Getting Prices Right : Mobile Phone Di¤usion , Market
E¢ ciency and Inequality1
Francis ANDRIANARISON2
May 2009.
Preliminary Version
Please do not quote
Abstract:
In this paper, we study the impact of uneven mobile phone di¤usion on rural markets.
We develop a static, stochastic model with spatial arbitrage between two neighboring
marketplaces. Producers with a phone in one market can learn the prevailing price in
the other market while those without a phone cannot. In a …rst stage, we assume that
the penetration rates of mobile phones are exogenous. We …nd that the introduction of
mobile phones reduces price dispersion and yields positive externalities within markets
but negative externalities across markets. Mobile phones of course bene…t their adopters.
When the penetration rate increases in a village, farmers without phones also bene…t as the
domestic price increases on average. In contrast, farmers in the other village (both with
and without phones) are penalized as the price in the other market decreases on average.
These e¤ects are stronger when the original di¤erence in penetration rates is higher. Thus,
the di¤usion of a new technology which is not uniform may reinforce existing patterns of
inequality. In a second stage, we show that these results are robust to endogenizing the
penetration rates.
Key Words: Mobile phones, technology di¤usion, market e¢ ciency,Welfare, inequality.
1
I would like to thank my supervisor yann Bramoulle for the guidance and the incisive comments he
has provided at many stages of this research project.
2
Département d’Économique et CIRPEE, GREEN Université Laval, Québec, Canada.
[email protected]
What would a small-scale farmer in Africa, Peru or India want with a mobile phone or
a Wi-Fi kiosk? Market information. Timely knowledge about who is buying potatoes today,
what the buyers are willing to pay and where they are located can be vitally important to
those who are just getting by. Markets aren’t only for the rich. Certain kinds of information, however, convey advantages to those have the right data at the right time.( Howard
Rheingold, Farmers, Phones and Markets: Mobile Technology In Rural Development, 2005)
I. Introduction
The importance of information is regarded by economists as a critical element in the e¢ cient
functioning of markets, going back at least to the seminal work of Stigler (1961). Therefore,
the lack of a¤ordable access to relevant information has been a concern in development
issues. Most developing countries have poorly functioning markets characterized by scarce
and poor internal ‡ows of information (Geertz ,1978).Lack of information, or situations of
asymmetric information, is rather the norm. There are virtually no sources of information
regarding market prices and other production-related information (Eggleston and al. 2002).
Therefore, the coordination of economic activity rarely performs well. Information ‡ows
are poor, the ‘law of one price’will not operate: the market will not work well.
The explosive growth of mobile phone in the developing countries during the last decade
has raised debate about its potential value as tool for development and …ghting poverty (see
e.g. Je¤rey Sachs 2008). Through mobile phones, the …rst digital information and communication technologies (ICTs) is now reaching the world’s masses, even in poorest countries.
And one of the most signi…cant economic bene…t of mobile phones is that they improve
the circulation of information.They enable …shermen or farmers to check prices at di¤erent
markets before selling products, they broaden trade networks and reduce transaction costs
(The economist, march 2005). Although increased access to more accurate information via
mobile phones should help farmers to increase their income and potentially improve their
welfare. Mobile phones improve the di¤usion of information, and improved information
could enhance market e¢ ciency that helping the poor. Indeed, a signi…cant proportion of
1
the world’s poor in rural areas are in agriculture, …sheries or forestry domains and they
depend heavily on markets. The functioning of markets for such products is important to
…ght poverty. However, the lack of interest in how the e¤ects of improving information
for producer (sellers) on market e¢ ciency is also surprising given the existence of a longstanding literature in information search3 . Speci…cally, we know little about what and how
the impact of improving access to market information a¤ects farmers’choices and market
e¢ ciency. To the best of our knowledge, the evidence on the e¤ects of increased market
information via mobile phone on market outcomes in developing countries is still an open
debate. Nevertheless, a small growing literature attempts to bring empirical evidence on
the e¤ects of increased market information on market outcomes. Most recently, Jensen
(2007) argues for the central role that information and mobile phone play in the functionning of markets in developing contries. From a study of …shermen in Kerala India, he …nds
that mobile phones help …shermen to choose a …sh market where they can sell their …sh
for the highest price. Jensen shows that, as mobile phone coverage became available from
1997, the proportion of …shermen who travelled beyond their usual markets in Kerala to
sell their …sh increased. Furthermore, the arrival of mobiles brought signi…cant reduction
in price dispersion, elimination of waste and near-perfect adherence to the Law of One
Price. Adoption of mobile phone by …shermen and wholesalers increases their ability to
arbitrage over price information from potential buyers. Coordinate sales have helped them
to increase income and to reduce wastage. Reduction in price dispersion insures price stability, so both consumer and producer welfare increase. Jenny Aker (2008) provides recent
…ndings from Africa that are broadly similar to Jensen’s. Her study of grain traders in
Niger suggests that the primary mechanism by which mobile phones a¤ect market-level
outcomes appears to be a reduction in search costs, as traders operating in markets with
mobile phone coverage search over and sell in a greater number of markets. Furthermore,
mobile phones have greater impact on price dispersion for market pairs that are farther
3
Since the 1960s, a large literature on consumer search theory has emerged, in an e¤ort to explain how
changes in search costs a¤ect market actors’behavior and equilibrium price dispersion (see Baye, and al.
[2007] for a review).
2
away. This e¤ect becomes larger as a higher percentage of markets have mobile phone
coverage.
This paper explore the e¤ects of information improvement on market performance,
welfare and inequality. It relates to the ongoing discussion about the role of Information and
communication technologies (ICTs), especially mobile phones on economic development.
It builds a stochastic model with spatial arbitrage between two neighboring marketplaces
upon Jensen (2007). Unlike Jensen (2007), we remove the conditions of symetry on market
size and the realization of the state of the world and explore mobile phone di¤usion e¤ects
on both intra and inter-markets outcomes. Especially, the paper points up the externalities
e¤ects which have not been adressed by Jensen (2007).
This paper bridges three di¤erent strands of the economics literature. It contributes to
a growing literature on the impacts of mobile phone di¤usion on development. It argues
that better access to information by mobile phone use enables users to access arbitrage or
trade opportunities that they otherwise would have missed out on. Our contribution to
this literature is twofold. First, we develop a theoretical framework in general equilibrium
approach to explore the e¤ects of mobile phone use on markets functioning. Our work
contribute to build theoretical basis to support the current debate over the potential for
mobile phones to promote economic development. Second, we focus on distributional aspects, namely the e¤ects on price received by those who have mobile phones and those who
don’t.We show that the di¤usion of the technology has heterogeneous e¤ects. Our results
suggest that di¤usion of a new technology which is not uniform may reinforce existing
patterns of inequality. To the best of our knowledge, this aspect has not received su¢ cient
attention in the growing debate4 .
Our research also contributes to the literature on search theory. Most search-theoretic
models have been used to explain the existence of price dispersion for homogeneous goods
(see Baye and al, 2007 for a review). In line with Jensen (2007) and Aker (2008), the
4
For instance, Jagun (2007) notes in his case study in the aso oke (hand-woven textile) sector in southwestern Nigeria that if ICTs also promise to make the situation more equal for everyone involved, yet it
appears that mobiles are increasing the di¤erence between those who can a¤ord access to a mobile (who
…nd greater opportunities to trade) and those who cannot (who …nd they have fewer orders).
3
model presented here is innovative. It focuses on search from the producer’s (supplier’s)
perspective, which has not been widely addressed in the search literature. And unlike
traditional search model, we develop a spatial model where there is competitive market
in each village with many small buyers and sellers5 . Finally, our research also makes a
contribution to the digital divide debate. Indeed, the critical issue of the digital divide and
of the role that di¤erent information and communication technologies, speci…cally mobile
phone, may be playing in deepening – or in helping reduce – the gap between the haves
and have-not of the information age.
In this paper, we treat farmer’s spatial arbitrage under uncertainty. The fundamentals
of our model are:
1.It is not possible for producer to visit more than one market per day6 . This is the
case for perishable commodities such as …sh, milk, tomatoes, eggs, fruits and vegetable.
Marketing perishable foodstu¤s requires a delivery process that allows prompt communication.
2. Lack of information due to uncertainty and existence of transaction costs induce
ine¢ cient allocations of goods and cause price dispersion across markets.
3. The availability of accurate, timely and appropriate information related to the selling
stage of the value chain production can enable farmers to make better decisions regarding
where to sell goods and at what prices.
4. Due partly to institutional failure, di¤usion of technology (mobile phone penetration)
is not uniform across space.
The fourth premise provides a basis for exploring the role of digital divide on the impacts
of mobile phones. Using a simple static, stochastic model with spatial arbitrage between
two neighboring marketplaces, we derive the decision rule for a producer’s search technology
and the impact on market prices dispersion and market outcomes We …rst characterize the
situation under pre-phone conditions and then derives the reported changes in individual
5
Traditionally, consumer search model assumes that there are many sellers but only one at any particular
location. (see Stiglitz [1989] or Baye and al. [2007]).
6
For example, because markets are open for only a few hours and travel is time consuming and storage
is expensive.
4
market-selection behavior resulting from the introduction of mobile phones. Our model
predicts that the addition of mobile phones reduces price dispersion within and across
markets and yields positive externalities within markets but negative externalities between
the markets. According to our knowledge, these results haven’t been addressed in the
literature on mobile phones impacts. However, similar result is obtained in the literature
on consumer search. When the number of uninformed consumers increases, prices become
less competitive for all consumers. Thus, the in‡ux of uninformed consumers generates
a negative externality increasing the prices paid by informed consumers (Morgan, 2001).
Furthermore, we show that equilibrium price dispersion decreases as search cost decreases.
There is heterogeneous e¤ects within producers. When the penetration rate increases in a
village, farmers without phones also bene…t as the domestic price increases on average. In
contrast, farmers in the other village (both with and without phones) are penalized as the
price in the other market decreases on average. These e¤ects are stronger when the original
di¤erence in penetration rates is higher. Thus, mobile phones spread would exacerbate
distribution of wealth and emphasize the existing pattern of inequality. Nevertheless,
greater access to mobile phones is good for the economy, it could signi…cantly improve
welfare.
The rest of this paper is structured as follows. Section 2 presents the model and the case
prior mobile phones availability as a baseline. In Section 3, we introduce mobile phones
to the model. At this stage, we assume that the mobile phone penetration rate is set
exogenously. We analyze its e¤ects on farmer’s spatial arbitrage and markets equilibrium.
Section 4 presents mobile phone’s e¤ects on market outcomes. In, section 5, we give an
extension of the model by assuming that farmer’s choice to buy mobile phones is endogenous. Section 6 illustrates all the results by computing a numerical example. Section 7
o¤ers concluding remarks. Finally section 8 details the proofs of the results stated in the
main text.
5
II. A Model of Price dispersion and Information Search
In this section we develop a static, stochastic model with spatial arbitrage between two
neighboring marketplaces. Uncertainty on market supply is the main source of price dispersion across markets To do so, we extend the model of Jensen (2007). We begin by
setting up the model, then we examine how farmers decide where to sell their output when
they only observe their own production. we show that an equilibrium with price dispersion
could persist due to the lack of information.
A. The setup
Consider two villages denoted by 0 and 1; each with an equal continuum measure of farmers
who produce an homogenous good q. Both villages have a circular form with radius M j
(j = 0; 1) and each has a marketplace located at the center of the circle. Farmers seek to
maximize the pro…ts they earn from their farms. Price information may help them to decide
where to sell their outputs, locally or at the opposite market. I assume that individual
levels of production are random variables with identical distributions across individual, but
with a positive correlation for farmers within the same village. Speci…cally, I assume that
a farmer’s production depends on the level of an uncontrollable state of the world !: The
state space has two elements : ! 2 fB; Gg : B indicates the "bad" state of nature where
yield production is lower than in the "good" state of nature G7 . The realization of the two
states are independent between the two villages. Farmers initially regard the realization
of the good state of nature with a probability . Formally, I assume that in each state
of nature !, each farmer draws his production q from a distribution (qj!) where q takes
on values from q ! to q ! with q B
q G < q B < q G . And, (qj!) satis…es the Monotone
7
In Jensen (2007), ! represents the density of …sh in the …shermen’s zone which a¤ects his catch. The
G state indicates that the zone has high density while the B state indicates a low density. For example,
in agriculture, ! can be interpreted as weather.: bad weather where production yeild is lower and good
weather where production yield is higher
6
Likelihood Ratio Property, so that the ratio
(qjG)
(qjB)
L(q)
(II.1)
is increasing in q: High productions are more likely in the G state than in the B state.
Observing his own production q; a farmer updates his belief about the state of nature in
his locality. When q < q G ; he knows that his local-village is in the B state and, when
q > q B ; he is certain that his village is in the G-state: When q G
q
q B ; he revises his
belief according to Bayes rule. Denote by (q) the updated probability that his village is
in G state. Using Bayes’rule, each farmer’s updated belief is given by :
(q) =
8
>
>
0
>
>
<
>
>
>
>
:
if q B
1
L(q)
+ L(q)
if q G
q < qG
q
qB
(II.2)
if q > q B
1
A farmer chooses wether to sell locally or to switch to the other market after comparing
the expected gains between selling locally and switching. The farmer’s objective is to
maximize pro…ts by choosing where to sell their products. The default option for each
farmer is to sell his product on his local market. Though goods can move from one market
to the other, such movements involve costs8 . Such costs may represent per-unit costs
of accessing markets associated with transportation9 or transaction-induced …xed costs
10
. When a farmer decides to switch, he pays transportation costs proportional to his
8
An extended description of the various components of transaction costs is given in Ja¤ee (1995). They
include costs of searching for exchange opportunities and partners, screening information about the goods
and prices, bargaining over the terms of trade, transferring the goods, services, titles, cash, etc., monitoring
the exchange to assess whether the agreed terms are complied with, and enforcing the contract.
9
Proportional transactions costs which include per-unit costs of accessing markets associated with
transportation and imperfect information, have been used to explain labor (Eswaran and Kotwal, Sadoulet,
de Janvry, and Benjamin) and food (Goetz, de Janvry and Sadoulet) market participation decisions in
developing countries.
10
Fixed transactions costs that are invariant to the quantity of a good traded may include the costs of:
(a) search for a customer or salesperson with the best price, or search for a market— search costs are often
lumpy since a farmer may incur the same search cost to sell either one ton or ten tons of a product, or to
work one day or one year; (b) negotiation and bargaining— these costs may be important when there is
imperfect information regarding prices (often negotiation and bargaining takes place once per transaction,
7
production level and a …xed cost . We denote by
the per unit transportation cost.
In each state of nature !, denote by pj! the market price in market j: Since in B state,
the aggregate production is lower than in G state, we assume at this stage that the market
price is higher and
pjG
pjB :
(II.3)
Note that market prices are endogenous in the model and we will check that assumption
(II.3) holds in the market equilibrium.
B. Market Choice Prior Mobile Phone
In this subsection, we analyze a farmer’s spatial arbitrage when his decision is only based on
his own private signal . Each farmer observes his own production q, then updates his belief
about the prevailing state of his local market and decides where to sell. As stated above,
his choice is binary: either the farmer sells locally or he switches to the other market.
The objective of this subsection is to study the determinants of the decision to switch.
Especially, we establish that a Bayes-Nash equilibrium with price dispersion exists.The
timing of events in the economy occurs according to the following sequence.
Nature chooses the state for each market;
Each farmer learns their level of production;
Observing their own production, each farmer updates their assessment of the state
of their local market;
Those who choose to switch then leave their local market to sell in the other market.
and these costs are invariant to the size of the transaction); (c) screening, enforcement, and supervision—
farmers who sell their product, land, or labor on credit may have to screen buyers to make sure they are
reliable, and they may have to pay legal enforcement costs in case of default.(Key and al. 2000)
8
Without loss of generality, consider a farmer located in market 0: Observing his own
production q, he updates his beliefs about the state of his own market according to (II.2).
If he decides to sell locally, his expected gain V (0) is given by
V (0) =
(q)] p0B q
(q)p0G + [1
(II.4)
And, if he decides to switch to market 1, his expected gain V (1) is
V (1) =
p1G + (1
)p1B
(II.5)
q
Farmer compares the expected gains between selling locally (II.4) and switching (II.5)then
he decides where to sell. He remains locally when the expected gains V (0) is greater than
the expected gain V (1) to switching, otherwise he switches to market 1. The net gain from
switching for a farmer with production q is:
V
with
p =
V (1)
V (0) = q [ p
p1G + (1
)p1B
(II.6)
]
(q)p0G + [1
(q)] p0B
(II.7)
p denote the expected price premium from switching :The market choice decision could
be formulated as below: A farmer whose level of production q satis…es V > 0 will choose
to switch, while a farmer whose production level satis…es V < 0 will stay and sell locally.
A farmer who is indi¤erent between the two options has a level of production qb such that
V
0:
Thus, the determinants of the spatial arbitrage decision are: (i) the level of production
q, (iii) the net expected price premium from switching
p and (ii) the transaction costs
; . Clearly, a rise in p1! or a decrease in p0! provides for a typical farmer q an increased
incentive to switch; so does an exogenous decrease in transaction costs.
9
Consider a farmer who is indi¤erent between selling locally or switching to the opposite
market. His level of production qb is such that V (0)
V (1): We have the following result :
Theorem II.1. Suppose condition (II.1) and (II.3) hold. When each farmer only observes
his own production, there exists a Bayes-Nash equilibrium characterized by a threshold level
@b
q
@b
q
of production qb( ; ) with
0 and
0 where
@
@
1. Farmers with level of production greater than qb switch to the other market while
those with production lower than qb sell locally. Indeed, the threshold level of production qb
is given by
8
>
q
>
>
< B
qb =
qG
>
>
>
:
if E [p1 ]
1
if E [p ]
2 ]q B ; q G [
p0B
+
p0G
+
qB
qG
if otherwise
2. A rise in price dispersion across markets increases spatial arbitrage opportunities.
3.There are thresholds
and
that when
or
; all farmers always sell in
their local market.
Theorem II.1 states that when producers observe only their own production, those with
the highest level of production switch to the nonlocal market because they assess a higher
likelihood of being in a G state and because their high level of production yields a greater
expected gain in pro…ts for a given expected price. Prices will di¤er across villages, farmers
typically know only the local price. So even if, say the price in the other market is higher,
they don’t know to sell their product there. Indeed, existence of transaction costs reduces
opportunities for arbitrage. And when transaction costs are so high, there may be no
switching because even for farmer with the highest level of production, the expected gain
is less than transaction costs
More precisely, Theorem II.1 states that the threshold qb is determined by transaction
costs and markets prices di¤erential. Especially, the cuto¤ for switching qb is increasing
with
and : Hence, two e¤ects in‡uence farmer’s arbitrage :
(i) An information e¤ect : to switch, farmer should be sure that expected price premium
from switching ( p) covers transportation costs. So, those who are only almost sure that
10
their local market is in a G state (the price is lower) are to be likely to switch.
(ii) An income e¤ect. : to be able to switch, the switching premium net transportation
cost q( p
) should cover the …xed cost. Here, information e¤ects and income e¤ects
move in the same direction.
C. Market Clearing
This part complete the market model by specifying the demand side and determining
the equilibrium price. We analyze the market equilibrium when farmers spatial arbitrage
are only based on their own private signal. At equilibrium, total demand equalizes total
supply in each market. We assume without loss of generality that transaction costs ( ; )
satisfy property 3 of Theorem II.1. This allows us to focus on the case where there is no
switching in equilibrium prior to mobile phone availability11 . Thus there is no switching
in equilibrium, so market supply is equal to the aggregate production for each market. We
assume that all consumers have an identical individual demand q(p) where p is the market
price and q(p) is the quantity demanded at price p and q 0 (p)
0
12
.This latter condition
assumes that the demand function is not increasing with the market price p .
In each market, the aggregate demand equals the individual demand multiplied by the
aggregate consumers’mass which equals the surface area of the circle
2
(M j ) . So, in the
state !; the aggregate demand D!j for the market j is
D!j =
Mj
2
q(p! )
(II.8)
where pj! is the market price. The quantity supplied to market j is equal to the aggregate
production Qj! . The aggregate production equals the average production Q! multiplied
11
For example, we assume that
: This allows us to focus on the case where there is no switching
in equilibrium while there is no search technology. All results remain availaible without this condition.
12
We assume that each consumer has a quasi-linear utility function, u(q) + y, where q is the quantity of
the homogeneous product and y is the quantity of some numeraire good whose price is normalized to be
unity. This implies that the indirect utility of a consumer who pays a price p per unit of the product and
who has an income of M is V (p; M ) = v(p) + M where v() is nonincreasing in p: By Roy’s identity, note
that the demand for the product of relevance is q(p)
v 0 (p).
11
by the total production mass
2
(M j ) . So in state !; the aggregate supply to market j is
Qj! = Q! M j
2
(II.9)
where Q! the average production in state ! is given by
Q!
Z
q!
q (qj!)dq
q!
Equalizing the aggregate demand (II.8) to the aggregate supply (II.9), we have the
markets prices equilibrium pj! :
pj! = q
1
(II.10)
Q!
Clearly, markets prices equilibrium (II.10) satisfy condition (II.3).
Uncertainty in production level and transaction costs are used in this model to explain
the dispersion in market prices. The model reproduces a market equilibrium with price
dispersion. Prices di¤er across village. Because of price uncertainty and transaction costs,
farmers are not able to pursue the highest price, they usually sell locally. When market
price in the other village is higher, they miss opportunities to earn more income, and
consumers face excess price. By not being able to pursue the highest price, farmers are not
sending their output to where they are most valued.
III. Market Equilibrium With Mobile Phone
Now, we introduce mobile phone and analyze how this new search technology a¤ects
farmer’s behavior and the market equilibrium. In this section, we assume that mobile
phone penetration rates are exogenously. Speci…cally, we assume that in village j; mobile
phones are only available within a circle of radius T j (T j
M j ) around the market. Hence,
the only source of mobile divide is the non availability of technology. All farmers located
within the coverage zone have a mobile phone. So, the mobile phone coverage rate tj which
12
represents also mobile phone penetration rate in village j is given by
tj =
Tj
Mj
2
(III.1)
Mobile phone allows farmer who have it to learn the true state of nature so price in
both markets and thereby avoid unpro…table switching while uninformed farmers (those
who don’t have mobile phone) always sell locally as before13 . The timing of events in the
economy occurs according to the following sequence.
Nature chooses the state for each market;
Each farmer learns his level of production;
Observing their own production, each farmer who has not mobile updates their assessment of the state of their local market;
Each farmer who has mobile phone do call to check markets prices;
Those who choose to switch then leave their local market to sell in the other market.
When both markets are in the same state, any arbitrage is unpro…table due to transaction costs and all farmers sell in their local market. When markets are in opposite
states, some informed farmers sell in the market o¤ering the highest price while uninformed farmers always sell locally. To illustrate, assume that marketplaces are in opposite
13
In practice, mobile phone allows farmer to check market price. For example, …shermen in India call the
landing centers to …nd where the highest prices for their catch are and subsequently land there (Jensen,
2007, Abraham 2007). In Niger, traders use mobile phone to check price information over a larger number
of market (Aker, 2008). In Kenya. with their mobile phone, farmers can access to market information.
Market information includes prices of commodities in di¤erent markets, and commodity o¤ers to sell and
bids to buy as well as short extension messages. Through the o¤ers and bids function, farmers are able
to advertise their stocks (o¤ers) for sale or their demands (bids) for farm inputs such as fertilizers and
improved seeds (Mukhebi, 2004). In Senegal, Farmers in the …eld can use their mobile phones to check
prices before they set o¤ and …nd out where they will get the best o¤er for their produce (The BBC News
2002). In Bangladesh’s Narshingdi, an isolated district, villagers who grow crops or raise livestock can use
their village cell phone to speak directly to wholesalers and are able to get better prices for their goods
in the marketplace (Ahmed, 2000). In Cote d’Ivoire co¤ee growers share mobile phones to follow hourly
changes in co¤ee prices in order to sell at the most pro…table time (Lopez, 2000)
13
states:Without loss of generality, we suppose that market 0 is in G state while market 1
is in B state14 . We …rst show the condition under which informed farmer gains to switch.
Consider an informed farmer located at market 0: By switching to market 1; he gains
[q (p1B
p0G
)
] in pro…t. Then the expected net gain R from search technology is
given by
R
(1
) (q) q p1B
p0G
(III.2)
He gains to switch if R > 0: Clearly, according to (II.2), we have R(q) = 0 if q < q G : This
suggests that informed farmers who have a higher level of production are more likely to
switch. Denote qI the quantity such that a farmer is indi¤erent between selling locally or
switching: We have the following Lemma.
Lemma 1. qI is given by
qI =
8
>
>
>
>
<
if p1B
qG
>
p1B p0G
>
>
>
:
qG
if
+
qG
if p1B
p0G
+
< p1B
p0G <
p0G
+
qG
+
qG
(III.3)
qG
As the bene…t (III.2) increases with q, informed farmer with a level of production
higher than qI switches to market 1, otherwise he/her sells locally. Even, informed farmer
knows prices in both markets, arbitrage is not always pro…table because of transaction
costs. When transaction costs are lower, all informed farmers pursue the highest price.
But when transaction costs are very high, even if farmers who have mobile phone realizes
that market 1 price is higher, they are not able to switch. Clearly, a rise in transaction
costs reduces opportunity for arbitrage. A rise in transaction costs increases the cut o¤
level qI : Furthermore, a rise in market 1 price p1B (or a decrease in local market price p0G )
gives more incentives to switch15 :
14
According to his belief, this event occurs with probability (q) (1
) (the probability that their home
market is in G state and the other market is in B state)
15
So a higher price dispersion gives more incentives to switch (speci…cally for farmer with lower
production).
14
The aggregate supply S 1 to market 1 derives from two components: quantity Q1B supplied by local farmers and I 0 by informed farmers who switch from market 0:
S 1 (p0 ; p1 ) = Q1B + I 0
(III.4)
Z
(III.5)
where
0
I =
T
0 2
qg
q (qjG)dq
qI
qI is the threshold as given by theorem II.1 above it informed farmer gains to switch.
In market 0, the aggregate market supply S 0 is equal to the aggregate production minus
the quantity from those who switch to market 1:
S 0 (p0 ; p1 ) = Q0G
I0
(III.6)
Now, we can characterize the market equilibrium.
De…nition 1. An equilibrium for this economy is a threshold level of production qI and a
price system (p0 ; p1 ) such
1. Informed Farmers (who have mobile phone) with level of production greater than qI
switch to the other market while those with production lower than qI sell locally
2. In each market, aggregate demand equals aggregate supply :
S 0 (p0 ; p1 ) = D0 (p0 )
S 1 (p0 ; p1 ) = D1 (p1 )
(III.7)
On the basis of this de…nition, we can state and prove the following results:
Theorem III.1. Suppose condition (II.1) hold. Assume that market 0 is in G state and
market 1 in B state. Then, a competitive equilibrium exists and is unique. In addition, it
0
1
> 0; (ii) @p
< 0 , (iii)
satis…es the properties (i) @p
@t0
@t0
@p0
@l
< 0, and (iv)
@p1
@l
> 0; l = ; :
The proof is given in the Appendix. Properties (i) and (ii) of Theorem III.1 are intuitive.
A rise in mobile phone penetration increases the number of informed farmers. More farmers
15
are sending their output to market 1 where they valued most. With the rise in mobile
phone penetration rate t0 ; more farmers are able to pursue the highest price in market 1,
so supplied to market 1 increases and lowering the price there. Inversely, because of these
more switching, market 0 supply decreases and increasing the price there.
Following tradional approach in information search and price dispersion outlined in
Baye, Morgan and Scholten (2007) , we examine now, how the variance in the distribution
of equilibrium prices varies with mobile phone di¤usion16 . Note that, in equilibrium, the
variance in market j prices is given by
2
j
=E
h
p
j 2
i
E pj
2
(III.8)
And the variance in prices between the markets is given by:
2
V ar(p1
p0 ) =
2
0
+
2
1
(III.9)
Thus, we have the following results :
Proposition 1. Price dispersion e¤ect:
(i) A rise in mobile phone penetration coverage reduces the variance of equilibrium
prices within markets.
(ii) A rise in mobile phone coverage reduces the variance of equilibrium prices across
markets.
Proposition 1 states that an expansion of mobile phone coverage reduces the dispersion
of prices. A rise in mobile coverage increases the number of farmers who are able to pursue
the highest price. Thus, more goods move to where they are valued most lowering the
16
The commonly used measures of price dispersion in the search literature are the sample variance
of prices across markets (Pratt, Wise and Zeckauser 1979, Aker 2008), the CV across markets (Eckard
2004, Jensen 2007), and the maximum and minimum (max-min) prices across markets (Pratt, Wise and
Zeckhauser 1979, Jensen 2007). We use variance of prices within and across markets and prices across
markets to assess mobile phone e¤ects on market performance. As our model is binary, this latter measure
is close to the max-min approach.
16
price there and increasing the price in the other market. And more e¢ cient allocation of
goods improves markets’functioning. Especially, mobile phones will have a larger impact
upon price dispersion once a higher percentage of markets have mobile phone coverage.
The next result gives the e¤ects of transaction costs on price dispersion.
Proposition 2. A rise in transaction cost increases the variance of equilibrium prices
within markets and across markets : (i)
@ 2j
@l
2
> 0 ; (ii) @@l > 0; l = ;
Proposition 2 states that price dispersion is greater where transaction costs are higher.
As transportation costs increase there will be less switching (because of information and
income e¤ects) and greater price dispersion in equilibrium.Thus, less goods move to where
they are valued most and price dispersion persists.
IV. Who gain from mobile phone access?
In this section, we explore the source of di¤erential gains from spatial arbitrage among
farmers. How does the introduction of mobile phones a¤ects gains from spatial arbitrage?
Mobile phone increases the opportunity of arbitrage for those who have it. So the model
predicts that the introduction of mobile phones promotes market exchanges for goods. Is
this change pro…table for everyone for those who have technology and those who have not,
and how does it a¤ect the existing pattern of inequality? To answer these questions, we
analyze two components of mobile phone impacts : price e¤ect and welfare e¤ect .
A. Mobile Phone And Information Externalities
In this subsection, we focus on the e¤ects of information improvement via mobile phone
use on market prices. We analyze information externalities and examine a key comparative
static implication of the model: what happens to prices as coverage rates of mobile phone
increase? The previous result states that uninformed farmers (those who don’t have mobile
phone) receive on average lower prices than informed farmers (those who have mobile
phone). However, mobile phones access creates a positive intra-village externality and all
17
producers can expect to receive a higher price. That is, the in‡ux of informed consumers
exerts a negative externality on producers located in the opposite market. We use theorem
II.1 to derive the following results.
Proposition 3. (i) Intramarket externality : An expansion of mobile phone coverage in
a market always raises the average price received by uninformed farmers located at this
market.
(ii) Intermarket externality : An expansion of mobile phone coverage in a market always
decreases the average price received by farmers in the other market.
The proof of Proposition 3 results from the Theorem III:1. Proposition 1 posits that
a rise in mobile phone penetration improves markets’ functioning. And Proposition 3
states that there are signi…cant spillover gains for producer who did not have phones
due to improved functioning of the markets. Thus, mobile phone users create a positive
externality on nonusers within his market and a negative externality on the other market.
B. Distributional e¤ects of mobile Phone’s spread
We examine in this subsection the distributional e¤ects of mobile phone di¤usion. By distributional consequences, we mean the e¤ects of mobile phones introduction or an increase
in coverage rate on inequalities in the distribution of revenue. To do so, we examines the
ex-post inequality when markets are in opposite states and the expected pro…t.
Farmers could be categorized in three types : within a village those who have mobile
phones and those who don’t have and those in the other village. Those who have mobile
phone and highest level of production always sell in the market giving the higher price.
Hence, the model predicts that this category of farmers always win. Those who don’t
have mobile phone always sell locally. And due to externalities e¤ects, they also bene…t
from mobile phone di¤usion in their market. For farmers from the other market, due to
externality e¤ect, the price they sells now their products will be lower than the price they
would received prior to mobile phones availability.
18
To formalize this, let a typical farmer with a level of production q with q > qI 17 : Here
are two possible cases, either he is located at market 0 or market 1:First, suppose he is
located at market 0. Here are two possible types, either he has mobile phone (informed
I), or he hasn’t (uninformed N I). Denote by pI (respectively pN I ) the price received by
the informed farmer I (respectively uninformed N I ). Second, if he is located at market
1; denote by F his type (either he has mobile or not) and by pF the price at it he sells
his product. We can de…ne the price premium net of transaction costs18 of information
ph (h = I; N I; F ) by the di¤erence between the
improvement (or having mobile phone)
price a producer is now selling his product by the price he would receive if there were no
mobile phones. When market 0 is in G state, prices premium are given by:
pI =
(1
) p1GB
pG
pN I =
(1
) p0GB
pG
(IV.2)
pF =
(1
) p1GB
pB
(IV.3)
Note that we always have
pI
019 ,
pN I
0 and
+
(IV.1)
q
pF
0. These results are
immediately from externalities e¤ects. Indeed, price premium for those who have mobile
phone is always higher than for those who don’t have it20 . Primarily, mobile phone bene…ts
those who have it. But farmers without phones also bene…t as the domestic price increases.
Moreover, the gain for those who have mobile phone is at least greater than for those who
don’t have it,
pI
pN I : In contrast, farmers in the other village (both with and
without phones) are penalized as the price in the other market decreases. As producers
who have higher level of production are more likely to purchase mobile phone,they are
more likely to gain higher incomes. Thus, these heterogeneity e¤ects will reinforce existing
patterns of inequality. The next two results examine the e¤ects of mobile phone di¤usion
on inequalities.
17
If q qI ; he always sells locally.
Note that, it measures also the per unit gain of information (having mobile phone).
19
Note that as q > qI ; we have pI R(q) > 0 according to (III.2) and (III.3).
20
pI
pN I 0:
18
19
Proposition 4. (i)
@ pI
@t0
< 0 ; (ii)
@ pN I
@t0
> 0 ; and (iii)
@ pF
@t0
< 0:
Proposition 4 tell us that the di¤erence in gain is important at the …rst stage (lower
penetration rate) of mobile phone di¤usion.This suggests that these e¤ects are stronger
when the original di¤erence in penetration rates between markets is higher. Thus, the
di¤usion of a new technology which is not uniform may reinforce existing patterns of
inequality. To see more clearly these results, we analyze the expected pro…t according to
the types of producers I Infomed (either in Market 0 or 1), N I j Uninformed in Market j.
To do so, we de…ne the expected gain
W i (i = I; N I 0 ; N I 1 ) for a typical producer q by
the di¤erence between the pro…t he/she obtains by the pro…t he/she would gain if there
were no mobile phones.
WI =
W NI
0
W NI
1
(1
)
p1GB
pG + p0BG
pB
=
(1
)
p0GB
pG + p0BG
pB
(IV.5)
=
(1
)
p1BG
pG + p1GB
pB
(IV.6)
Note againe that under (III.2) and (III.3).we always have
+
WI
(IV.4)
q
0. And we have the next
results
Proposition 5. Let condition (III.2) and (III.3) hold. Then we have
i = N I 0; N I 1 ;
0
@ WI
(ii)
@t0
@ WI
0 ; (iii)
@t0
0
@ W NI
0 ; and (iv)
@t0
(i)
WI
W i;
1
0:
We can set the bene…t of mobile phone access by the value of information measured by
the increase in utility from receiving information and from optimally reacting to it (Birchler
& Bütler 2007). In monetary terms, the value of information equals the expected monetary value of the decision with the information (here mobile phone) minus the expected
monetary value of a decision without the information (without mobile phone). Denote by
V I this value, we have :
V I = (1
) p1GB
20
p0GB
+
q
(IV.7)
and we have as a corollary of Proposition 5:
Corollary 1. Information Value decreases in mobile phone coverage. Formally,
@V I
@t0
0
Proposition 5 tell us that despite negative externality e¤ects of a rise in mobile phone
penetration in a market, informed producers in the other market lose less than uniformed.
The corollary indicates that at the …rst stage of mobile phone di¤usion, having this search
technology is most valued. And when more higher percentage of markets have mobile
coverage, the bene…t from having mobile phone is lower.
C. Mobile Phone Expansion and Welfare E¤ects
The previous results suggest that there are potential welfare improvement associated with
the introduction of mobile phones. Primarily due to the more e¢ cient allocation of goods
across markets. Nevertheless, the net welfare gains, and how such gains are distributed
among farmers and consumers are ambiguous. The change in producers surplus will arise
through changes in price and quantity sold and the costs associated due to arbitrage. When
the markets are in opposite states, producer surplus in an B-state declined while producer
surplus in an G state increase. In an B state, switching from an G-state are added to
the market. and producers are now selling for a lower price than if there were no mobile
phones. Thus net change in producer surplus is ambiguous.
The …gure 1 shows consumer and producer surplus after and prior to mobile phone
availability when one marketplace is in an G-state and the other is in an B-state. In the
G-market, consumers lose A + C + D while producers gain A and lose E + F when mobile
phones are introduced. I products are moving to the opposite marketplace. These changes
can be viewed as a net loss of C +D+E+F and a transfer of A from consumers to producers
(because producer are now selling for a higher price than if there were no mobile phones).In
the B-market, consumers gain A1 + C1 + D1 ,while producers lose A1 and gain E1 + F1 ,
representing a net gain of C1 +D1 +E1 +F1 and a transfer of A1 from producers to consumers
(since producers are now selling for a lower price than if there were no mobile phones).The
net change in total welfare is the di¤erence (C1 + D1 + E1 + F1 )
21
(C + D + E + F )
price
p
price
p
G-Marketplace
B-Marketplace
With mobile
phones access
p02
Prior mobile
phones
A1
A
p01
C1
p11
D
D1
p11
Prior mobile
phones
C
With mobile
phones access
F1
E1
E
F
Q
Q01
Q02
Q
Quantity Q
Q10
Q11
Quantity Q
Figure 1: Figure 1 : Welfare e¤ects
The size and direction of the net transfer from consumers to producers, as well as the
net gain for each group will depend on the shape of the demand curve and the amount of
arbitrage. This latter will depend on the penetration rate of mobile phone, transaction costs
and relative size of the markets. Thus, how the net welfare gain is shared between the two
groups, and whether, in fact, one group gains while the other loses in response to increased
arbitrage, is a priori ambiguous. This unfortunately implies that the model cannot be
solved generically. For this reason, we discuss the welfare impacts in the numerical example
in the section 6.
V. Endogenizing the Mobile Phone Demand
Previously, the penetration rate of mobile phone is setting exogenously. Hence, the only
source of mobile divide is the non-availability of the technology. In this section, we assume
that the decision to buy mobile phone, so to do search is endogenous. When the mobile
phone is available, producer can buy it at cost
: With this technology, he can learn the
state of the nature so the prices in both markets. The farmer’s problem is whether to
purchase the technology and decide where to sell their product. Hence, the second source
of digital divide is una¤ordability of the technology. Thus, farmer doesn’t buy mobile
22
because it’s not available or it’s available but too expensive and he can’t a¤ord it.
As before, we assume again that transaction costs are that prior to mobile phone
availability, there were no switching. This allows us to focus on the case where there is
no switching in equilibrium while there is no search technology. When both villages are
in opposite states, farmers from the village where the price is lower (in G state) will gain
by switching to the opposite village where market price is higher (in B state). So, search
allows farmer to learn price in both markets and thereby avoid unpro…table switching. The
timing of events in the economy occur according to the following sequence.
Nature chooses the state for each market;
Each farmer learns his quantity of production;
Observing their own production, each farmer who has not mobile updates their assessment of the state of their local market;
Each farmer who has mobile phone access buys search technology if it’s pro…table;
Those who choose to switch then leave their local market to sell in the other market.
We …rst show the condition under which farmer gains from purchasing the search technology. Without loss of generality, let a farmer whose local market 0 is in G state and
assume that market 1 is in B state :This event occurs with probability (q) (1
purchasing the search technology, the farmer gains [q (p1B
p0G
)
)21 . By
] in revenue . Then
the expected net gain R from purchasing technology is given by
R
(1
) (q) q p1B
p0G
(V.1)
The net expected bene…t to switch is equal to the net expected gains minus the search cost
Vm
21
R
The probability that their local market is in G-state and the other market is in B-state.
23
When
> R; the information is too expensive and no one purchases the technology. The
equilibrium condition for purchasing the technology is that the bene…t of search is at least
greater than the search cost R(:)
: We assume this condition is satis…ed, speci…cally,
satis…es the condition
(V.2)
R(q G )
As the bene…t (V.1) increases with q, farmers with higher production are more likely to
purchase mobile phone. Search is purchased up to the point of expected gain from arbitrage
(net of transaction cost) equals the cost of search. A farmer who is indi¤erent between
selling locally or switching to the opposite market has a quantity of product qem that :
Vm
0
(V.3)
Like the exogenous case in section 3, we can show that when each farmer only observes
his own production, there exists a Bayes-Nash equilibrium characterized by a threshold level
of production qeI ( ) above it, buying mobile phone is pro…table. Farmer located within
mobile phone coverage and whose production level is greater than this value buys search
technology and switches while those whose level of production is lower than it doesn’t
buy technology and sells locally. Using again the de…nition of competitive equilibrium
(De…nition 1), we can show that all previous results are robust22 . In particular, we have
the following result.
Theorem V.1. Let conditions (II.1) and (V.2)hold. When each farmer observes only
their own production,then, a competitive (e
qI ; pe0 ; pe1 ) equilibrium with qeI0 ( ) > 0 exists and
@ pe1
@ pe0
@ pe0
is unique. In addition, it satis…es the proprieties (i) 0 >0; (ii) 0 < 0; (iii)
< 0;
@t
@t
@
@ pe1
and (iv)
>0
@
The proof of the this theorem is the same as those of Theorem V:123 . As before,
22
The exogenous case of mobile phone penetration rate can be considered as and endogenous case by
setting
0: This can be interpreted as mobile phone had been purchased before doing arbitrage.
23
When < , i.e., there would be some switching even without the search technology, Theorem V.1
24
producers with higher level of production are more likely to believe they are in a G state
and thus may gain by switching. They are therefore more likely to purchase search (mobile
phone)24 .
Following standard approach in literature on consumer search theory, we examine how
changes in search costs a¤ect market actors’ behavior and equilibrium price dispersion
(Baye, Morgan and Scholten 2007)25 . In equilibrium, we can extend Proposition 1 to the
endogenous case. Speci…cally, we have the following results:
Proposition 6. A reduction in mobile phone (search) cost
reduces price dispersion
within and between the markets.
In the next result, we derive equivalents results like in the exogenous case about externalities e¤ects.
Proposition 7. A reduction in mobile phone cost in a village creates positive externalities on local price (increasing price) and create negative externality in the other
market (lowering price).
VI. Numerical Example
In this section we present the results of a numerical simulation of the model economy. The
intuition behind the previous qualitative results can be obtained with a simple numerical
continues to hold but only when search costs are below a threshold,
( ). If search costs are high relative
to transportation costs, two cases can arise: (1) no producers purchase search, but those with the highest
level of production switch anyway (as in Theorem II.1 or V.1) producers with the highest level of production
switch without purchasing search and producers with production in an intermediate range below this buy
search and switch only when the markets are in opposite states .
24
In a repeated game where the search technology is a durable good like a mobile phone, producers purchase
search when the discounted stream of expected gains from switching markets over the life of the technology
exceeds the cost. Variation in the stream of expected gains can arise through heterogeneity in average
production.
25
Comparative static predictions of the existing literature on price dispersion are contrasting. They are
due to di¤erent assumptions with respect to consumers’demand functions, the …xed or sequential nature
of search and …rm cost heterogeneity.For example, the sequential search models of Reinganum (1979) and
Stahl (1989) predict that a reduction in search costs will decrease the variance of equilibrium prices, while
MacMinn (1980) shows that a reduction in search costs can increase price dispersion.
25
example. We start by assigning values to relevant parameters parameterize the main
functions studied in the previous section. In particular, we suppose that risk a¤ects supply
multiplicatively with a shock T (!)such T (G) > T (B) and T (!) = 1 + !:Assume that
follows Pareto distribution with density (q) =
q3
; q 2 [1; q] :De…ne (qj!) the distribution
of q in the ! state :
(qj!) =
q
T (!)
1
T (!)
where q 2 [T (!); qT (!)] :
Clearly, (qj!) satis…es the monotone likelihood property26 . For the demand side, we
assume that the individual demand function is linear27 q(p) =
p with
> 3 and
> 0:
For numerical simulation, we set B =
:5; G = :5. Farmer updates their assessment of
the state of their local market according to :
(qi ) =
8
>
>
0
>
<
if
3
if
4
>
>
>
: 1
1
2
qi <
3
2
if 50
3
2
(VI.1)
qi < 50
qi
150
Transaction costs are setting that prior to mobile phone, there were no switching28 . For
numerical simulation, parameters and basics parameters of the model are given in the Table
1 below.
2
1+ q1
26
The average production in ! state is Q! = Q T (!) with Q =
27
Under these conditions, the price markets equilibrium when there are no arbitrage are
2
pj! =
Q
2
2
when ! = B
3Q
2
when ! = G
that require > 3
28
Arbitrage condition requires that transaction costs satisfy
=
q( 2Q
is the mean of distribution
)
26
2 [0; ] where
=
Q
2
and
2 [0; ] where
Table 1 : Parameters of the model
qB
qB
qG
qG
QB
QG
0:5
50
1:5
100 0:99 2:97 0:1
14:8 :5
3:12 2
2
The following empirical simulation compares how changes in the outcomes of interest
(price dispersion, price levels and welfare) correspond to the introduction of mobile phone.
We assume that service is introduced gradually throughout the village, rather than all at
once29 . Section A and B present the exogenous case . In section A, we explore mobile
phone impact under the hypothesis M 0 = M 1 while in section B, we assume an unequal
size of the markets by setting M 0 = (M 1 )=2: Section C presents the endogenous case.
A. Exploring the Impact of Mobile Phone di¤usion
This section presents simulation results under the exogenous case of mobile phone penetration rate. We suppose that markets have equal size.
A.1. E¤ects on Market Performance
In this subsection, we investigate the e¤ects of mobile phone coverage expansion on market
performance. The model posits that equilibrium price dispersion will decrease as mobile
phone penetration rate increases. Simulation results in Figure 2 indicate that the introduction of mobile phone reduces price dispersion. Variance of prices within both markets
and across markets become lower as higher percentage of villages are covered by mobile
phone.
When we increase the per unit transaction cost from
1
= 0:99 to
2
= 0:36; the variance
of prices becomes larger (Figure 3). When transportation cost is higher, it becomes less
pro…table to switch (information e¤ect). As transportation costs increase there will be less
29
For the three Kerala’s districts in India considered by Jensen (2007) for example, service became
available …rst in Kozhikode (Kozhikode city, e¤ective January 29, 1997), followed by Kannur (Kannur city
on July 6, 1998, and Thalassery on July 31, 1998) and then Kasaragod (Kasaragod city and Kanhangad
on May 21, 2000).
27
switching and greater price dispersion in equilibrium.
Pric e Va ria nc e
Within Market 0
Within Market 1
Between Markets
0.25
0.25
0.5
0.245
0.245
0.49
0.24
0.24
0.48
0.235
0.235
0.47
0.23
0.23
0.46
0.225
0.225
0.45
0.22
0.22
0.44
0.215
0.215
0.43
0.21
0.21
0.42
0.205
0.205
0.41
0.2
0
0.5
0.2
1
0
0.5
0.4
1
0
0.5
1
Mobile C ov e ra ge t 0 =t 1
Figure 2 : Impact of Mobile Phone on variance of prices
Within Market 0
W it hin Ma rk e t 1
0.25
0.5
ta u =ta u 1
ta u =ta u 2
ta u =ta u 1
ta u =ta u 2
0.245
0.49
0.24
0.24
0.48
0.235
0.235
0.47
0.23
0.23
0.46
0.225
0.22
Pric e Va ria nc e
0.245
Pric e Va ria nc e
Pric e Va ria nc e
B e t w e e n Ma rk e t s
0.25
ta u =ta u 1
ta u =ta u 2
0.225
0.22
0.45
0.44
0.215
0.215
0.43
0.21
0.21
0.42
0.205
0.205
0.41
0.2
0
0.5
Mobile C ov e ra ge t 0 =t 1
1
0.2
0
0.5
Mobile C ov e ra ge t 0 =t 1
1
0.4
0
0.5
1
Mobile C ov e ra ge t 0 =t 1
Figure 3 : E¤ect of Transfert Cost on Variance of Prices
28
A.2. E¤ects on Prices Levels
To illustrate externalities e¤ects, we simulate the impact of mobile phone di¤usion on
market prices levels. Figure 4a depicts e¤ects of mobile phone expansion on market
prices. Prior to mobile phone availability, there were large max-min spread across markets.
When mobile phone service was introduced, this di¤erential prices spread declined. This
decline becomes larger as higher percentage of villages are covered by mobile phone. Figure
4b shows the e¤ects on average price when di¤usion of mobile phones is not symetric30 .
Average spread is larger when the original di¤erence in penetration rates is higher. The
addition of mobile phone in Market 0 is associated with a substantial reduction of average
spread.
Average Market Prices
Market Prices in G-B State
1.4
0.595
Mar k et 1
Prior to Mobile Phone
Mar k et 0
0.59
Mar k et in G-State
Mar k et in B- State
1.2
0.585
1
Av e rge Pric e
Pric e le v e l
0.58
0.8
0.6
0.575
0.57
0.565
0.4
0.56
0.2
0.555
0
0
0.2
0.4
0.6
0.8
0.55
1
0
Mobile C overage t0= t1
0.2
0.4
0.6
0.8
1
Mobile C overage t0
t 1=0.65
Figure 4 : Mobile Phone E¤ect on Market Prices
A.3. Mobile Phone Di¤usion and Inequality
The model predicts that improvements in market information bene…t primarily the producer who adopted mobile phones. When the penetration rate increases in a village, there
are signi…cant spillover gains for the producer who did not has phones due to the improved
30
We assume that in the village 1; mobile phone is available within coverage rate t1 = 0:65 and we
analyze the e¤ects of mobile phone coverage expansion in the village 0:
29
functioning of markets. To see these e¤ects even more clearly, we simulate the inequality ex
post when the markets are in opposite states and the inequality in expected gain according
to the three types of producers described in section IV Figure 5a presents the e¤ects of
mobile di¤usion when Market 0 is in G state and Market 1 in B state. When mobile phone
coverage increases in village 0, farmers without phones also bene…t as the price in this
market increases. Phone users had a clear positive externality on nonuser. In contrast,
farmers from Market 1 (both with and without phones) are penalized as their market price
decreases. These e¤ects are stronger when the original di¤erence in penetration rates is
higher.
Gains in G-B state
Average Gains
0.3
Average Gains
0.3
0.3
In fo r me d Ma r k e t 0
U n in fo r me d Ma r k e t 0
Fa r me r Ma r k e t 1
In fo r me d Ma r k e t 0
U n in fo r me d Ma r k e t 0
U n in fo r me d Ma r k e t 1
In fo r me d
U n in fo r me d
0.25
0.25
0.25
0.2
0.2
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
0
0
0
-0.05
0
0.5
Mobile C ov e ra ge t 0 =t 1
1
-0.05
0
0.5
Mobile C ov e ra ge t 0 = t 1
1
-0.05
0
0.5
1
Mobile C ov e ra ge t 0
t 1 =0 .6 5
Figure 5 : Mobile Phone Impact on Gains
Figure 5b and 5c examines the changes in expected pro…ts among mobile phone users
versus nonusers. Producers using mobile phones bene…ts more than nonusers.They gained
more in part because they have higher level of production and because they are more likely
to be able to pro…tably exploit arbitrage opportunities, thus bene…t higher price.
30
A.4. Welfare e¤ects
We use producer and consumer changes in surplus to provide simple estimates of the
welfare changes. For the economy, changes in total surplus (the sum of consumer surplus
and producer surplus) are used to measure the net changes in welfare. Figure 4 shows the
e¤ects of the introduction of mobile phone on producer surplus, consumer surplus and net
welfare. Simulation results suggest that mobile phone spread are bene…cial for producers.
The net gains measured by producer surplus changes are positive and increasing with mobile
phone penetration. For consumers, gains from reduced price variability are negative.This
result can be explained by the fact that the demand is less price elastic31 . Therefore, the
net welfare gain has an inverted U-shape. At …rst stage of mobile di¤usion, consumers’
loss are lower than producers’gain because there are less switching. Beyond some turning
point, net welfare gain (always positive) declines with mobile phone coverage because there
are more switching so consumers’loss becomes larger.
Producer Surplus
Consumer Surplus
0.1
Net Welfare
0
t1 =.6 5
t0 =t1
t1 =.2 5
0.09
0.012
t1 =.6 5
t0 =t1
t1 =.2 5
t1 =.6 5
t0 =t1
t1 =.2 5
-0.01
0.01
0.08
-0.02
0.07
-0.03
0.008
0.05
Ne t Surplus
Ne t Surplus
Ne t Surplus
0.06
-0.04
-0.05
0.006
0.04
-0.06
0.004
0.03
-0.07
0.02
0.002
-0.08
0.01
0
0
0.5
Mobile Coverage t0
1
-0.09
0
0.5
Mobile Coverage t0
1
0
0
0.5
1
Mobile Coverage t0
Figure 6 : Mobile Phone E¤ect On Welfare
The previous results suggest that net welfare gains are likely to be associated with the
31
In general, the gains for consumers will be smaller (or even negative) when demand is less price elastic.
31
Producer Surplus
Consumer Surplus
0.1
Net Welfare
0
0.015
ta u =ta u 1
ta u =ta u 2
ta u =ta u 1
ta u =ta u 2
0.09
ta u =ta u 1
ta u =ta u 2
-0.01
0.01
0.08
-0.02
0.005
0.07
-0.03
0.05
Net Surplus
Net Surplus
Net Surplus
0.06
-0.04
-0.05
0
-0.005
0.04
-0.06
0.03
-0.01
-0.07
0.02
-0.015
-0.08
0.01
0
-0.09
0
0.5
Mobile C ov e ra ge t 0 =t 1
1
-0.02
0
0.5
Mobile C ov e ra ge t 0 =t 1
1
0
0.5
1
Mobile C ov e ra ge t 0 =t 1
Figure 1: Figure 7: E¤ect of Transfer Cost on Welfare
introduction of mobile phones. This is due to the more e¢ cient allocation of goods i.e.,
reallocating them to where they are more highly valued on the margin. The next simulation
describes mobile phone e¤ects when transportation cost is higher. The net producers’gains
are again positive (Figure 7) . When transportation cost is higher, there are less switching.
Producer surplus is lower because …rstly there is reduction of the number of farmers who
are able to pursue the higher price, and secodly there are less goods moving to the other
market so the externality intra-market is lower.
B. Exploring Mobile Phone e¤ects under Unequal Market’s Sizes
In this subsection, we explore the e¤ects of mobile phone di¤usion we market’s size are
unequal32 . To do so, we set the relative size of market 0 to market 1 to
=
M0
M1
2
= 0:5
and analyze how the impact of mobile phone di¤ers across space.
Figure 5a shows that externalities e¤ects are more stronger in the smaller market. When
markets are in opposites states, Ceteris paribus there are more switching from market 1.
32
This address a key issues in rural urban linkage well known as the rural-urban divide. The existence
of many isolated smaller rural markets around a greater urban market characterizes markets in developing
countries. A key question is to know if mobile phones will be pro…table for these rural markets.
32
Thus, negative externality to market 0 is stronger. Figure 5b shows the impact of uneven
mobile phone di¤usion on Market prices. Lower the mobile penetration rate in market 0
is; greater the di¤erence between the average prices is.
Market Price in G-B State
Average Market Price
1.4
0.59
Ma r k e t 0
Ma r k e t 1
Pr io r Ph o n e Ma r k e t 0
_ _ _ _ _ Ma r k e t 0
- - - - - Ma r k e t 1
1.2
0.58
1
Av e ra ge Pric e
Pric e le v e l
0.57
0.8
0.6
0.56
0.55
0.4
0.54
0.2
0
0
0.2
0.4
0.6
0.8
0.53
1
Mobile Coverage t0= t1
0
0.2
0.4
0.6
0.8
1
Mobile Coverage t0
t1=0.65
Figure 8 : Market Size E¤ect on Market Prices
To see more clearly distributional e¤ects, Figure 9 depicts ex-post and average producers’gains. When markets are in GB states33 , uninformed producers in market 0 bene…t
from positive externality e¤ect. Thus externality e¤ect to nonusers in the smaller market
is stronger than for those in the bigger one. Simulation results suggest that mobile phone
di¤usion is more likely pro…table for users in the smaller market. Whereas nonusers in the
smaller market lose in average due to the stronger negative externality. Lower the mobile
penetration rate in market 0 is; stronger is the loss for nonusers in this market.
33
market 0 is in G state and market 1 in B state
33
Gains in G-B State
Gains in B -G State
Average Gains
0.3
0.3
0.3
0.25
In fo r me d
U n in fo r me d Ma r k e t 0 0.25
Fa r me r Ma r k e t 1
In fo r me d
U n in fo r me d Ma r k e t 1
0.25
Fa r me r Ma r k e t 0
0.2
0.2
0.2
0.15
0.15
0.15
0.1
0.1
0.1
Average Gains
0.2
In fo r me d
U n in fo r me d Ma r k e t 0
U n in fo r me d Ma r k e t 1
In fo r me d
U n in fo r me d Ma r k e t 0
U n in fo r me d Ma r k e t 1
0.15
0.1
0.05
0.05
0.05
0.05
0
0
0
0
-0.05
0
0.5
1
Mobile C ov e ra ge t 0 =t 1
-0.05
0
0.5
-0.05
1
0
Mobile C ov e ra ge t 0 =t 1
0.5
Mobile C ov e ra ge t 0 =t 1
1
-0.05
0
0.5
1
Mobile C ov e ra ge t 0
t 1 =0 .6 5
Figure 9 : Market Size E¤ect on Gains
C. The endogenous case
Next results show the case to endogenizing the mobile phone demand in both markets.We
set
= 2 the cost of mobile phone. All qualitative results describe previously remain
valid. Speci…cally, the penetration rate of mobile phone is higher in the smaller village
when markets size are unequal. When markets size are unequal, more goods move to the
bigger market. Thus externality e¤ect to nonusers in the smaller market is stronger than
for those in the bigger one.We simulate the e¤ects of the mobile phone costs reduction on
markets’outcomes. A decrease in search cost gives more incentives to buy mobile phone
and more goods moves to where they are valued most. Thus, a decline in mobile phone
cost reduces variance of prices within and across markets (Figure 12).
34
Within Market 0
Within Market 1
0.19
Between Markets
0.2
0.37
M0 =M1
M0 =0 .5 M1
M0 =M1
M0 =0 .5 M1
0.18
M0 =M1
M0 =0 .5 M1
0.36
0.19
0.35
0.16
0.34
Pric e Va ria nc e
0.18
Pric e Va ria nc e
Pric e Va ria nc e
0.17
0.17
0.15
0.16
0.14
0.15
0.33
0.32
0.31
0.3
0.29
0.13
0
0.5
1
Inc re a s e in Mobile C os t
0
0.5
Inc re a s e in Mobile C os t
1
0
0.5
1
Inc re a s e in Mobile C os t
VII. Concluding Remarks
In this paper we …nd that introduction of mobile phones provide information that enables
markets to perform well. The addition of mobile phones reduced price dispersion across
markets and yields positive externalities within markets but negative externalities across
markets. Price dispersion decline is higher as di¤erence in penetration rate of mobile
phones between markets is lower and a greater access to mobile phones could signi…cantly
improve welfare. Further, while it was primarily those who adopted mobile phones bene…t
it, there were signi…cant spillover gains for those who did not use phones, due to the improved functioning of markets. Our results demonstrate the importance of information for
the functioning of markets and the value of well-functioning markets; information makes
markets work, and markets improve welfare. These issues are central to the current debate
concerning the relevance of ICTs, speci…cally mobile phones and market information systems as a development tool. Nevertheless, our results suggest that the di¤usion of a new
technology which is not uniform may reinforce existing patterns of inequality.
35
VIII. Appendix
A. Proof
In this section, we provide the proofs for the main results of the paper.
B. Proof of Theorem II.1
h
i
0 to admit a unique solution qb 2 q B ; q G are
i
h
the following: (i) V (q) has strictly monotonic variations in q B ; q G ; and (ii) 0 2 V ; V ,
The su¢ cient conditions for the equation V
where V = inf(V (q B ); V (q G )) and V = max(V (q G ); V (q G );
First, using (II.4), (II.5) and rearranging terms, the net gain function is given by
V
q
p1G + (1
)p1B
(q)p0G + [1
(q)] p0B
Di¤erentiating V (:) with respect to q yields
@V
=
@q
with p =
Denote that the third term in
+ q 0 (q) p0B
p
p1G + (1
@V
@q
p0G
)p1B
(q)p0G + [1
(q)] p0B
expression is always positive since (q) is increasing with
q. Furthermore
p
E p1
p0G
qG
h
i
implying that the function V (q) indeed is strictly monotonically increasing in q B ; q G :
Thus V = V (q B ) and V = V (q G ):
Second, notes that (q B ) = 0 and (q G ) = 1: So we have
V (q B ) = q B E p1
p0B
V (q G ) = q G E p1
p0G
36
= q B '(q B )
0
= q G '(q G )
0
clearly, 0 2 V ; V . Hence the result.
Since V is increasing with q; then (i) if q > qb then V > 0 and the farmer switches to
the opposite market, and (ii) if q
C. Proof of Theorem III.1
qb then V < 0 and the farmer sells locally.
When both markets are in the same state, there are no arbitrage and the theorem is valid.
So we give the proof for the case when markets are in opposite states. For example, assume
that market 0 is in the G state and market 1 is in the B state.
Here are two possible cases, either tj = 0 or tj > 0. First, suppose that tj = 0, it
reproduces the situation prior to mobile phone availability so theorem is valid. Second,
suppose that tj > 0 at least for one market, for example t0 > 0. The proof of Theorem
III.1 then involves two claims:
Using de…nition of markets demands (II.8) and markets supplies (III.6) (III.4), I can
characterize the market equilibrium. Given properties of functions qI (:) and qN (:), mobile phones penetration rates tj , transaction costs
and , the price equilibrium (p0 ; p1 )
expunges markets’excess demand :
S 0 (p0 ; p1 )
D0 (p0 )
0
(VIII.1)
S 1 (p0 ; p1 )
D1 (p1 )
0
(VIII.2)
Given above notations, I can now state markets prices equilibrium. We begin with the
characterization of market equilibrium price p0 ; solution of (VIII.1) given market price p1
and others parameters:Assume the solution is interior and let it be described by a realvalued function f : R+ ! [pG ; pB ] such that 8p1 2 R+ ,
p0 = f (p1 )
(VIII.3)
First, I establish the following results.
Claim 1.The real-valued function f (:) exists and admit the following property f 0 (p1 ) > 0.
37
Proof. The su¢ cient conditions for system (VIII.1) to admit a unique solution p0 =
f (p1 ) 2 [pG ; pB ] given p1 are the following: (i) Excess demand
S 0 (p0 ; p1 )
D0 (p0 ) has
strictly monotonic variations in [pG ; pB ]; and (ii) 0 2 [ ; ], where = (pG ) and = (pB );
First, since
@I 0
@p0
< 034 , clearly
@
=
@p0
@I 0
@p0
(M j )2 q 0 (p0 ) > 0
implying that the function (p0 ) indeed is strictly monotonically increasing in [pG ; pB ] :Second,
from (III.6) and (II.10), it can be shown that
qI (pG ; p1B )
p1B
qI (pB ; p1B ) = q G
< qG
pG
(VIII.5)
So I 0 (pG ; p1 ) > 0 and I 0 (pB ; p1 ) = 0.We can rewrite S 0 (pG ; p1 ) and S 0 (pB ; p1 ) as
S 0 (pG ; p1 ) = D0 (pG )
I 0 (pG ; p1 ) < D0 (pG )
S 0 (pB ; p1 ) = D0 (pG ) > D0 (pB )
34
Using Leibniz’s Theorem, we have
@I 0
=
@pj
T0
2
qI (qI jG)
@qI
; j = 0; 1
@pj
and
@qI
@p0
=
@qI
@p1
=
(p1
(p1
and hence the result
38
(VIII.4)
p0
p0
2
)
2
)
= S 0 (pG ; p1 )
D0 (pG ) < 0
= S 0 (pB ; p1 )
D0 (pB ) > 0
clearly, 0 2 [ ; ]. Hence the result.
Furthermore, we have
@I 0
<0
@p1
@p0
@ =@p1
f 0 (p1 ) =
=
>0
@p1
@ =@p0
@
=
@p1
Second, taking (VIII.3) and replacing in (VIII.2), we have
S 1 (f (p1 ); p1 )
D1 (p1 )
0
(VIII.6)
Likewise, assume that price market equilibrium p1 exists also interior, and let be de…ned
by a real-valued function g : R2+ ! [pG ; pB ] such that 8(t0 ; ; ) 2 R3+ ,
p1 = g(t0 ; ; )
(VIII.7)
@g
Claim 2. The real-valued function g (:) exists and admits the following properties: (i) 0 <
@t
@g
@g
0, (ii)
> 0 and (iii)
>0
@
@
Proof The su¢ cient conditions for system (VIII.6) to admit a unique solution p1 =
g(t0 ; ; ) 2 [pG ; pB ] are (i) Excess demand "(p1 )
S 1 (f (p1 ); p1 )
D1 (p1 ) has strictly
monotonic variations in [pG ; pB ] and (ii) 0 2 ["; "], where " = "(pG ) and " = "(pB );
First, taking derivative of S 1 in respect of p1 , we have :
dS 1
@S 1 @p0 @S 1
=
+ 1
dp1
@p0 @p1
@p
39
Note that using () ,we can decompose this second e¤ect as :
dS 1
@I 0 @p0 @I 0
=
+
dp1
@p0 @p1 @p1
dS 1
=
dp1
dS 1
=
dp1
@qI @p0 @qI
+
@p0 @p1 @p1
(T0 )2 qI (qI jG)
(T0 )2 qI (qI jG)
(p1
p0
)2
@p0
@p1
1
or
@p0
=
@p1
@p0
=
@p1
@S 0 =@p1
=
@S 0 =@p0 @D0 =@p0
@I 0 =@p1
@I 0 =@p0
(M0 )2 q 0 (p0 )
(T0 )2 qI (qI jG)
(M0 )2 q 0 (p0 ) (p1
(T0 )2 qI (qI jG) (p1 p0 )2
p0
We can rewrite this latter expression as:
1
@p0
=
<1
1
@p
1+x
"
Where x
0
q (p0 )
M0
T0
2
2
(p1 p0
)
qI (qI jG)
#
>0
So
dS 1
> 0
dp1
dD1
and
< 0
dp1
Since
"0 (p1 ) =
dS 1
dp1
dD1
>0
dp1
therefore, the function "(p1 ) is strictly monotonically increasing in [pG ; pB ]
40
)2
Remark 1. Note that an increase in p1 has two opposite e¤ects on supply S 1
@S 1
@I 0
=
>0
@p1
@p1
and
@S 1
@I 0
=
<0
@p0
@p0
Firstly, as price market p1 costs increases, there will be more switching from market 0
(a greater price dispersion, then an decrease in qI ). Secondly, more switching to market 1
reduces goods supplies to market 0 and induces an increase in p0 : A lower price dispersion
reduces arbitrage opportunities (an increase in in qI ): Figure (??) resumes theses situations.
price
p
2
p0
p2
p1
1
Quantity Q
Second, from (III.4) and (II.10), it can be shown that
Since (pG )
pG and (pB )
pB we have
qI (f (pG ); pG )
qI (f (pB ); pB ) =
(VIII.8)
qG
pB
41
(pB )
< qG
(VIII.9)
So I 0 ( (pB ); pB ) > 0 and I 0 ( (pG ); pG ) = 0.We can rewrite S 1 (pG ; p1 ) and S 1 (pB ; p1 ) as
We can rewrite S 0 (pG ; p1 ) and S 0 (pB ; p1 ) as
S 1 ( (pG ); pG ) = D1 (pB ) < D1 (pG )
S 1 ( (pB ); pB ) = D1 (pB ) + I 0 (f (pB ); pB ) > D1 (pB )
" = S 1 (f (pG ); pG )
D1 (pG ) < 0
" = S 1 (f (pB ); pB )
D1 (pB ) > 0
clearly, 0 2 ["; "]. Hence the result.
Furthermore, we have
@ [S 1 D1 ]
@ (I0 + N 0 )
=
>0
@t0
@t0
To establish this latter inequality, note that we can rewrite I 0
0
I =
M
0 2
t0
Z
qN
q (qjG)dq +
Z
qG
q (qjG)dq
qN
qI
so
@p1
=
@t0
@ [S 0
@ [S 0
D0 ] =@t0
<0
D0 ] =@p1
And we have
@ [S 1 D1 ]
@I 0
=
<0
@
@
@ [S 1 D1 ]
@I 0
=
<0
@
@
42
and so we have :
@ [S 1
@ [S 1
@ [S 1
@ [S 1
@g
=
@
@g
=
@
D1 ] =@
>0
D1 ] =@p1
D1 ] =@
>0
D1 ] =@p1
Using results of claim 1 and claim 2, we have
@p0
@f @p1
=
>0
@t0
@p1 @t0
@p0
@f @p1
=
<0
@
@p1 @
@f @p1
@p0
=
<0
@t0
@p1 @
(VIII.10)
(VIII.11)
(VIII.12)
D. Proof of Proposition 1
(i) Variance of equilibrium price within both markets
2
j
=E
h
p0
2
i
E p0
2
, j = 0; 1
with
E pj
E
h
pj
2
i
= (1
)2 pB +
2
= (1
)2 (pB )2 +
pG + (1
2
)pjGB + (1
(pG )2 + (1
) pjGB
Using properties (i) and (ii) in Theorem III.1, we have
@E [p0 ]
=
@t0
@E [p1 ]
=
@t0
(1
(1
43
@p0GB
>0
@t0
@p1
) GB
<0
@t0
)
) pjBG
2
+ (1
)
pjBG
2
and
h
0 2
@E (p )
i
0
i
h@t
2
@E (p1 )
@t0
@ 20
= 2 (1
@t0
@ 21
= 2 (1
@t0
= 2 (1
)p0GB
@p0GB
>0
@t0
= 2 (1
)p1GB
@p1GB
<0
@t0
) p0GB
E p0
) p1GB
E p1
@p0GB
<0
@t0
@p1GB
<0
@t0
(ii) Variance accross markets
2
=
2
0
+
2
1
@ 20 @ 21
@ 2
= 0 + 0 <0
@t0
@t
@t
E. Proof of Proposition 2
Using properties (iii) and (iv) in Theorem III.1, we have
@ 2j
= 2 (1
@l
)
"
pjGB
E p
j
@pjGB
+ pjBG
@l
@ 2
@ 20 @ 21
=
+
>0
@l
@l
@l
44
E p
j
@pjBG
@l
#
>0
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