Getting Prices Right: Mobile Phone Di usion, Market E ciency and Inequality 1

Transcription

1 Getting Prices Right: Mobile Phone Di usion, Market E ciency and Inequality 1 Francis ANDRIANARISON 2 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 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. francis.andrianarison.1@ulaval.ca

2 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

3 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

4 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

5 of goods and causes price dispersion across markets 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 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

6 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

7 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 q B q G < q B < q G. And, (qj!) satis es the Monotone Likelihood Ratio Property, so that the ratio L(q) (qjg) (qjb) (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: 8 >< (q) = >: 0 if q B q < q G L(q) if q 1 + L(q) G q q B 1 if q > q B (II.2) 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

8 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 p j! 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 p j G pj B : (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

9 sell locally (or to switch), his expected gain V (0) (or V (1)) is given by V (0) = p 0 G + [1 ] p 0 B q (II.4) V (1) = p 1 G + (1 )p 1 B 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 V (1) V (0) = q [p ] (II.6) with p = p 1 G + (1 )p 1 B p 0 G + (1 ) p 0 B (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 p 1! or a decrease in p 0! 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 production q (; 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 = >: q B if E p 1 p 0 B + q B q G if E p 1 p 0 G + q G 2 ]q B ; q G [ if otherwise 8

10 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

11 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 M j 2. So, in the state!, the aggregate demand D! j for the market j is D j! = M j 2 q(p j! ) (II.8) where p j! is the market price. The quantity supplied to market j is equal to the aggregate production Q j!. The aggregate production equals the average production Q! multiplied by the total production mass M j 2. So in state!, the aggregate supply to market j is Q j! = Q! M j 2 (II.9) where Q! the average production in state! is given by Q! Z q! q! q(qj!)dq (II.10) Equalizing the aggregate demand (II.8) to the aggregate supply (II.9), we have the market prices equilibrium p j!: p j! = 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

12 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 t j, which also represents the mobile phone penetration rate in village j, is given by T t j j = M j 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

13 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 p 1 B p 0 G (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 q I the quantity such that a farmer is indi erent between selling locally or switching. q I is given by 8 >< q I = >: q G if p 1 B p 0 G + q G if + q < p 1 B p 0 G < + G q G p 1 B p 0 G q G if p 1 B p 0 G + q G (III.3) As the bene t (III.2) increases with q, the informed farmer with a level of production higher than q I 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 q I. Furthermore, a rise in market 1 price p 1 B (or a decrease in local market price p0 G ) 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 Q 1 B supplied by 12

14 local farmers and I 0 supplied by informed farmers who switch from market 0: S 1 (p 0 ; p 1 ) = Q 1 B + I 0 (III.4) where I 0 = T 0 Z qg 2 q I q(qjg)dq (III.5) q I 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 (p 0 ; p 1 ) = Q 0 G I 0 (III.6) Now, we can characterize the market equilibrium. De nition 1. An equilibrium for this economy is a threshold level of production q I and a price system (p 0 ; p 1 ) such that: 1. informed farmers (who have mobile phones) with a level of production greater than q I switch to the other market, while those with production lower than q I sell locally; 2. in each market, aggregate demand equals aggregate supply: S 0 (p 0 ; p 1 ) = D 0 (p 0 ) S 1 (p 0 ; p 1 ) = D 1 (p 1 ) (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 (q I ; p 0 ; p 1 ) exists and is unique. In addition, it satis es the 0 l = ; : > 0; < 0, < 0, > 0; 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 t 0 enables farmers to pursue the highest price in market 1, so the supply to 13

15 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 h 2 j = E p j 2 i E p j 2 (III.8) And the variance in prices between the markets is given by 2 V ar(p 1 p 0 ) = (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: > 0 > 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

16 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

17 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 > q I. 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 de ned by w j m (or w j ), the expected gain from the farmer s arbitrage if s/he has a mobile phone (or does not). 17 We have w 0 = (1 )q p 0 GB + p 0 BG w 1 = (1 )q p 1 BG + p 1 GB (IV.1) (IV.2) w 0 m = (1 ) q p 1 GB + p 0 BG (IV.3) w 1 m = (1 ) q p 1 GB + p 0 BG (IV.4) where p j GB (or pj BG ) 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). Note that following (III.2) and (III.3), we always have w j m w j. 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 q I, he always sells locally and the discussion is not interesting. 17 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 16

18 0 0 ; m 0 0 0; and (iii) dw 0 m dt 0 dw 0 dt 0 ; dwm 1 dt 0 dw 1 dt 0 : 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 with mobile phone wm j minus the expected bene t of a decision without mobile phone w j : V I = w j m w j (IV.5) Lemma 1. The value of information is (i) increasing in q; and (ii) decreasing in mobile phone coverage. The proof of Lemma 1 is immediate using the de nition of w j m and w j 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 q 1 > q 2, then we have w j m(q 1 ) w j m(q 2 ) w j (q 1 ) w j (q 2 ) 17

19 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, we can calculate the aggregate gain for farmers with phones in village j, Wm j = R wmdw j m; j and for those without phones, W j = R w j dw j. Using (IV.1) and (IV.3), we can establish that W 0 m = (1 ) p 1 GB p 0 GB I 0 + p 0 GBQ G + p 0 BGQ B F 0 (IV.6) W 0 = (1 ) p 0 GBQ G + p 0 BGQ B (IV.7) W 1 m = (1 ) p 0 BG p 1 BG I 1 + p 1 BGQ G + p 1 GBQ B F 1 (IV.8) W 1 = (1 ) p 1 BGQ G + p 1 GBQ B (IV.9) where F j = I j = Z qg q I Z qg q I (qjg)dq denotes the number of farmers who buy mobile phones in village j and q(qjg)dq the amount of their production; Q B and Q G are the average productions in states B and G, as given by (II.10). Thus, the aggregate gain j for the village j is given by : j = t j W j m + (1 t j )W j (IV.10) Now, consider an expansion of mobile phone coverage t 0 in village 0. We have the following proposition. Proposition 6. We > 0; 0 < 0 and (ii) 0 > 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

20 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

21 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 V m R(q) (V.1) When > 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 eq I 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 eq I ( ), 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 (eq I ; ep 0 ; ep 1 ) equilibrium with eq I 0 ( ) > 0 exists and >0; (ii) < 0; (iii) 0 0 addition, it satis es the < 0; > 0 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

22 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 purchase mobile phones in a village when it is in a G state is R q G eq I (qjg)dq. Corollary 2. The proportion of farmers who adopt mobile phones is given by Z qg Z qb = (qjg)dq + (1 ) (qjb)dq (V.3) eq I eq I 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 which follows the Pareto distribution, with density (q) = ; q 2 [1; q]. In state!, we suppose that risk multiplicatively a ects the q 3 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