Economy and network_effect_(modeling _and_analysis)

Revision: Network ExternalitiesThe Economy without Network Effects

The Economy with Network Effects

Part 3: The Economy and Network Effects

Sumant Kulkarni

International Institute of Information Technology, Bangalore

Sumant Kulkarni Externalities and Network Effects 1/48



Agenda

Revision: Network Externalities.

Economy without Network Effect.

Economy with Network Effects.




Revision: Network Externalities




Externality

Two parties do business willingly only if there is a profit for

both of them1.

Business may be the exchange of financial value (like renting

house) or social welfare (like marriage).

Externality either puts some cost or provide some benefit to

the people not involved in the business.

For example:

Renting out a house to a night club in the residential complex

(assume that it is legal).

Renting out a house to a very influential politician with

mindset of helping people.1Kelvin Hartnall, Externalities and Network Effects




Network Externalities

We are part of many networks. For example,

Network of same company car users.

Network of same telephone service.

Network of people using same social network.

Network Externality is a phenomenon in which entry of new

user into the network, has either benefit or cost to the

other user of the network.

If the entry costs something to other users, then it is

Negative Externality.

If the other users are benefited, it is Positive Externality.




Network Externalities

In the networks showing network externality, the users have

two separate sub part in the value he receives by being a part

of the network2.

1 Autarky value: The value from the product/service he is

using (consumer has paid for it). User gets this even if there is

no other person using the same product/service.

2 synchronization value: The value from the network as the

result of joining it (complementary but not optional).

The latter part of the value decides whether it is Positive

Externality or Negative Externality.

2Network Externalities (Effects) by S. J. Liebowitz and Stephen E. MargolisSumant Kulkarni Externalities and Network Effects 6/48



Negative Externalities

If the entry of a new user into the network costs something to

other users of the network, then it is Negative Externality.

A classic example is the traffic congestion.

The negative externalities can often be seen in the later stage

of networks, where resources are finite.

What other reasons can be there for a network to have

negative externality?

Can their be a network which is having negative externality

from the first user of the network?

Is negative externality a manifestation of the indication of

resource crunch?




Positive Externalities

If the other users are benefited by the entry of a new user into

the network, then it is Positive Externality.

In positive externality, “The value of the service or product

will increase as its installed base expands3”.

Positive Externality is known as Network Effect.

Though many networks have Network Effect initially, once

they start facing resource crunch and once they scale above a

level, they might start showing negative externality.

3Network Effects and the Impact of Free Goods: An Analysis of the Web

Server MarketSumant Kulkarni Externalities and Network Effects 8/48



Setup of MarketFormally Modeling the Lack of Individual Effect on MarketHow Market looks with no Network EffectsThe Equilibrium Quantity of the Good

The Economy without Network Effects





The Setup of the Economy without Network Effects

We make many assumptions to simplify the complexity of the

market.

The market is for one good and has huge number of

consumers.

Basic Condition = No Network Effect in the Market

Condition ⇒ Consumers do not care how many other

users of the good are there.





The Economy without Network Effects

Let us analyse the way market function with the assumption.

Assumption: Large number of potential purchasers with very

little individual share in purchase.

⇒Each user can make independent individual decisions

without affecting other users.

Example: User buying a car does it without thinking about

whether his decision affects the price of the car in market.

Real markets with finite real users do behave like this.

The effect of each individual can be very negligible on the

aggregate. Hence, we completely ignore the effect of each

individual on the market while modelling the economy.





Modeling Consumers

Consumers are represented as the set of all real numbers in

the interval strictly between 0 and 1.

Q1: set of all real numbers in the interval strictly between 0

and 1 is infinite. How do we map them to finite number of

users (say N)? Ex. (Map(n) = n+1N ), (Map(n) = N−n+1

N )

Each consumer is named after a different unique real number.





Modeling Consumers

Due to uniform distribution, set of consumers between 0

and x < 1 represent x fraction of population.

We can think of this model of consumers as the continuous

approximation of market with large but finite number of

consumers.

Q2: How does the continuous model avoid having to deal

with the explicit effect on any one individual on the overall

population? (May be due to the uniform distribution of the

consumers between 0 and 1. How how exactly does it help?)





Modeling Consumers Willingness to Buy

Assumption: Each consumer wants to buy at most one unit

of the good.

Value of that one unit of good for the consumer is determined

by the intrinsic interest of the consumer to buy it.

No other factor than the intrinsic interest motivates him to

buy the good.





Reservation Prices

Let us consider how market looks with the above assumptions.

Each consumer’s interest in the good is specified by a single

price called reservation price.

Reservation price ( r(x) ) is the maximum amount the

consumer x is willing to pay for one unit of the good.

Assumption: Consumers are arranged in the decreasing order

of their reservation price between 0 and 1.

If r(x) > r(y) then x < y .

To be more clear r(0) > r(1) and 0 < 1

Assumption: r(·) is a continuous function and no two

consumers have exactly the same reservation prize.

r(·) is strictly decreasing over the increasing interval 0 to 1.





Market Price for a Unit of Good

Market Price (p) for a unit of good is the minimum price at

which the good can be bought and there will not be any unit

of the good sold below price p.

Assuming that there will not be any unit of the good sold

below price p.

Any x having r(x) >= p can buy the good and any x having

r(x) < p can not buy the good. (Why?)

At p > r(0), nobody can buy the good. (Why?)

At p <= r(1), everyone can buy the good. (Why?)





Figure: When there are no network efforts, the demand for a product at a

fixed market price p can be found by locating the point where the curve

y = r(x) intersects the horizontal line y = p.





Market Price for a Unit of Good

r(·) is strictly decreasing continuous function.

For r(·), in the region between 0 and 1 (the region ofinterest), their lies a unique sweet point for which r(x) = p.

This means:The consumers between 0 and x (including x), can buy thegood.The consumers named greater than x can not buy the good.Hence, x fraction of the consumers buy the product (due touniform distribution assumption).





Market Demand for the Good

For every prize p, there will be an x , which specifies the

fraction of population that will purchase at price p.

The x (determined from price), is an indicator of Market

Demand for the good.

Increase in x shows the increase in demand .





Market Demand for the Good

Increase in x shows the increase in demand .

r(·) describes the inverse demand function. (Why?)

p = r(x) and hence x = r−1(p).

This relation between number of units consumed (x) and the

price p is very interesting. To sell more units we need to

reduce the price.Sumant Kulkarni Externalities and Network Effects 20/48




The Equilibrium Quantity of the Good

Assuming that constant production cost/unit of good is p∗

Assuming that there are many producers so that no one can

influence the market.

The producers will be willing to supply any amount of goods

at the prize p∗ per unit.

The producers will not be willing to supply any amount of

goods at the prize lesser than p∗ per unit.

It is highly unlikely that the price of the per unit good will

remain above p∗ (competition).

Profit is ZERO.

This is due to long-run competitive supply for any good

produced by a constant-cost industry.





The Equilibrium Quantity of the Good

If p∗(constant production cost/unit) is above r(0), no one can

buy the good.

If p∗ is below r(1), everyone buys the good.

Thus, the interesting point is r(0) > p∗ > r(1)

When r(0) > p∗ > r(1):

When p∗ = r(x∗), we call x∗ the equilibrium quantity of the

good for given reservation prices and cost p∗.

Usually 0 < x∗ < 1 for a stable market for a good.





The Equilibrium Quantity of the Good - Reservation Price

and Cost

Figure: When copies of a good can be produced at a constant cost p∗

per unit, the equilibrium quantity consumed will be the number x∗ for

which r(x∗) = p∗





Equilibrium Quantity

x∗ represents an equilibrium in the population’s consumptionof the good.

If consumption < x∗, then there will be “upward pressure” onthe consumption of good. (Want to Buy as r(x) = p > p∗ )

If consumption > x∗, then there will be “downward pressure”on the consumption of good. (Regret as r(x) = p < p∗)





Social Welfare (SW)

Social Welfare is the the difference between total reservation

prices of consumers who bought a copy of the good and total

production cost of those many units of good.

For x units of goods, the Social Welfare will be possible only

when they are allocated to all consumers between 0 and x .

When x = x∗ (equilibrium), then the Social Welfare is

maximum.




Effect of Network Effects on Purchase of a GoodEquilibria with Network Effects






Effect of Network Effects on Purchase of a Good

The price of an unit of good is determined by

Intrinsic interest - (own reservation price) - r(x)

Number of consumers already using the good - z

There will be two independent factors influencing the

reservation price (RP) of a consumer - r(·) and f (·).

r(x) - Intrinsic interest for the consumer x .

f (z) - Benefit to each consumer for having z fraction of

population using the good.

RP(x) = r(x) · f (z)

Multiplication means, increase in the fraction of people using

the good (z) increases the reservation price even when there

is no change in the intrinsic interest.

Increase in any or both increases the reservation price.Sumant Kulkarni Externalities and Network Effects 27/48




Pricing the Good

Assumption: f(0) = 0 ⇒ If no units of good purchased, then

no one will buy it.

The consumer willingness to pay depends on the fraction of

population using the good.

The prediction of fraction of population (z) using the good is

very important.

Assumption: p∗ is the price of one unit the good and z

fraction of population will use the good, then

A consumer x will buy the good only if r(x)f (z) > p∗





Self-fulfilling Expectations Equilibrium (SFEE)

Assumption: The prediction about number of users of the

good (z) is always correct.

What do we mean by always correct (exact) prediction of z?

“the consumers as a whole form a shared expectation that the

fraction of population using the good is z and buy it. Due to

this, the exact fraction of population reaches z fraction”.

This is self-fulfilling expectations equilibrium for the

quantity of purchasers z .

In self-fulfilling expectations equilibrium every purchaser of z

fraction predicts that z fraction of population is using it.

The expectation in turn is fulfilled by people’s own behavior.

Coming slides assume that the prediction about number of

users of the good is always correct.Sumant Kulkarni Externalities and Network Effects 29/48




When Do We See Self-fulfilling Expectations Equilibrium

We observe 2 self-fulfilling expectations equilibria.

When z = 0 (i.e. When no fraction of populations has bought

the good.)

When 0 < z < 1 (i.e. When some fraction of populations has

bought the good.)

Assumption: Price/Unit of good = p∗ > 0.





Self-fulfilling Expectations Equilibrium When z = 0 (i.e.

None of the populations has bought the good.)

When z = 0

No one will buy the good.

Reservation Price of any consumer x can be given as

RP(x) = r(x) · f (0) = 0

RP(x) < p∗(price of the good)

No one will buy the good as the reservation price is 0

(RP(x) < p∗).

The state persists (no increase or decrease in the fraction of

consumers).

Hence, this is an equilibrium.





Self-fulfilling Expectations Equilibrium When 0 < z < 1

(i.e. Some of the populations have bought the good.)

If exactly z fraction of population can buy the good, then

If any x , where x <= z can buy the good. Hence, only the

consumers between 0 and z can buy the good.

The price p∗ at which these consumers want to purchase the

good can be determined as below.

z has lowest reservation price of all the people who can buy.

This is because only consumers who can buy are 0 to z .

Hence RP(z) = p∗

The Reservation price of z = RP(z) = r(z) · f (z)

p∗ = r(z)f (z)

As only z fraction can purchase at this price, this is a SFEE.





Characteristics of SFEE with an Example

To confirm whether Self-fulfilling Expectations Equilibria exists, weneed to know both r(·) and f (·).

Consider an example where,

r(x) = 1− x

f (z) = x .

p = r(z)f (z) = (1− z)z = z(z − 1) = z2 − z

This is a quadratic equation representing a parabola.





SFEE - Example

Figure: The plot of the consumer Fraction z versus the Price (p). The

quadratic equation p = z(z − 1) = z2 − z is represented in the plot.





SFEE - Example

The curve reaches its maximum (i.e. p∗ = 14) when z = 1

2

There is no equilibrium for p∗ > 14 .

This means, if p∗ > 14 , then the good is considered too

expensive and no one will buy it.





SFEE - Example

When z = 0,

There price of the good for any consumer x is

r(x)f (z) = r(x)f (0) = 0

No one will buy the good as p∗ > 0 i.e p∗ > reservation price

There will not be any increase in z due to this.

Hence, z = 0 is an equilibrium.Sumant Kulkarni Externalities and Network Effects 36/48




SFEE - Example

When 0 < z < 1, there are two equilibria

Earlier Equilibrium z ′

Later Equilibrium z ′′





Pressures in the SFEE

Any fraction other than z = 0, z = z ′ and z = z ′′ do not form

SFEE.

Hence, if the fraction z is any point other than z = 0, z = z ′

and z = z ′′, then there will be different kinds of pressures

acting in the system.Sumant Kulkarni Externalities and Network Effects 38/48





If z is between 0 and z ′

The actual fraction of purchasers (z) is lesser than the SFEE

fraction z ′.

(p = r(z)f (z)) < (p∗ = r(z ′′)f (z ′′))

Value of the purchased good due to z fraction consumers is

less than the price of the good p∗.

People have got good which has lower value than their RP.

People feel that they should not have bough that good.

Number of people buying reduces, pushing the demand down.

This is Downward Pressure on consumption.






If z is between z ′ and z ′′

The actual fraction of purchasers (z) is greater than the SFEE

fraction z ′.

(p = r(z)f (z)) > (p∗ = r(z ′)f (z ′))


more than the price of the good p∗.

People have got good which has more value than their RP.

People feel good about it and more people start buying.

Number of people buying increases, pushing the demand up.

This is Upward Pressure on consumption.






If z is between z ′′ and 1

The actual fraction of purchasers (z) is greater than the SFEE

fraction z ′′.

(p = r(z)f (z)) < (p∗ = r(z ′′)f (z ′′))


less than the price of the good p∗.

People have got good which has lower value than their RP.

People feel that they should not have bough that good.

Number of people buying reduces, pushing the demand down.

This is Downward Pressure on consumption.





Stability of z′′

More stable Equilibrium.

If z crosses z ′′, downward pressure will pull it towards z ′′.

If z is between z ′ and z ′′ upward pressure will push it to z ′′.





Stability of z′

If z is between 0 and z ′ - approach 0.

If z is between z ′ and z ′′ - approach z ′′.

Highly unstable.

It is known as critical point or tipping point.

If z crosses z ′, it will increase till z ′′.

If z is lesser than z ′, then the fraction of people consuming

the good will reduce and becomes 0.

Very important to cross the z ′, to success in the business.





SFEE - Some Observations

Two important observation (for the same good, at the same price):

Effect of consumer confidence.

Effect of relationship between the price and the equilibrium

quantity.





Effect of Consumer Confidence.

Self-fulfilling expectations equilibrium corresponds to

consumer confidence.

If no consumer confidence in the success of the good, no

success will be seen.

If population is confident in the success of the good, the

success will be seen.

Multiple Equilibria are due to the different characteristics of

the markets in which NE works. The number of equilibria will

depend on the type of Market.





Effect of the Relationship between the Price and the

Equilibrium Quantity

In the market with NE, the relationship between price and

equilibrium quantity is more complicated than that with out

NE.

For example, as p∗ goes on dropping below 14 , z

′moves to the

left and z′′

moves to the right. This means that each

equilibria move away from each other. This means that, z′

moves towards smaller fraction while z′′

moves towards the

larger fraction. The gap between two equilibria increases.





References

Network, Crowds and Markets - book

Network Effects, http://www.moreno.marzolla.name/

teaching/CS2011/NetworkEffects.pdf

The Economy with Network Effects,

http://www.systems.ethz.ch/education/fs11/

struct-social-inf-networks/lectures/Lecture%209.

pdf

Reverse Network Effect,

http://www.readwriteweb.com/archives/is_there_a_

reverse_network_effect_with_scale.php


http://www.moreno.marzolla.name/teaching/CS2011/NetworkEffects.pdf

http://www.moreno.marzolla.name/teaching/CS2011/NetworkEffects.pdf

http://www.systems.ethz.ch/education/fs11/struct-social-inf-networks/lectures/Lecture%209.pdf



http://www.readwriteweb.com/archives/is_there_a_reverse_network_effect_with_scale.php

http://www.readwriteweb.com/archives/is_there_a_reverse_network_effect_with_scale.php




Network effects: related pages

Barriers to entry - Anything that makes it difficult for a new entrant to

break into a market.

First mover advantage - The competitive advantage that the first

company to launch a new type of product should have over those that

start later.

Natural monopoly - A monopoly that arises from the nature of the

industry, rather than being imposed by law or resulting from

anti-competitive practices.

Product differentiation - Making a product or service look different in the

eyes of consumers.

Submarine patent - A patent that is deliberately kept quite, in the hope

of extracting money later from those who use an idea believing it not to

be patented.

Cross licensing - Exchange rights to patent portfolios, which reduces

litigation and R & D costs, while simultaneously erecting barriers to entry.

Razor-blade model - A razor-blade model is a business model based on

selling a product at a loss in order to profit from the sale of consumables

necessary for its use.

Regulatory capture - The dominance of regulators by those they regulate

rather than the public good they ostensibly serve.


Economy and network_effect_(modeling _and_analysis)

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