial reluctanceHow are issues of security and convenience perceived by consumers?

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Negative word-of-mouth effects

"Banking is founded on trust. We want an e-commerce service we can feel safe with, because if even one customer somewhere gets hacked - well that's bad for the customer but we suffer the impact to a greater extent because of the damage to customer trust."

(Bob Lounsbury of Scotiabank, 1999)

Scotia Bank was the 1998 NetCommerce Award winner in the Canada Information Productivity Association competition

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Online Banking Adoption Decision

Kennikel and Kwast (1997) 33% of respondents reported that friends and relatives who already used online banking affected decision to adopt online bankingHighest reported source of information in adoption decision

(next is financial consultants/brokers at 26.8%)

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Word-of-mouth Effects

StochasticCan be positive or negativeMean and varianceAffects adoption of online banking in future periods

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How to model W-o-M effects?

q

µ

1− µ

1- p - q

p

t t + 1

Positive

No Effect

Negative

Figure 1. Transition probabilities and outcomes

qq y probabilitwith )(

- p - 1y probabilit with )( y probabilitth wi)(

)1(

−

+=+

µµµ

µ

ltmtm

phtmtm

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Modeling the Stochastic Network Effect

The trinomial tree can be shown to follow a Geometric Brownian motion processApart from “customer-talk”, expert opinion also influences demandWe model word-of-mouth effect, g, as a jump-diffusion process

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Word-of-Mouth as jump-diffusion process

)(tkgdQgdZgdtdg gg ++= σµdZ is the increment of a Wiener process, Z, with mean, µg, and s.d. σg

dQ(t) is the increment of a Poisson process with mean arrival rate, λ

k is a draw from a normal distribution, or in other words, k ~ N(µp, σp

2).

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Demand function

where, D(t) is demand at time tS(t) is size of network at time tp(t) is the price at time t, andg(t) is the stochastic network effect

[ ])(),(),()( tgtptSftD =

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Maximizing profit

Stochastic Optimal controlBellman’s equation

∫∞

− −o

t

pdttDtSctpeE )())](()([max 0

ρ

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Effects of Word-of-Mouth on prices

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Pricing Strategy

µg

Positive

Negative

HighLow σ2

Price to Penetrate MarketPrice to Build Network

Price to Recover Sunk CostsPrice Myopically

Table 1. Pricing Strategy with Word-of-mouth Effects

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Stochastic Cross-Product Network Effects

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Consumer Surplus EquationsFirst period

V1(h, p1) = h – p1, for online banking= 0, for non-online banking

Period i, i ≥2

V1(h, p1, qi-1) = (h – p2+ γ Di-1+ ηi Di-1), for online banking

= - Cjk, for non-online banking

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Customer’s ProblemAt the beginning of each period, the customer chooses a mode (online or not). The problem is to choose an optimal sequence of modes that will maximize value

To switch from mode j to mode k costsCjk

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Dynamic Program FormulationCustomer chooses to maximize value over the T periodsConsider the last period, period T:

Choose that mode that will give maximum value after discounting switching costSuppose customer arrives in this period in mode

M

VT = Max(VmT – CMm), m ∈ {Online, Non-online}

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Dynamic Program Formulation (contd.)

For any period, j (0 < j)

Vj-1 = Max (Vmj – C(j-1)m + δE[Vj])

E[] being the expectation, and δ being the one-period discount factor

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The Model

Value of a product exhibiting both types of network effects is given by:

where Zt is the size of the network at time t, the parameter αrepresents the value without network effects, γ represents network externality effects, and η represents word-of-mouth effects. τ is the time delay for the word-of-mouth effects.For simplicity, we assume τ = 1

ττηγα −++= tt ZZV

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Variation of Optimal prices with Mean of Word-of-mouth Effect

-8

-6

-4

-2

0

2

4

6

-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

mean w_o_m ------>

pric

e ---

----->

p2_w_o_m

p1_w_o_mp2

p1

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Optimal Prices with Variance of Word-of-mouth Effect

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.05 0.1 0.15 0.2 0.25 0.3p ---

>

p1

p2

p1_W_of_Mouth

p2_W_of_Mouth

s.d. Word-Of-Mouth externality ------->

p1 and p2 are without word-of-mouthk=0.15, δ = 0.6, C01=0.4; C10=0.3

mean for word_of_mouth = 0.1

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Multiple Periods: Prices with Increasing Lag in Word-of-mouth Effects

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7

period

pric

e

price_1D

_2D

price_3D

η

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Multiple Periods: Demands versus Prices with Increasing Lag in Word-of-mouth Effects

Not much variation in optimal demand

Optimal prices increase about 5% for every additional period of lag

Banks seem to be more sensitive to word-of-mouth than customers

Back to Lounsbury’s comment

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Anecdotal Evidence: Bank Strategies Some Online Banking Options and Prices (March 2002)

Bank

Free first 3 months, then $4.95/monthHuntington

PriceBank

Free first 3 months, then $5.95/monthWachovia

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Bank Strategies (contd.)

Wells FargoCharged for online banking in 1998Now, it is free