Getting Prices Right: Mobile Phone Di¤usion, Market E¢ ciency and
Inequality1
Francis ANDRIANARISON2
CSAE Conference 2010
Economic Development in Africa. 21st - 23rd March 2010, Oxford.
Abstract:
In this paper, we study the impact of uneven mobile phone di¤usion on market functioning. We
develop a search theoretic model with spatial arbitrage between two neighbouring marketplaces.
Producers with a phone in one market can learn the prevailing price in the other market, while
those without a phone cannot. In the …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 users, but when the penetration rate increases in a village, farmers
without phones also bene…t because the average domestic price increases. In contrast, farmers
in the other village (both with and without phones) are penalized as the average price in the
other market decreases. These e¤ects are stronger when the original di¤erence in penetration
rates is higher. Thus, non-uniform di¤usion of a new technology may reinforce existing patterns
of inequality. In our second stage, we show that these results are robust to endogenizing the
penetration rates.
JEL:O12; D80;D82; D83; Keywords: Mobile phone, Technology Di¤usion, Market E¢ ciency,
Welfare, Inequality.
1
I would like to thank Yann Bramoulle for the guidance and incisive comments he has provided at many stages
of this research project. I am grateful for comments by participants at the 49e congrès of the SCSE 2009 and the
43rd Annual Conference of the CEA 2009. Financial support from the FQRSC is gratefully acknowledged
2
Département d’Économique et CIRPÉE, Université Laval, Pavillon J.A. De Seve Québec, QC, G1K7P4,
Canada. [email protected]
What would a small-scale farmer in Africa, Peru or India want with a mobile phone? 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.
Rheingold (2005)
I. Introduction
Information has been regarded by economists as a critical element for the e¢ cient functioning of
markets since at least the seminal work of Stigler (1961). Market participants must possess good
information about market states and prices to engage in optimal arbitrage. In reality, however,
lack of a¤ordable access to relevant information is more or less the norm in most developing countries, especially in rural areas. Markets there often function poorly and are characterized by meagre, low-quality internal ‡ow of information (Geertz, 1978). Information about production-related
matters and market prices has been lacking until recently (Eggleston et al., 2002). Therefore,
economic activity is rarely well-coordinated in these markets and one of their features is deviation
from the “Law of One Price”.3 Thus, …nding ways to reduce information ine¢ ciencies is a key
challenge for developing economies. Yet despite the fact that information is central to market
functioning, economists have devoted little attention to the e¤ects that improved information
transmission can have on market outcomes in developing countries.4 A signi…cant proportion of
the world’s poor in rural areas depends heavily on markets. Thus, the question of how much the
market e¢ ciency can be enhanced by giving farmers basic access to agricultural prices is relevant
to the debate over the potential value of market information di¤usion for economic development.
Beyond the bene…ts such improvements bring to society, how inequality patterns can be a¤ected
remains a largely unanswered question. In this paper, we examine these points by exploring the
e¤ects of mobile phone di¤usion in a search theoretic model with spatial arbitrage between two
neighbouring marketplaces.
The recent explosive growth of mobile phones in developing countries has raised questions
3
This law is an important economic principle holding that the price of a homogenous good should not differ between any two markets by more than the transport cost between them. Otherwise,“price dispersion is a
manifestation— and, indeed, it is the measure— of ignorance in the market” (Stigler, 1961).
4
There is an extensive literature on the e¤ects of increased market information due to information technology
di¤usion in developed economies, and since the 1960s, numerous studies of information search and price dispersion
have emerged (see Baye et al. [2007] for a review). Jensen (2007) and Aker (2008) are notable exceptions, as their
studies focus on developing countries.
1
about their potential value as a tool for development.5 Anecdotal evidence shows that if farmers
are given basic access to agricultural prices in nearby markets, their incomes can signi…cantly improve. Indeed, mobile phone acquisition enables …shermen or farmers to check prices at di¤erent
markets before selling products, broadens trade networks, and reduces transaction costs (BBC,
2002; The Economist, 2005; Sullivan, 2007). In the epigraph to this paper, Howard Rheingold
(2005) makes a simple yet powerful statement about how access to market state and price information, enabled by mobile phones, enhances e¢ ciencies in output markets and thereby allows
farmers to increase pro…ts and income. The linkage between information improvement and market
e¢ ciency is central in determining the income and welfare of a signi…cant number of households
in developing countries. Not everyone shares this optimistic view, however, and some researchers
argue that while the “haves” are getting richer, the “have-nots” are losing income. The new
technology might exacerbate inequality rather than reduce it. For instance, Molony (2009) shows
how in the case of tomato and potato markets in Tanzania, those farmers in isolated rural communities are in a weaker bargaining position. He argues that farmers who have access to mobile
phones gain the most by bene…ting from …rst-hand exchanges of information, while those farmers
without this new communication technology are often caught in a credit dilemma whereby they
have little choice but to accept the price they are given by their creditor.6 Our search-theoretic
model reconciles these two views by considering unequal di¤usion of mobile phones.
This paper studies the e¤ects of information improvement on market performance, welfare and
inequality. As such, it contributes to a small but growing literature on the e¤ects of increased
market information on development (Jensen, 2007; Aker, 2008; Svensson et al., 2009). Jensen
(2007) evaluates the e¤ects that the introduction of mobile phones have had on the …shing markets
in Kerala, India, and …nds that the adoption of mobile phones by …shermen and wholesalers
increases their ability for arbitrage over price information from potential buyers. By improving
5
Between 2001 and 2007, mobile phone subscriptions in developing countries have almost tripled, constituting
58 percent of mobile phone subscribers worldwide in 2007 (UNCTD [2008], p. 23). By the beginning of 2009, their
share had grown to three-quarters of the world’s 4 billion mobile phone subscribers (The Economist, September
2009 ).
6
In the same vein, Jagun et al. (2007) notes in his case study of the aso oke (hand-woven textile) sector in
south-western Nigeria that although information and communications technologies (ICTs) have the ability to make
the situation less unequal for everyone involved, it appears that mobile phones are increasing the di¤erence between
those who can a¤ord access to a mobile (and …nd greater opportunities to trade) and those who cannot (and …nd
they have fewer orders).
2
access to market information, mobile phones enable users to choose a market where they can sell
their …sh at the highest price. This results in a signi…cant reduction in price dispersion and waste
across geographic markets. Reduction in price dispersion insures price stability, so both consumer
and producer welfare increase. Aker (2008) provides recent …ndings from grain traders in Niger
that show broadly similar e¤ects on price dispersions across grain markets when mobile phones
were introduced in Niger. Svensson et al. (2009) show that better-informed farmers managed to
bargain for higher farm-gate prices on their surplus production.
In this paper, we study the e¤ects of the introduction of mobile phones on market outcomes
and inequality in a model with spatial arbitrage, building on Jensen’s (2007). The paper particularly identi…es key externalities associated with mobile phone di¤usion that have not been
studied in previous economic analyses. The model departs from Jensen’s (2007) in two aspects:
(i) we abandon the assumptions of symmetry in market size and in the realization of the state of
the world, and (ii) we focus on asymmetric di¤usion of mobile phones.7
This paper also contributes to the literature on search theory. Most search-theoretic models
used to explain the existence of price dispersion for homogenous goods focus on search from the
consumers’perspective (Baye et al., 2007). The present paper is innovative in two respects. First,
following Jensen (2007), we focus on search from the producers’perspective, which has not been
widely addressed in the search literature. Second, we develop a spatial model in which there is a
competitive market in each village, with many small buyers and sellers.8
Finally, our research addresses the traditional debate on “the digital divide”between the information “haves” and “have-nots”. We focus on distributional issues among users and non-users,
speci…cally discussing whether mobile phone di¤usion deepens or helps to reduce the existing
inequality.
In this paper, we study farmers’(sellers’) spatial arbitrage under uncertainty. The fundamentals of our model are:
1. Lack of information, due to uncertainty and transaction costs, induces ine¢ cient allocation
7
Our model extends Jensen’s framework into another dimension: (i) it considers per-unit costs and …xed transaction costs to capture the information and income e¤ects on spatial arbitrage; (ii) it distinguishes the homogenous
case of mobile phone penetration rate from the endogenous one, allowing us to consider two types of “digital
divide”: the availability and the a¤ordability of mobile phones.
8
Traditionally, consumer search models assume there are many sellers but only one at any particular location
(see Stiglitz [1989] or Baye et al. [2007]).
3
of goods and causes price dispersion across markets.9
2. The availability of accurate, timely, and appropriate information related to the selling stage
of value chain production can enable farmers to make better decisions about where to sell goods
and at what prices.10
3. Due in part to institutional failure, the di¤usion of search technology (i.e., mobile phone
penetration) is not uniform across space.
Using a simple static search theoretic model with spatial arbitrage between two neighboring
marketplaces, we derive the optimal decision rules for producers. First we characterize the situation under pre-phone conditions and then we derive the reported changes in individual marketselection behaviour resulting from the introduction of mobile phones. Our model predicts that
the addition of mobile phones will reduce price dispersion within and across markets and will
yield positive externalities within markets but negative externalities between markets.11 Uninformed producers (those who don’t have mobile phones) receive on average lower prices than
informed producers (those who have mobile phones). However, mobile phone access creates a
positive intra-village externality whereby all producers can expect to receive a higher price. That
is, 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. The in‡ux of informed
producers exerts a negative externality on producers located in the other market, lowering the
price there. Our results suggest that non-uniform di¤usion of a new technology may reinforce
existing patterns of inequality. When combined with an initial endowment inequality, technology
di¤usion increases welfare inequality. These e¤ects are stronger when the original di¤erence in
penetration rate is higher. Thus, the spread of mobile phones may exacerbate existing inequalities
of wealth distribution. Nevertheless, greater access to mobile phones is good for the economy,
9
FFor example, because markets are open for only a few hours, travel is time-consuming, and storage is expensive
(Jensen, 2007), it is not possible for a producer to visit more than one market per day. 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 (Molony, 2009).
10
Following Hirsheleifer (1971), the acquisition of information will take the form of warranted revisions in the
probability of the prevailing state of nature. We will distinguish here private information (available only to a single
producer) from public information (available to everyone), and sure information from merely better information.
11
We are, to our knowledge, the …rst to identify these e¤ects in the literature on mobile phone impacts. Some
related results appear in the literature on consumer search. For instance, 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).
4
since phones can signi…cantly improve social welfare. Furthermore, we show that equilibrium
price dispersion decreases as search costs decrease.
The rest of this paper is structured as follows. Section 2 presents the model and the case prior
to mobile phones. In Section 3, we introduce mobile phones into the model and analyze their
e¤ects on farmers’ spatial arbitrage and on market equilibrium; at this stage, we assume that
mobile phone penetration rate is set exogenously. Section 4 presents the e¤ects of mobile phones
on market outcomes. In section 5, we extend the model by assuming that a farmer’s choice to
buy a mobile phone is endogenous. Section 6 illustrates the results with a numerical example,
and section 7 o¤ers concluding remarks. Proofs of the results stated in the main text are detailed
in section 8.
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 over market supply, depending on a realization of the state of
nature, is the main source of price dispersion across markets. We begin by setting up the model,
and then we examine how farmers decide where to sell their output when they observe only their
own production. We show that an equilibrium with price dispersion can persist due to lack of
information.
A. The Setup
Consider two neighboring villages, denoted by 0 and 1, each with an equal continuum measure
of consumers and farmers who produce a homogenous good q. Both villages have a circular form
with radius M j (j = 0; 1) and each has a marketplace located at the centre 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 output, locally or at the other market. We assume that individual
levels of production are random variables with identical distributions across individuals, but
with a positive correlation for farmers within the same village. Speci…cally, we 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 in which yield
5
production is lower than in the “good” state of nature G.12 The realization of the two states is
independent between the two villages. Farmers initially regard the realization of the good state
of nature with a probability . Formally, we 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
qB
q G < q B < q G . And, (qj!) satis…es the Monotone Likelihood Ratio Property, so that the
ratio
(qjG)
(qjB)
L(q)
(II.1)
is increasing in q. High production is 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 a G state. Using Bayes’rule, each
farmer’s updated belief is given by:
(q) =
8
>
>
0
>
>
<
>
>
>
>
:
q < qG
if q B
1
L(q)
+ L(q)
if q G
q
qB
(II.2)
if q > q B
1
A farmer chooses whether 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 his 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 costs. Such costs may represent per-unit costs of accessing markets, associated
with transportation or transaction-induced …xed costs.13 When a farmer decides to switch, he
12
In Jensen (2007), ! represents the density of …sh in the …sherman’s zone, which a¤ects his catch. The G state
indicates that the zone has high density while the B state indicates low density. In agriculture, ! can be interpreted
as weather: bad weather, when production yield is lower, and good weather, when production yield is higher.
13
Proportional transaction costs— which include per-unit costs of accessing markets, associated with transportation and imperfect information— have been used to explain labour (Sadoulet and al., 1998) and food (Goetz, 1992)
market participation decisions in developing countries. Fixed transactions costs that are invariant with 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; (b) negotiation and bargaining— these costs may be important when there is imperfect information
about prices (often negotiation and bargaining takes place once per transaction, and these costs are invariant with
the size of the transaction); (c) screening, enforcement, and supervision— farmers who sell their product, land,
or labour on credit may have to screen buyers to make sure they are reliable, and they may have to pay legal
6
pays transportation costs proportional to his production level, plus 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 a B state, the
aggregate production is lower than in a 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 the assumption
(II.3) holds in the market equilibrium. We exclude the existence of waste and suppose here that
consumers purchase all goods o¤ered in the market. There is no saturation point in the demand.
B. Market Choice Prior Mobile Phone
In this subsection, we analyze a farmer’s spatial arbitrage when his decision is based only 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. The farmer has a binary decision:
either he sells locally or he switches to the other market. When the villages are in opposite states,
farmers from the village where the price is lower will gain by switching to the other village, where
the market price is higher. The objective of this subsection is to study the determinants of the
decision to switch. In particular, 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 ω
Each farmer learns
his/her level of
production q
Farmer observes his/her
own q and updates
his/her assessment of
the state of the local
market
Those who choose to
switch then leave their
local market to sell in
the other market
Payoffs
Figure 1 : Timing of Events Prior to Mobile Phone
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
enforcement costs in case of default (Key et al., 2000).
7
sell locally (or to switch), his expected gain V (0) (or V (1)) is given by
V (0) =
p0G + [1
] p0B q
V (1) =
p1G + (1
)p1B
(II.4)
q
(II.5)
The farmer compares the expected gains from selling locally (II.4) and from switching (II.5), then
he decides where to sell. For a farmer with production q, the net gain from switching is:
V
with
p =
V (1)
V (0) = q [ p
p1G + (1
)p1B
]
(II.6)
p0G + (1
) p0B
(II.7)
p denotes the expected price premium from switching. The market choice decision could be
formulated thus: 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 q such that V
0.
Thus, the determinants of the spatial arbitrage decision are: (i) the level of production q, (ii)
the expected price premium from switching
p, and (iii) 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.
Consider a farmer who is indi¤erent between selling locally or switching to the other market.
His level of production q 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 of
@q
@q
production q ( ; ) with
0 and
0 where
@
@
1. Farmers with a level of production greater than q switch to the other market while those
with production lower than q sell locally. Indeed, the threshold level of production q is given
by
8
>
>
q
>
>
< B
q =
qG
>
>
>
>
: 2 ]q ; q [
B G
if E p1
p0B
+
if E p1
p0G
+
if otherwise
8
qB
qG
2. A rise in price dispersion across markets increases spatial arbitrage opportunities.
3.There are thresholds
and
such 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, but 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, the existence of transaction costs reduces opportunities for
arbitrage. And when transaction costs are above a certain point, there may be no switching
because even for a farmer with the highest level of production, the expected gain is less than the
transaction costs.
More precisely, Theorem II.1 states that the threshold q is determined by transaction costs
and market price di¤erentials. In particular, the cuto¤ for switching q increases with
and .
Hence, two e¤ects in‡uence a farmer’s arbitrage:
(i) An information e¤ ect: to switch, a farmer should be sure that the expected price premium
from switching ( p) covers transportation costs. So, only those who are almost sure that their
local market is in a G state (the price is lower) are likely to switch.
(ii) An income e¤ ect: for a farmer 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 completes the market model by specifying the demand side and determining the equilibrium price. We analyze the market equilibrium when farmers’spatial arbitrage is based only
on their own private signal. 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 availability. Henceforth, we assume that
. Thus,
there is no switching in equilibrium, so market supply is equal to the aggregate production for
each market. At equilibrium, total demand equalizes total supply in each market. We assume
9
that all consumers have an identical individual demand q(p), where p is the market price, q(p) is
the quantity demanded at price p, and q 0 (p)
0. This last 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(pj! )
(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 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
(II.10)
q!
Equalizing the aggregate demand (II.8) to the aggregate supply (II.9), we have the market prices
equilibrium pj! :
pj! = q
1
Q!
(II.11)
Clearly, the market prices equilibrium (II.11) satis…es the condition (II.3). The model reproduces
a market equilibrium with price dispersion across villages. Uncertainties in production level and
transaction costs are used in this model to explain the dispersion in market prices. Because of
price uncertainty and transaction costs, farmers are not able to pursue the highest price, so they
usually sell locally. When the 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.
10
III. Market Equilibrium with Mobile Phones
Now, we introduce mobile phones and analyze how this new search technology a¤ects farmers’
behaviour and the market equilibrium. In this section, we assume that mobile phone penetration
rates are set 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 the technology. All farmers located within the coverage
zone have a mobile phone. So, the mobile phone coverage rate tj , which also represents the mobile
phone penetration rate in village j, is given by
tj =
Tj
Mj
2
(III.1)
Mobile phone technology allows farmers who have it to learn the true state of nature— the prices
in both markets— and thereby avoid unpro…table switching, while uninformed farmers (those who
don’t have mobile phones) always sell locally, as before.14 The timing of events in the economy
occurs according to the following sequence.
Nature chooses
the state ω
Each farmer
learns his/her
level of
production q
Mobile Phone holder do calls to
check market prices;
Farmers without phones
update 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
Payoffs
Figure 2 : Timing of Events with Mobile Phone
14
In practice, mobile phones allow farmers to check market prices. For example, …shermen in India call the
landing centres to learn where to …nd the highest prices for their catch, and subsequently land there (Jensen, 2007;
Abraham, 2007). In Niger, traders use mobile phones to check price information over a larger number of markets
(Aker, 2008). In Kenya, mobile phones enable farmers to access market information, which includes the prices of
commodities in di¤erent markets, 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¤, …nding out where they will get the best o¤er for their
produce (BBC, 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).
11
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 the two marketplaces are in opposite states. Without loss of generality,
we suppose that market 0 is in a G state while market 1 is in a B state. According to the farmer’s
belief, this event occurs with probability
(1
), the probability that his local market is in a G
state and the other market is in a B state. We …rst show the condition under which an informed
farmer gains by switching. Consider an informed farmer located at market 0. By switching to
market 1, his expected net gain R is given by
R
(1
)
q p1B
p0G
(III.2)
He gains by switching 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. qI
is given by
qI =
8
>
>
>
>
<
if p1B
qG
>
p1B p0G
>
>
>
:
qG
if
+
qG
if p1B
p0G
< p1B
p0G
+
qG
p0G <
+
+
qG
(III.3)
qG
As the bene…t (III.2) increases with q, the informed farmer with a level of production higher than
qI switches to market 1, otherwise he/she sells locally. Even when an 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 phones realize that the price in market 1 is
higher, they are not able to switch. Clearly, a rise in transaction costs reduces the 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 incentive to switch. Indeed,
a higher price dispersion across markets also provides more incentives to switch.
The aggregate supply S 1 to market 1 derives from two components: quantity Q1B supplied by
12
local farmers and I 0 supplied 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 which the informed farmer gains by switching.
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 that:
1. informed farmers (who have mobile phones) with a 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) holds. Assume that market 0 is in a G state and
market 1 in a B state. Then, a competitive equilibrium (qI ; p0 ; p1 ) exists and is unique. In
@p0
@p1
@p0
@p1
addition, it satis…es the properties (i) 0 > 0; (ii) 0 < 0 , (iii)
< 0, and (iv)
> 0;
@t
@t
@l
@l
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
are sending their output to market 1, where they are valued most. A rise in mobile phone
penetration rate t0 enables farmers to pursue the highest price in market 1, so the supply to
13
market 1 increases and lowers the price. Inversely, because more farmers are switching, the
supply in market 0 decreases and the price there increases.
Following the traditional approach in information search and price dispersion outlined in Baye
et al. (2007), we examine how the variance in the distribution of equilibrium prices varies with
mobile phone di¤usion.15 Note that, in equilibrium, the variance in prices within market j is
given by
2
j
=E
h
pj
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. (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 in
prices both within and between markets. 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 price there and increasing the price in the other market. Plus, more
e¢ cient allocation of goods improves the markets’functioning. In particular, mobile phones 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 costs 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
15
In the search literature, the commonly used measures of price dispersion are the sample variance of prices across
markets (Pratt et al., 1979; Aker, 2008), the coe¢ cient of variation (CV) across markets (Eckard, 2004; Jensen,
2007), and the maximum and minimum (max-min) prices across markets (Pratt, et al., 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, the latter measure is close to the max-min approach.
14
transportation costs increase, there will be less switching and greater price dispersion in equilibrium. Thus, fewer goods move to where they are valued most and price dispersion persists.
IV. Who Gains 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¤ect gains from spatial arbitrage? For those who
have them, mobile phones increase the opportunity for arbitrage. The model thus predicts that
the introduction of mobile phones promotes market exchanges for goods. Is this change pro…table
for everyone? How does it a¤ect the existing pattern of inequality? To answer these questions,
we analyze two components of mobile phone impacts: redistributional and welfare e¤ects.
A. Mobile Phones and Information Externalities
In this subsection, we focus on the e¤ects that mobile phones have on market prices by improving
information ‡ow. We analyze information externalities and examine a key comparative static
implication of the model: what happens to prices as mobile phone coverage rates increase? The
previous result states that uninformed farmers (those who don’t have mobile phones) receive on
average lower prices than informed farmers (those who have mobile phones). However, mobile
phone access creates a positive intra-village externality whereby all producers can expect to receive
a higher price. That is, the in‡ux of informed farmers exerts a negative externality on farmers
located in the other market. We use Theorem II.1 to derive the following results.
Proposition 3. (i) Intra-market externality: An expansion of mobile phone coverage in a market
always raises the average price received by uninformed farmers located at this market.
(ii) Inter-market 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 Theorem III.1. Proposition 1 posits that a rise in
mobile phone penetration improves markets’functioning, and Proposition 3 states that there are
still signi…cant spillover gains for producers who do not have phones, due to improved functioning
of the markets. Thus, mobile phone users create a positive externality on nonusers within their
local market and a negative externality on farmers in the other market.
15
B. Redistributional E¤ects of Mobile Phone Spread
We examine in this subsection the distributional consequences of mobile phone di¤usion, by
which we mean the e¤ects that mobile phone introduction or an increase in mobile coverage rate
has on inequalities in the distribution of revenue. To do so, we examine the expected pro…ts
among farmers within a market, across markets, and for the whole economy. Previous results
have shown that mobile phone holders with higher levels of production always sell in the market
o¤ering the higher price. Hence, the model predicts that this category of farmers always wins.
Those who don’t have mobile phones also bene…t from mobile phone di¤usion in their market,
due to externality e¤ects. When mobile phones are available in one market, the prices at which
the farmers in the other market now sell their products will be lower than the price they would
have received prior to mobile phones becoming available.
To formalize this, consider a typical farmer located in village j with a level of production
q, with q > qI .16 There are two possible types of farmer: either he/she has a mobile phone
(informed), or he/she doesn’t (uninformed). When markets are in opposite states, these are
j
de…ned by wm (or wj ), the expected gain from the farmer’s arbitrage if s/he has a mobile phone
(or does not).
17
We have
w0 =
(1
)q p0GB + p0BG
(IV.1)
w1 =
(1
)q p1BG + p1GB
(IV.2)
0
wm
=
(1
) q p1GB + p0BG
(IV.3)
1
wm
=
(1
) q p1GB + p0BG
(IV.4)
where pjGB (or pjBG ) denote market price in market j when market 0 is in the G state (or B state),
and market 1 is in the B state (or G state).
j
Note that following (III.2) and (III.3), we always have wm
wj . Now, consider a rise in the
penetration rate of mobile phones within the village 0. We then have the following results.
Proposition 4. Suppose an increase in mobile phone penetration rate in village 0; we then have
16
If q qI , he always sells locally and the discussion is not interesting.
We can also use the net expected gain de…ned as the di¤erence between the pro…t he/she obtains by the pro…t
he/she would gain if there were no mobile phones. The results remain valid
17
16
0
@wm
@w0
0,
0;
@t0
@t0
@w1
@w1
0; and
(ii) 0m 0,
@t
@t0
0
0
1
dwm
dw
dwm
(iii)
;
dt0
dt0
dt0
(i)
dw1
:
dt0
The proof of Proposition 4 follows immediately after Theorem III:1. Proposition 4 states that
mobile phones primarily bene…t those who have them. But, farmers without phones also bene…t
when a greater percentage of their village is covered by mobile phones. In contrast, the di¤usion of
mobile phones in a village penalizes farmers in the other village (both with and without phones),
as the price in their market decreases. Moreover, property (i) indicates that at the …rst stage of
mobile phone di¤usion, having this search technology is most valued. When a higher percentage
of markets is covered by mobile phones, the bene…t from searching is lower. We then have the
following corollary.
Corollary 1. When the penetration rate of mobile phones increases in a village, the expected
inequality between users and non-users in this village decreases, but increases in the other village.
Now, we can determine the bene…t of mobile phone access based on the value of information,
measured by the increase in utility after receiving information and optimally reacting to it. Indeed,
the value of information V I for a farmer in village j equals the expected bene…t of the decision
j
with mobile phone wm
minus the expected bene…t of a decision without mobile phone wj :
j
V I = wm
wj
(IV.5)
Lemma 1. The value of information is (i) increasing in q; and (ii) decreasing in mobile phone
coverage.
j
The proof of Lemma 1 is immediate using the de…nition of wm
and wj in (IV.1), (IV.2),
(IV.3), and (IV.4). And we have the next results.
Proposition 5. Let condition (III.2) and (III.3) hold. If q1 > q2 , then we have
j
wm
(q1 )
j
wm
(q2 )
17
wj (q1 )
wj (q2 )
Proof of Proposition 5 is immediate following Lemma 1. Proposition 5 shows that technology di¤usion increases welfare inequality when combined with an initial endowment inequality.
Indeed, the expected inequality is larger within a market where mobile phones are available,
compared with situations where they are not.
To link mobile phone di¤usion to inequality across markets, and to the whole of the economy,
R j
j
j
we can calculate the aggregate gain for farmers with phones in village j, Wm
= wm
dwm
; and
R
for those without phones, W j = wj dwj . Using (IV.1) and (IV.3), we can establish that
0
Wm
=
(1
)
p1GB
W0 =
(1
) p0GB QG + p0BG QB
1
Wm
=
(1
)
W1 =
(1
) p1BG QG + p1GB QB
p0BG
p0GB
I 0 + p0GB QG + p0BG QB
p1BG
F0
(IV.6)
(IV.7)
I 1 + p1BG QG + p1GB QB
F1
(IV.8)
(IV.9)
Z qG
where F j =
(qjG)dq denotes the number of farmers who buy mobile phones in village j and
qI
Z qG
j
q (qjG)dq the amount of their production; QB and QG are the average productions in
I =
qI
states B and G, as given by (II.10).
Thus, the aggregate gain
j
for the village j is given by :
j
j
= tj W m
+ (1
tj )W j
(IV.10)
Now, consider an expansion of mobile phone coverage t0 in village 0. We have the following
proposition.
Proposition 6. We have (i)
@
@ 0
@ 1
>
0;
(ii)
< 0 and (ii)
0
0
@t
@t
0
@t0
1
>0
The proof of Proposition 6 follows immediately by taking the derivative of (IV.6), (IV.7),
(IV.8), (IV.9) and using Theorem III:1. Proposition 6 says that a rise in mobile phone coverage
within a market leads to increased inequality between villages.
C. Mobile Phone Expansion and Welfare E¤ects
Primarily due to the more e¢ cient allocation of goods across markets, increased arbitrage due to
the introduction of mobile phones is associated with potential welfare improvement. Nevertheless,
18
the net welfare gains— and how such gains are distributed among farmers and consumers— remain
ambiguous. A change in producers’surplus will arise through changes in the price and quantity
sold at each market and in the costs associated with arbitrage. When the markets are in opposite
states, producer surplus in a B state declines and consumer surplus increases, while producer
surplus in a G state increases and consumer surplus declines. In a B market, farmers switching
from a G state are added to the market, so producers are now selling for a lower price than if
there were no mobile phones. Consumers gain because they are now buying for a lower price,
and the surplus transfers from producers to consumers. The inverse situation occurs in the other
market.
The size and direction of the net transfer from consumers to producers, the net change in
total welfare, and the net gain for each group will all depend on the shape of the demand curve
and the amount of arbitrage. The latter will depend on the penetration rate of mobile phones,
on transaction costs, and on the 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 welfare impacts through the numerical
example in section 6.
V. Endogenizing the Mobile Phone Demand
In this section, we assume that the decision to buy a mobile phone, and thus to search, is
endogenous. When a mobile phone is available, a producer can buy it at cost
. The farmer’s
decision process is whether or not to purchase the technology, and then where to sell his/her
product.18 As before, we assume that transaction costs existed prior to mobile phone availability,
satisfying property 3 of Theorem II:1, and that no switching was occurring. Each farmer who
has access to mobile phones buys this search technology if it will be pro…table.
We …rst show the condition under which a farmer gains from purchasing the search technology.
Without loss of generality, assume a farmer whose local market 0 is in a G state and assume that
market 1 is in a B state. By purchasing the search technology, a farmer q expects to gain in
18
In a repeated game where the search technology is a durable good like a mobile phone, the decision of whether
or not to buy a mobile is a binary choice: either he/she buys a mobile phone at a given point in time, or he/she does
not buy it at all. Thus, the farmer has to decide when to adopt the search technology that has been introduced.
19
revenue R(q), as given by (III.2). Thus, the net expected bene…t of switching is equal to the
expected gains minus the search cost:19
Vm
When
R(q)
(V.1)
> R, the information is too expensive and no one purchases the technology. The
equilibrium condition for purchasing the technology is that the search bene…t is at least greater
than the search cost R
. We assume this condition is satis…ed; speci…cally,
satis…es the
condition
R(q G )
(V.2)
Note that the expected gain R(q) is increasing in q, so farmers with higher production are more
likely to purchase mobile phones. Search is purchased up to the point when the 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 other market has a quantity of product qeI that V m
0.
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 which buying a mobile phone is pro…table. A farmer located within a mobile phone
coverage area and whose production level is greater than this value buys the search technology and
switches markets, while a farmer whose level of production is lower than the threshold doesn’t buy
the technology and remains selling locally. Using again the de…nition of competitive equilibrium
(De…nition 1 ), we can show that all previous results remain valid. Speci…cally, the exogenous
case of mobile phone penetration rate can be considered as an endogenous case by setting
0.
This can be interpreted as a mobile phone being purchased before arbitrage. In particular, we
have the following result.
Theorem V.1. Let conditions (II.1) and (V.2)hold. When each farmer observes only his/her
own production, then a competitive (e
qI ; pe0 ; pe1 ) equilibrium with qeI0 ( ) > 0 exists and is unique.In
@ pe0
@ pe1
@ pe0
@ pe1
addition, it satis…es the properties (i) 0 >0; (ii) 0 < 0; (iii)
< 0; and (iv)
>0
@t
@t
@
@
19
In a repeated game, producers purchase search when the discounted stream of expected gains from switching
markets over the life of the technology exceeds the cost. Search is purchased up to the point (the optimal date for
adoption) that the expected gain from arbitrage (net of transaction cost) equals the cost of search.
20
The proof of the theorem is the same as for Theorem III:1:20 Farmers with higher levels of
production are more likely to believe that they are in a G state and thus may gain by switching.
They are therefore more likely to purchase a mobile phone. Thus, the number of farmers who
Rq
purchase mobile phones in a village when it is in a G state is qeIG (qjG)dq.
Corollary 2. The proportion of farmers who adopt mobile phones is given by
=
Z
qG
(qjG)dq + (1
)
qeI
Z
qB
(qjB)dq
(V.3)
qeI
Clearly, we can derive results about price dispersion and externality e¤ects equivalent to those
for the exogenous case. Indeed, using properties (i) and (ii) of Theorem V:1, we can show that
all previous results remain valid. Speci…cally, following a standard approach in the literature on
consumer search theory (Bay et al., 2007), we examine how changes in search costs a¤ect market
actors’behaviour and equilibrium price dispersion.
Proposition 7. A reduction in mobile phone (search) cost
reduces price dispersion within and
between the markets.
A decrease in mobile phone cost increases the opportunity for arbitrage and reduces price
dispersion, due to more e¢ cient allocation of goods across markets. More goods move to where
they are more valued in the margin.21
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 con…rmed with a simple numerical example.
We start by assigning values to relevant parameters of the main functions of the model. Assume
that farmers draw their production from a distribution
with density (q) =
q3
which follows the Pareto distribution,
; q 2 [1; q]. In state !, we suppose that risk multiplicatively a¤ects the
20
When <
and < , there would be some switching even without the search technology, Theorem V:1
continues to hold, but only when search costs are below a threshold,
( ; ).
21
Comparative static predictions in the existing literature on price dispersion are con‡icting, due to di¤erent
assumptions about 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.
21
supply with a shock "(!) such that "(G) > "(B). That is, the distribution of q in each state of
1
q
nature ! is given by (qj!) such that (qj!) =
, where q 2 ["(!); q"(!)]. Clearly,
"(!)
"(!)
(qj!) satis…es the monotone likelihood property. Farmers update their assessment of the state
of their local market according to
(qi ) =
8
>
0
>
>
<
>
>
>
:
1
10
1
if
1
2
qi <
if
3
2
qi < 50
if 50
qi
3
2
150
For the demand side, we assume that the individual demand function is linear q(p) =
with
> 3 and
> 0. For numerical simulation, we set "(!) = 1 + !, B =
p,
:5 and G = :5.
To concentrate on mobile phone e¤ects, transaction costs are set such that no switching occurred
prior to mobile phones. We assume that property (3) of Theorem II:1 is satis…ed. That is, we
set
=
0:099. The following empirical simulation compares how changes in the outcomes
of interest (price dispersion, price levels, and welfare) correspond to the introduction of mobile
phones. The parameters of the model are given in Table 1.
Table 1 : Parameters of the model
q
100
0:099
14:85
:5
3:12
2
2
We assume that mobile phone service is introduced gradually throughout the village rather than
all at once. For simplicity, we present here simulation results from the exogenous case. For the
endogenization of mobile phone demand in both markets, all qualitative results described below
remain valid.
A. E¤ects on Market Performance
Primarily, we assume that the markets are equal in size, M 0 = M 1 , and we investigate the
e¤ects of mobile phone coverage expansion on market performance. We measure performance
on the basis of price dispersion indicators, namely variance in prices within and across markets.
Figure 3a and 3b shows variance in prices within and between markets, according to mobile phone
expansion for two transportation cost values (
1
22
=
and
2
= 4 ). Mobile phone expansion
reduces price dispersion. Variance in prices within both markets and across markets lowers when
a higher percentage of villages are covered by mobile phones. A rise in the transportation cost
leads to larger price dispersion. When the transportation cost increases, it becomes less pro…table
to switch. Ceteris paribus, less switching leads to greater price dispersion in equilibrium.
Prior to mobile phone availability, there was a large max-min spread across the markets.
When mobile phone service was introduced, this large price spread declined (Figure 3c and 3d).
The reduction in price di¤erential grows when a higher percentage of villages are covered by
mobile phones. Mobile phone di¤usion leads to the “Law of One Price”. To clearly illustrate this
convergence, we assume a heterogeneous di¤usion of the technology. We …x the mobile phone
coverage in one village and let it vary in the other village. We also assume that in village 1,
mobile phones are available at a coverage rate t1 = 0:65, and we analyze the e¤ects of mobile
phone coverage expansion in village 0. Simulation results suggest that the addition of mobile
phones is associated with a substantial reduction in the average spread until the convergence of
average market prices.
(a) Variance Within Market
(b)Variance Between Markets
0.5
0.26
τ = 4τ*
τ = τ*
0.24
τ = 4τ*
τ = τ*
0.48
0.22
0.46
0.2
0.44
0.18
0.42
0.16
0
0.2
0.4
0.6
0.8
0.4
1
0
0.2
0.4
0.6
0.8
1
t0=t1
t0=t1
(c) Market Price in GB State
(d) Average Market Price
0.6
1.2
0.59
1
0.58
0.8
0.57
0.6
0.56
0.4
0.55
0.2
0.54
0
0
0.2
0.4
0.6
0.8
0.53
0
1
0.2
0.4
0.6
t0
t1=0.65
t0=t1
Figure 3 : E¤ects on Market E¢ ciency
23
0.8
1
B. Mobile Phone Di¤usion and Inequality
Next, we examine the e¤ects of mobile phone di¤usion on inequality among producers. We
measure inequality on the basis of expected gains, as discussed in section 4. Figure 4 depicts
the simulation results. When the markets are in opposites states, mobile phone di¤usion creates
signi…cant spillover gains to producers without phones, due to improved market functioning.
Figure 4a shows the case when a market is in a G state and the other one is in a B state.
Producers who adopt mobile phones bene…t in this case, but those without phones also bene…t
because the price in this market increases. Phone users thus exert a clear positive externality on
nonusers. In contrast, producers from the market in a B state (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.
Equal Diffusion
(a) Net Gains in GB State
w
0
m
w
(b) Inequality Pattern
0.9
0.3
1
0
0
Ω ,Ω
1
m
w ,w
1
Ω
0.8
0.2
0.7
0.6
0.1
0.5
0
0.4
-0.1
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
Unequal Diffusion
t0 = t1
w
m
0.8
1
(d) Inequality Pattern
0.3
w0
0.6
t0 = t1
(c) Net Gains in GB State
0.9
w1, w1
0
m
Ω
0.8
0
Ω
1
Ω
0.2
0.7
0.1
0.6
0.5
0
0.4
-0.1
0
0.2
0.4 t0 0.6
t1=0.65
0.8
1
0
0.2
0.4
0.6
t0
t1=0.65
0.8
1
Figure 4 : E¤ects on Inequality
Furthermore, producers using mobile phones bene…t more than nonusers, partly because they
have a higher level of production and are more likely to be able to take advantage of pro…table
arbitrage, thus bene…ting from higher prices. Clearly, mobile phone di¤usion has redistributional
24
implications. Even equal di¤usion of the technology across markets emphasizes the existing inequality within the economy, while unequal di¤usion increases the inequality between the markets
(Figure 4c and 4d). Indeed, the aggregate gain increases within market 0 and decreases within
market 1. The aggregate gain for the whole economy increases.
C. Welfare E¤ects
To study the welfare e¤ects of mobile phone di¤usion, we use producer and consumer changes
in surplus to provide simple estimates of welfare changes.22 For the economy, changes in total
surplus (the sum of consumer surplus and producer surplus) are used to measure the net changes
in social welfare. Simulation results are reported in Figure 5, and suggest that mobile phone
spread is primarily bene…cial for producers. The net gains measured by producer surplus changes
are positive and increase with mobile phone penetration (Figure 5a), while consumers lose from
reduced price variability (Figure 5b). Consumers cannot engage in intertemporal substitution so
they may not prefer more variable prices.23 Indeed, there is no wealth e¤ect, and the consumers’
demand is less price elastic.24 However, society as a whole prefers price stability (Figure 5d).
The net welfare gains are positive for the whole economy, the gainers (producers) being able to
compensate the losers (consumers). Furthermore, the net welfare gain has an inverted U -shape.
In the …rst stage of mobile di¤usion, consumers’loss is lower than producers’gain because there
is less switching. Beyond some turning point, net welfare gain (always positive) declines with
mobile phone coverage because more switching occurs, so consumers’loss increases. These results
suggest that net welfare gains are likely to be associated with the introduction of mobile phone.
This is due to the more e¢ cient allocation of goods— i.e., they are reallocated to where they are
22
In general, using consumer surplus as a measure of welfare change is not appropriate. Speci…cally, when there
is no wealth e¤ect (e.g., if the underlying preferences are quasilinear, as is the case here), Marshallian consumer
surplus gives an exact measure of welfare change (Mas-Collel et al., 1995, p. 89). Turnovsky et al. (1980)
have identi…ed restrictions on preferences for which expected Marshallian consumer surplus is a valid indicator of
individual welfare change when prices are stochastic. Indeed, consumer surplus is an accurate measure when the
income elasticity of demand equals the income elasticity of the marginal utility of income, which in turn is the
Arrow-Pratt measure of relative risk aversion.
23
Under linear supply and demand, Massel (1969) argued that when the stochastic variation in prices originates
from the supply side of the market, consumers lose and producers gain when price is stabilized at its arithmetic
mean. Introducing risk aversion, Turnovsky et al. (1980) have shown that the consumers’ preference for price
instability depends upon four parameters: the income elasticity of demand, the price elasticity of demand, the
share of the budget spent on the commodity, and the coe¢ cient of relative risk aversion. Speci…cally, they argued
that if consumers are risk neutral, they will prefer price instability. And in the case of consumers having a downward
sloping (uncompensated) demand curve, they lose from price stabilization.
24
In general, the gains for consumers will be smaller (or even negative) when demand is less price elastic.
25
more highly valued on the margin.
(a) Producer Surplus
(b) Consumer Surplus
0.1
0
0.08
-0.02
0.06
-0.04
0.04
-0.06
0.02
-0.08
0
0
0.2
0.4
0.6
0.8
-0.1
1
0
0.2
t0
0.4
0.6
0.8
1
t0
(c) Net Welfare
0.012
0.01
0.008
0.006
t1=.65
0.004
t1=t0
t1=.25
0.002
0
0
0.2
0.4
0.6
0.8
1
t0
Figure 5 : Welfare E¤ects
D. Exploring Mobile Phone E¤ects with Unequal Market Sizes
The following results explore the e¤ects of mobile phone di¤usion when market sizes are not
equal. To do so, we set the relative size of market 0 in relation to market 1 as
M0
M1
2
= 0:5
and analyze how the impact of mobile phones di¤ers across space. First, we suppose an equal
di¤usion of the search technology across markets (Figure 6a and 6b). The average price increases
in market 1 while it decreases in market 0. This suggests that equal di¤usion is not good for
farmers within market 0 (which is smaller). As the mobile phone penetration rate increases, those
who don’t have mobile phones in market 0 lose more, on average. Indeed, when the markets are
in opposite states, ceteris paribus, there is more switching from market 1. Thus, the negative
26
externality for market 0 is stronger.
Equal Diffusion
(a) Average Market Price
0.585
(b) Average Gains
0.3
Market 0
Market 1
0
m
Prior to Phone
0.575
0.2
Price Premium
0.25
0.57
0.565
0.56
0
w
1
0.1
0.05
0
0
0.2
0.4
0.6
0.8
t0= t1
-0.05
1
0
0.2
0.6
0.4
0.6
0.8
1
t0= t1
Unequal Diffusion
(c) Average Market Price
(d) Average Gains
0.3
Market 0
Market 1
Prior to Phone
0.59
w0
m
0.25
0.58
w
0
w1
m
w
1
Price Premium
0.2
0.57
0.56
0.55
0.15
0.1
0.05
0
0.54
0.53
w
0.15
0.555
0.55
1
m
w ,w
0.58
0
0.2
0.4
0.6
0.8
-0.05
1
0
0.2
0.4
0.6
0.8
1
t0, t1= 0.65
t0, t1= 0.65
Figure 6: Unequal Market Sizes
Next, to suppose an unequal di¤usion of mobile phones across markets, we …x t1 = 0:65 and let
it vary in village 0. In contrast with the situation of equal di¤usion, the average price increases
in market 0 while it decreases in market 1. Indeed, the lower the mobile penetration rate in
market 0, the greater the di¤erence between the average prices. In the …rst stage, mobile phone
di¤usion is more likely pro…table for users in market 0 than for users in market 1. Nonusers in the
smaller market lose, on average, due to the stronger negative externality. The lower the mobile
penetration rate in market 0, the stronger the loss for nonusers in this market.
VII. Concluding Remarks
In this paper we have developed a simple search theoretical model to analyze how the improvement
of information via mobile phone use by farmers (sellers) enhances market e¢ ciency. We …nd
that the addition of mobile phones reduces price dispersion across markets, and yields positive
externalities within markets but negative externalities across markets. Price dispersion decline
27
is higher as the original di¤erence in penetration rates of mobile phones between markets is
lower, and greater access to mobile phones may signi…cantly improve welfare. Further, while it
is primarily those who adopt mobile phones who bene…t, there are signi…cant spillover gains for
those who do not use phones, due to improved market functioning. On the other hand, we show
that when combined with an initial endowment inequality or unequal market sizes, technology
di¤usion increases welfare inequality.
Our results con…rm 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 appropriate tools to enhance development.
Nevertheless, our results suggest that the non-uniform di¤usion of a new technology may reinforce
existing patterns of inequality.
VIII. Appendix
In this section, we provide the proofs for the paper’s main results.
A. Proof of Theorem II.1
h
i
0 to admit a unique solution q 2 q B ; q G
h
i
are: (i) V (q) has strictly monotonic variations in q B ; q G , and (ii) 0 2 V ; V , where V =
The su¢ cient conditions for the equation V
inf(V (q B ); V (q G )) and V = max(V (q G ); V (q G ).
Di¤erentiating V (:) with respect to q yields
q 0 (q) p0B
>
qG
p0G
@V
@q
=
p
+ q 0 (q) p0B
p0G . Denote that
E p1 p0G
h
i
, implying that the function V (q) is indeed strictly monotonically increasing in q B ; q G .
0, since (q) is increasing with q. Furthermore, we have
p
Thus, V = V (q B ) and V = V (q G ).
Second, note that (q B ) = 0 and (q G ) = 1. So we have
V (q B ) = q B E p1
p0B
0; and V (q G ) = q G E p1
p0G
0
Clearly, 0 2 V ; V and hence the result.
Since V is increasing with q, then (i) if q > q then V > 0 and the farmer switches to the
28
other market, and (ii) if q
q then V
0 and the farmer sells locally
B. Proof of Theorem III.1
When both markets are in the same state, there is 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 a G state and market 1 is in a B state.
Here are two possible cases, either tj = 0 or tj > 0. First, suppose that tj = 0, which
reproduces the situation prior to mobile phone availability so the 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 the de…nition of market demands (II.8) and market supplies (III.6), (III.4), we can
characterize the market equilibrium. Given tj ,
and , the price equilibrium (p0 ; p1 ) expunges
the markets’excess demand:
S 0 (p0 ; p1 )
D0 (p0 )
0
(VIII.1)
S 1 (p0 ; p1 )
D1 (p1 )
0
(VIII.2)
Given the above notations, we begin with the characterization of market equilibrium price p0 ,
the solution of (VIII.1) given market price p1 and others parameters. Assume an interior solution
and let it be described by a real-valued function f : R+ ! [pG ; pB ] such that 8p1 2 R+ ,
p0 = f (p1 )
(VIII.3)
First, we establish the following results.
Claim 1. The real-valued function f (:) exists, and admit the following property f 0 (p1 ) > 0.
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
monotonic variations in [pG ; pB ] and (ii) 0 2 [ ; ], where
First, since
25
@I 0
@p0
< 025 , clearly
Using Leibniz’s Theorem, we have
@
@p0
@I 0
@pj
=
=
@I 0
@p0
T0
S 0 (p0 ; p1 )
= (pG ) and
D0 (p0 ) has strictly
= (pB ).
(M j )2 q 0 (p0 ) > 0, implying that the function
2
@qI
qI (qI jG) @p
j = 0; 1 and
j;
29
@qI
@p0
=
(p1
p0
)2
;
@qI
@p1
=
(p0 ) is indeed strictly monotonically increasing in [pG ; pB ]. Second, from (III.6) and (II.11), it
can be shown that qI (pG ; p1B ) < q G and qI (pB ; p1B ) = q G . Indeed, I 0 (pG ; p1 ) > 0 and I 0 (pB ; p1 ) =
= S 0 (pG ; p1 )
0. Therefore, we have:
0 2 [ ; ]. Hence the result.
Furthermore, we have
@
@p1
=
@I 0
@p1
D0 (pG ) < 0 and
< 0 and f 0 (p1 ) =
= S 0 (pB ; p1 )
@p0
@p1
@ =@p1
@ =@p0
=
D0 (pB ) > 0. Clearly,
> 0:
Second, taking (VIII.3) and replacing it in (VIII.2), we have
S 1 (f (p1 ); p1 )
D1 (p1 )
0
(VIII.4)
Likewise, assume that price market equilibrium p1 also exists interior, and let it be de…ned by a
real-valued function g : R2+ ! [pG ; pB ] such that 8(t0 ; ; ) 2 R3+ , p1 = g(t0 ; ; ).
@g
Claim 2. The real-valued function g(:) exists and admits the following properties: (i) 0 < 0,
@t
@g
@g
(ii)
> 0 and (iii)
>0
@
@
Proof The su¢ cient conditions for system (VIII.4) 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 the derivative of S 1 in respect of p1 , we have
dS 1
dp1
=
@I 0 @p0
@p0 @p1
+
@I 0
.
@p1
Note that using (III.4) and (III.3), we have
dS 1
=
dp1
(T0 )2 qI (qI jG)
(p1
p0
)2
@p0
@p1
1
Using the implicit function theorem on (VIII.1) and rearranging terms, we have:
@p0
=
@p1
dS 1
dp1
So,
@S 0 =@p1
@S 0 =@p0 @D0 =@p0
> 0 and
dD1
dp1
1
1+
q 0 (p0 )
< 1 where
< 0. And since "0 (p1 ) =
dS 1
dp1
dD1
dp1
"
M0
T0
2
p1 p 0
qI (qI jG)
2
#
>0
> 0. Therefore, the function "(p1 ) is
strictly monotonically increasing in [pG ; pB ].
Furthermore, since f (pG )
pG and f (pB )
pB , we have qI (f (pG ); pG )
q G and qI (f (pB ); pB ) <
q G . And since I 0 (f (pB ); pB ) > 0 and I 0 (f (pG ); pG ) = 0, we have S 1 (f (pG ); pG ) = D1 (pB ) +
(p1
p0
)2
and hence the result.
30
I 0 (f (pG ); pG ) < D1 (pG ) and S 1 (f (pB ); pB ) = D1 (pB ) + I 0 (f (pB ); pB ) > D1 (pB ).
So, " = S 1 (f (pG ); pG )
D1 (pG ) < 0 and " = S 1 (f (pB ); pB )
D1 (pB ) > 0. Clearly, 0 2 ["; "].
Hence the result.
Furthermore, using the implicit function theorem we have:
@p1
=
@h
@ S0
@ [S 0
D0 =@h
; h = t0 ; ;
D0 ] =@p1
Where
@ S 1 D1
@I 0
=
@h
@h
Using the properties of Theorem II:1, it can be established that
@p1
@t0
1
< 0; @p
@ > 0 and
@p1
@
> 0:
And using the results of Claim 1 and Claim 2, we have:
@f @p1
@p0
@f @p1
@p0
@f @p1
@p0
=
>
0
;
=
<
0
;
and
=
<0
@t0
@p1 @t0
@
@p1 @
@t0
@p1 @
(VIII.5)
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