Switching costs

In the middle of the 1980s AT&T succeeded in becoming the supplier of digital switches (5ESS) to Bell Atlantic. From then on, all the changes in Bell Atlantic’s telephone system had to be provided by, and negotiated with, AT&T.

My tax consultant closed his office and sold his customer data to another tax consultant.

My bank closed the office I used to frequent.

Network effects and compatibility

Apple Computer are less attractive to consumers because its client base is smaller than that of Microsoft and Intel.

Other examples:– Direct current versus alternating current – Typewriters´ keyboards– Cash machines

Installed bases

If switching costs are present, old customers (repeat customers) are locked in and can be exploited.

In case of network effects the products’ attractiveness depends on the number of both old customers and new customers.

It may pay to build an installed base (customers that bought the product previously).

Competitive situations

new customers only old customers only new and old customers

(no switching costs) (switching costs) (switching costs)

homogeneousgoods

heterogeneousgoods

heterogeneousnetwork effectgoods

Fundamental assumptions

Two firms, 1 and 2 Constant, identical marginal costs c The sum of sales is given. Each customer (old

or new) buys one and only one unit of good 1 or of good 2.

1: Homogeneous goods, no SC

The buyers’ decisions depend on prices only.

It nearly always pays to underbid the rival.

Equilibrium:

21

21

21

1

1

2/1

0

ppif

ppif

ppif

x

cc,

2: Homogenous goods, SC, I

Installed base (number of old customers) for firm 1 is equal to b1. No new customers, repeat customers only.

Customers have to incur switching costs amounting to w in the case of buying good 2 rather than good 1.

Only prices and switching costs are relevant for the purchasing decisions.

2: Homogenous goods, SC, II

Demand functions:

Equilibrium :

Profit of firm 1:

112

211

211

21

1 2

0

xbx

wppifb

wppifb

wppif

x

cwc , 1bw

3: The Hotelling model t are costs of transport per unit of distance

– t=0: homogeneous goods– t>0: heterogeneous goods

Consumers are distributed evenly along the Hotelling space.

10 h

th ht 1

3: Heterogeneous goods, no SC

The buyers’ decisions are made in terms of the prices and the costs of transport.

Demand for good 1:

– Goods are ordinary.– Product differentiation reduces competition

intensity. Equilibrium:

2121 121

21

xppt

x

tctc ,

4: Network-effect goods, no SC, I Only new customers consume, old customers

of firm 1 form installed base. Expected network size:

Expected network effects :Product of network effect strength e and expected network size.

erwerwerwerwerwerw xbsxnsxxbn 11222111 ,

4: network-effect goods, no SC, II

Purchasing decisions depend on prices, costs of transport and expected network effects.

Demand for given expectations:

– Self-fulfilling prophecy effective.– Compatibility reduces expected advantage of

network size.

221121 121

21

xnneppt

x erwerw

4: network-effect goods, no SC, III Demand for fulfilled expectations

– In case of fulfilled expectations network effects increase competition intensity.

– If network effects are important, the goods could be non-ordinary (demand depends positively on price).

– Compatibility decreases competition intensity . Equilibrium :

setwhere

xbseppx

121

1121

21121

11 1

31

21

,131

21

bsecbsec

5: Network-effects goods, SC, I

Installed base (number of old customers) of firm 1 is equal to b1. 1- b1 new customers enter the market.

Equilibrium :

11 3

121

,31

21

wbcwbc

5: New customers´ segment

In equilibrium, firm 2 sells

– Fat cat effect (firm 1 is the fat cat): In case of relatively slight network effects firm 2’s market share rises with the value of firm 1’s installed base.

– Top dog effect (firm 1 is the top dog): In case of relatively high network effects, firm 2’s market share depends negatively on the value of the installed base.

tset

estwbx n

12132

31

21

12

6: Hardware and Software I Two computer firms, A and B offer computer

A or computer B, respectively. Prices for computers: pA and pB, respectively.

Consumers are uniformly distributed (indexed by h) on the interval [0,1] according to their preference towards product B:

10 hMore A-oriented More B-oriented

6: Hardware and Software II Each consumer spends Y on one computer

and on software packages compatible with the computer bought.

Each software package costs 1. Therefore: Ei =Y-pi is the number of software packages the user of computer i can afford.

Utility function

user -B a ish if ,

user-Aan ish if ,)1(

B

Ah

hE

EhU

6: Hardware and Software III Consumer h will by computer A, if

Demand functions:

*:

1

hEE

Eh

hEEh

BA

A

BA

AB

BA

A

BA

AA

xx

pYpYpY

EEE

x

1

,

6: Hardware and Software IV

Assume that firms have identical constant unit costs of c.

We find a symmetric equilibrium

.31

32

,31

32

cYcY

Exercise (Software supply)

Let Ni be the number of different software packages supplied for computer i. Software production takes place in firms other than A and B. Realistically, Ni will depend on the expenditures for software packages for computer i, xi Ei. We assume Ni= xi Ei.

Is the following statement correct: If the price of computer B goes up, the software supply for computer A users goes up.

For any given pA determine firm B’s prohibitive price for its computer.

Exercise (IT expenditure)

Suppose pA > pB .

If the expenditures for IT technology double for all the consumers, what is the effect on the hardware market shares?

Exercise (network effects I)The potential consumers of a network-effect product are uniformly distributed on the interval [0,1]. Consumer h (0 h 1) has the utility

xerw is the expected demand. How do you charac-terize consumers with low values of h?

Derive the demand function x(p, xerw ) for given expectations. Can you identify the workings of the self-fulfilling prophecy?

otherwise , 0

unit one buys he if ,)1( phxU

erwh

Exercise (network effects II)

Derive the indirect demand function p(x) for fulfilled expectations. Sketch it and determine which points are stable and which are not.

Assume there is only one firm offering the network-effect good. Calculate its profit maximizing price.

Business strategy: how to overcome the critical mass Expectations and self-fulfilling prophecy

– vapor ware (non-realized sales, channel stuffing),– preannouncement.

Price differentiation– Low prices for pioneer customers,– Low prices for targeted groups (students).

Complementary goods– Invite competition for hardware production,– Produce software yourself.