pricing online banking amidst network effects
TRANSCRIPT
Pricing Online Banking amidst Network Effects
Baba PrasadAssistant Professor
Carlson School of ManagementUniversity of Minnesota, Minneapolis, MN 55455
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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