### Université Libre de Bruxelles

^{ }

### Académie Universitaire Wallonie‐Bruxelles

^{ }

### FACULTÉ DES SCIENCES SOCIALES ET POLITIQUES /

### SOLVAY BRUSSELS SCHOOL OF ECONOMICS AND MANAGEMENT

**The
Industrial
Organization
of
Financial
** **Services
in
Developing
and
Developed
**

**Countries
**

### Thèse de Doctorat présentée en vue de l’obtention du titre de Docteur en Sciences Economiques et de Gestion

### Par Paolo Casini

### Directeur:

### Co‐directeur:

### Membres du jury :

### Professeur Georg Kirchsteiger – ULB Professeur Estelle Cantillon – ULB

### Professeur Jean‐Marie Baland – FUNDP Namur Professeur Mathias Dewatripont – ULB

### Professeur Victor Ginsburgh – ULB Professeur Janet Mitchell – NBB

### The Industrial Organization of Financial Services in Developing and Developed Countries

Paolo Casini February 16, 2010

### Contents

Introduction 9

1 Competition and Altruism in Microcredit Markets 13

1.1 Introduction . . . 14

1.2 The Model . . . 18

1.3 The Entrant Strategy . . . 21

1.4 The Incumbent Strategy . . . 26

1.4.1 The Profit maximizing Incumbent (PM Model) . . . 26

1.4.2 The Altruistic Incumbent (AI Model) . . . 31

1.5 Conclusions . . . 37

1.6 Appendix . . . 38

2 Ex-ante Incentives for Multiple Borrowing 51 2.1 Introduction . . . 52

2.2 The model . . . 55

2.2.1 Incentives for Multiple Borrowing . . . 57

2.3 The Equilibria . . . 60

2.3.1 No Multiple Borrowing . . . 60

2.3.2 Multiple Borrowing Allowed . . . 65

2.4 Conclusions . . . 68

2.5 Appendix . . . 69

3 Cooperative vs. Third-Party Provision of Financial Services 77 3.1 Introduction . . . 78

3.2 The Model . . . 81

3.3 Investment Decisions . . . 84

3.3.1 Cooperative Provision . . . 84

3.3.2 Private Service Provision . . . 86

3.4 Pooling and Quasi-Pooling Equilibria . . . 87

3.5 Separating Equilibria . . . 91 3.6 The Investment Level . . . 94 3.7 Conclusion . . . 96

### List of Figures

1.1 Entrant strategies as a function of the Incumbent strategies . . 25

1.2 Incumbent Profit: Example 1. . . 28

1.3 Incumbent Profit: Example 2. . . 29

1.4 Entrant Profit: Comparison AI model and PM model . . . 37

2.1 MFI iStrategies as a function of C^{j} . . . 63

### Acknowledgments

Doing a Ph.D. is like running a marathon: at the end of the day it’s about mastering your endurance, going thorough some pain and a long series of ups and downs. And the time flies... It’s tough, but a lot of fun, too.

I have been a lucky runner, a bit slow maybe, but definitely lucky. First of all, I have had three wonderful coaches: Estelle, Georg and Paola. Estelle and Georg, as my supervisors, made me work hard, very hard! But they made available for me their whole experience in a fantastic way. Their advice and support has been invaluable to me. Paola (besides coaching me for real marathons) taught me the passion and the special taste in discussing your ideas even in front of the toughest of the audience. She has been a real friend to me. The three of them gave me a chance when my career had had a bad break. Without that bit of trust, I would have never managed. I will always be grateful for that.

Second, running is much more fun if you do it with friends. And I did.

Alexander, Laura, Claudia, Joachim, Paulo, Cristina became a fundamental part of my life. Having met them, is worth the entire effort I exerted in writing my papers and much more.

Third, my family supported me in an amazing way. I think at the begin- ning they thought I was crazy. I still remember my father’s reaction when I told him about this project: ‘A Ph.D.? In Belgium? Why in the world should you do that?’ But they never even tried to make me change my mind.

Their support has been constant and complete. I admire them for their open- mindedness and courage.

Many other persons ‘made the difference’ during these years: Arend, Lorena, Giovanna, Marcello, Pablo, Il Gallo, Alexandre, David, Francesca, Maria Caterina, the wonderful CRED group... I could name many more!

Each of them had his role but together they managed to never make me feel alone.

One marathon is done. But, you know, running is addictive (Paola had warned me about it). So I am not planning to stop yet.

### Introduction

Financial markets in different areas of the world have many similarities, but also some idiosyncratic features making them special. The similarities come from the fact that most of the basic financial needs of household and en- trepreneurs are, in a broad sense, analogous across countries and regions.

Credit, saving and insurance are demanded everywhere to smooth consump- tion, make investments and face risks. But substantial differences arise in the way these needs are met by the local financial institutions. Culture, geogra- phy, politics and economics can, in fact, influence the interaction between the institutions and their clients in a relevant manner.

In the first part of the thesis I focus on credit markets in developing coun- tries, and describe the competitive interaction between Microfinance Insti- tutions (MFIs). Microfinance has recently attracted a lot of attention from investors, politicians, scholars and, most of all, people working on develop- ment. As a results, a huge number of MFIs are being created all over the world so that, as of today, practitioners reckon that about 100 millions of customers are being served. Remarkably, about 67% of them are women.

The reason of this extraordinary effort is that Microfinance is considered the most promising development tool currently available. This belief is based on two important features of Microfinance: (i) It promises to be financially viable (and in some cases even profitable) since poor people have proven to be reliable clients. As a result, Microfinance is potentially a zero-cost devel- opment tool. (ii) It hinges on the entrepreneurial abilities of the poor. It is designed to help the poor to help themselves, in their own home coun- tries, by allowing them to use their skills, ideas and potentials. This should progressively make developing countries independent of rich ones’ help.

The growth of Microfinance has been so fast that many issues and related research questions are still not answered. In my thesis I try to address one of them, that I believe particularly important: the increase of competition between MFIs. As economic theory predicts, competition can have dramatic consequences in terms of borrower welfare, profitability of the institutions and,

therefore, on the attractiveness of the business for potential investors, donors and entrants. I use the tools of industrial organization and contract theory to understand these effects, measure them, and give some interesting policy advice.

In the first paper, I analyze the effects of entry of a new MFI in a previ- ously monopolistic microcredit market. In order to catch the salient features of financial markets in developing countries, I use a model of asymmetric in- formation and assume that institutions can offer only one type of contract. I consider different behavioral assumptions for the MFIs and study their influ- ence on equilibrium predictions. The model allows showing that competition can lead to equilibria in which MFIs differentiate their contracts in order to screen borrowers. This process can, unfortunately, make the poor borrowers worse off. Interestingly, the screening process we describe creates a previously unexplored source of credit rationing. I also prove that the presence in the market of an altruistic MFI, reduces rationing and, via this channel, affects positively the competitor’s profit.

In the second paper, I study the effects of competition in those markets in which, due to the absence of credit bureaus, small entrepreneurs can si- multaneously borrow from more than one institution. As in the first paper, I analyze an oligopolistic microcredit market characterized by asymmetric in- formation and institutions that can offer only one type of contract. The main contribution is to show that appropriate contract design can eliminate the ex-ante incentives for multiple borrowing. Moreover, when the market is still largely unserved and particularly risky, a screening strategy leading to con- tract di?erentiation and credit rationing is unambiguously the most e?ective to avoid multiple borrowing. The result of this paper can also be read as important robustness checks of the findings of my first paper.

In the last part of the thesis, I depart from the analysis of developing countries to consider, more generally, the corporate governance of financial infrastructures. The efficient functioning of financial markets relies more and more on the presence of infrastructures providing services like clearing, set- tlement, messaging and many others. The last years have been characterized by interesting dynamics in the ownership regime of these service providers.

Both mutualizations and de-mutualizations took place, together with entry and exit of different players.

Starting from this observation, in the last paper (with Joachim Keller), we analyze the effects of competitive interaction between differently owned nan- cial providers. We mainly focus on the incentives to invest in safety enhancing measures and we describe the different equilibrium market congurations. We use a model in which agents need an input service for the nancial market they

operate in. They can decide whether to provide it them selves by forming a Cooperative or outsource it from a Third Party Provider. We prove that the co-existence of differently governed infrastructures leads to a signicant re- duction in the investment in safety. In most cases, monopolistic provision is preferable to competition. Moreover, the decision rule used within the Coop- erative plays a central role in determining the optimal market conguration.

All in all, throughout my thesis, I use the tools of industrial organization and contract theory to model the competitive interaction of the different ac- tors operating in financial markets. Understanding the dynamics typical of developing countries can help in gaining a deeper comprehension of the mar- kets in richer countries, and vice-versa. I am convinced that analyzing the differences and the similarities of financial markets in different regions of the world can be of great importance for economic theorists, in that it provides a counterfactual for the assumptions and the results on which our predictions and policy advices are based.

### Chapter 1

### Competition and Altruism in Microcredit Markets

Abstract: We analyze the effects of entry in a previously monopolistic mi- crocredit market characterized by asymmetric information and by institutions that offer only one type of contract. We consider different behavioral assump- tions concerning the Incumbent and study their influence on equilibrium pre- dictions. We show that competition leads to contract differentiation and that this can make borrowers worse off. Moreover, the screening process creates a previously unexplored source of rationing. We show that if the incumbent in- stitution is altruistic, rationing is reduced and that its presence in the market is strategically complement to the entrant’s profit.

Keywords: Microfinance, Competition, Altruism, Differentiation, Credit Ra- tioning

JEL Classification: G21, L13, L31, O16

I wish to thank Jean-Marie Baland, Estelle Cantillon, Mathias Dewatripont, Victor Gins- burgh, Georg Kirchsteiger, Janet Mitchell, Alexander Sebald and Edilio Valentini for pre- cious comments, as well as seminar participants at ECARES, SMYE 2007 (Hamburg), EARIE Conference 2007 (Valencia), ENTER Jamboree 2008 (Madrid), ‘Midi de la Mi- crofinance’ at CERMi (Brussels), CRED Workshops (Namur), DEST Summer Workshop in Economics 2008 (Pescara), Toulouse School of Economics, Stockholm School of Economics, IDEA (Universitat Aut`onoma de Barcelona).

### 1.1 Introduction

Microfinance is considered as one of the most promising instruments to reduce poverty and promote economic development in many areas of the world. Its potential is based on the idea that poor people have an unexplored amount of entrepreneurial skills that ought to be taken into account in any sustain- able development plan. Microcredit was designed to help the poor to help themselves.

Microfinance is a diverse phenomenon. NGOs, banks, international orga-
nizations and various other forms of financial institutions are crowding into
the markets to supply the poor with affordable credit. Despite being active
in the same markets, these institutions are motivated by different objectives,
spanning from poverty reduction to profit maximization, passing through dif-
ferent definitions of financial sustainability. The effects of the competitive
interaction among these players on poverty reduction is unclear from both a
theoretical and empirical perspective. First, since Micro Finance Institutions
(MFIs) are often motivated by goals different than profit maximization, there
is no clear reason to believe that more competition necessarily lead to lower
prices. Indeed, empirical evidence shows that interest rates are not lower in
markets in which competition is very harsh.^{1} Second, financial sustainability
and lending technologies impose tight constraints on governance and man-
agement, so that asymmetric information cannot be addressed with standard
tools like, for instance, a menu of contracts. For these reasons, applying exist-
ing theories on competition (and, more specifically, on competition in credit
markets) to Microcredit is not straightforward.

In our paper we take explicitly into account some idiosyncrasies of mi- crocredit markets. Our goal is to understand the effects of competition on credit supply, borrower welfare and MFI profit. To capture the idea that MFIs cannot offer the same variety of products that a standard bank would, we assume that MFIs, although operating in a market with different types of borrowers, can only offer one type of contract. We show how equilibrium pre- dictions respond to different assumptions on MFIs objectives, and we prove that altruistic behavior can be beneficial for both borrowers and competing MFIs.

The good performances of some MFIs, together with the strong emotional impact on public opinion, have attracted a large number of financial institu- tions, banks, NGOs and donors to this emerging market. In countries like Bangladesh, Uganda and Bolivia a process of sequential entry of institution

1See, for instance, Kaffu and Mutesasira (2003)

has been observed. The market is usually pioneered by a small NGO, and it is then followed by competitors that build on the experience of the predecessor.

The consequence of this process is that many institutions have now to deal with the effects of competition. In countries like Bangladesh and Bolivia the increase of credit supply is already affecting the incentives for repayment, the fidelity of clients and the quality of the pool of borrowers. This is all the more important that these are considered as key factors to explain the success of microcredit.

Increased differentiation in terms of contract type has been one of the first visible consequences of the increase in the number of competitors, although, as many practitioners state, there is still a considerable overlap of geographic areas and customers’ pools.

Standardizing to Compete: Lending money is not costless. Capital is
expensive, and so are enforcement of repayments, accountancy systems and
even storing of money. A large part of these costs is independent of the loan’s
size. For instance, the wage for a bookkeeper is the same no matter how small
the loan is. This makes microcredit relatively more expensive than standard
credit, leaving MFIs with a smaller profit margin. For this reason many of
them struggle for financial sustainability even though they use repayment in-
centives whose effectiveness has been widely tested. Reducing the managerial
cost is essential for the profitability of a microcredit program. To achieve this
goal, simplification of all the procedures is needed: microfinance contracts
need to be as standardized as possible.^{2} As a consequence, most of the MFIs
operating in competive markets offer extremely few contract types, and often
only one. ^{3}

The most convincing explanation of this phenomenon comes from the fact that lending money to the poor is possible only via the design and implementa- tion of widely studied mechanisms such as group lending, dynamic incentives, regular repayment schedules etc. These tools allow MFIs to tackle issues

2One of the highest costs for an MFI is labor. Microcredit is based on a strict personal relation between MFIs’ employees and borrowers. They need to meet regularly, collect the periodic repayments and control the quality of the investment. Hence, workforce is essential.

Nonetheless some MFIs prefer to hire less specialized personnel. This allows them to pay lower wages, reducing the operational costs. But it also reduces the average quality of the firm’s human capital. Standardization is the used to reconcile this trade-off.

3Some big and viable MFIs highlight this strategy as the main factor of their success. For instance, ASA, in Bangladesh defines its organization as theFord Motor Model of Microfi- nance. TheGrameen Bank, also operating in Bangladesh and probably the most celebrated Microfinance Institution in the world, offers loans with a unique interest rate, and this is certainly a special feature for a bank managing a portofolio of several millions of clients

such as moral hazard, absence of collateral, adverse selection, gender speci- ficity and so on. But the implementation of these mechanisms is complex, often delicate. Moreover the choice of such mechanisms has important conse- quences for the organization of the firms, both in terms of management and infrastructure. Since the contracts offered by each MFI are an essential part of these mechanisms, inevitably the choice of a particular interest rate has a strong commitment power (at least in the short run) and makes it particularly difficult to offer various contract types.

Our paper models a microcredit market with these characteristics. We
use a simple sequential game, with two firms (Incumbent and Entrant) and
two types of borrowers (Safe and Risky).^{4} We first assume that both firms
are profit maximizing. This framework fits a mature microcredit market (like
Bangladesh or Bolivia), dominated by few and large institutions, often with
an official Bank legal status. Then, we consider the case where the Incumbent
is altruistic. An altruistic institution maximizes the borrower welfare under
a non-bankruptcy constraint. We define two types of altruism that we label
asnaive and smart. The difference is the way the Incumbent MFI takes into
account the reaction of the Entrant. This approach better describes a younger
microcredit market and is empirically very relevant. Indeed, in most countries,
microcredit has been pioneered by NGO programs with a clearly stated social
aim. Some of them have then transformed into profit maximizing institutions,
but others have kept their status unchanged and have started competing with
profit maximizing entrants.

We show that MFIs have incentives to differentiate their contracts. This leads to equilibria in which competitors offer incentive compatible contracts that allow for screening of the borrower types. In these equilibria, the Risky borrowers enjoy an informational rent and the Safe ones are rationed. Yet, rationing is not merely a consequence of adverse selection as in Stiglitz and Weiss (1981). In our model, the level of rationing depends in fact on the outside options of the competing institutions.

The presence of more than one MFI introduces some competitive pressure, and this have a negative effect on expected profits. On the other hand it makes screening possible even when MFIs can offer only one contract. Thus, MFIs can offer more targeted contracts and extract more rent. As a consequence, from the borrowers’ point of view, competition is not necessarily welfare en- hancing: we show that under some conditions the borrower welfare is lower under competition than under monopoly.

4The sequential structure of the game is very helpful to ease exposition but is not essential, since all the results are valid also in a simultaneous setting. See Casini (2009).

Our model also relates to one of the most controversial debates in the microfinance literature, concerning the long run strategic behavior that MFIs should adopt in order to increase the outreach of microfinance. One side of this debate claims that microfinance should abandon the NGOs non-profit behavior and turn into a profit seeking business, independent of any form of subsidy. The argument is that profit maximizing behavior leads to more rigorous financial management. This, in turn, attracts more investors and enlarges the market capacity. More poor people can then be served in a profitable way, leading to a clear welfare gain. On top of that, the demand for credit is believed to be quite inelastic. This would allow to increase interest rates with limited consequences on the outreach.

But other researchers and practitioners fear that such a behavior might end up hurting the poor. In their view, microfinance is helpful only if it allows poor borrowers to accumulate capital to be reinvested in their small business.

An MFI too focused on profit maximization could, in an oligopolistic market, be able to extract most of the rent, reducing the beneficial effect of access to credit. This phenomenon seems relevant since in some countries many standard banks are currently scaling down part of their business to enter the microfinance market. Moreover, there is experimental evidence that the demand for credit is actually elastic (See Karlan and Zinman (2007)).

Our model shows that this threat is realistic. In particular we find that in equilibrium a profit maximizing MFI is able to extract the entire surplus from at least one borrower type. By contrast, if the Incumbent is altruistic, all the borrowers have positive rent and credit rationing is lower in equilibrium.

More surprisingly this is possible while letting the profit maximizing Entrant earn a strictly positive profit that is, under certain conditions, even higher than the profit she would earn when the Incumbent maximizes her profit.

In other words, the presence of an altruistic firm in the market makes not only all the borrowers better off, both in terms of rationing and rent, but can also result into an incentive for profit maximizing firms to enter the market.

This is due to the fact that the Incumbent’s altruism reduces the amount of rationing necessary to screen the borrowers, so that in equilibrium the Entrant can benefit from serving a larger number of clients.

Other papers have examined the issue of increasing competition in mi- crocredit Markets. McIntosh and Wydick (2005) present a model in which MFIs maximize the number of borrowers served and cross-subsidize the non- profitable borrowers using the profits earned by serving the profitable ones.

They show that as competition increases, the profits from profitable borrowers shrink, so that more poor borrowers are excluded from credit. Their result is based on the assumptions that poor borrowers are less profitable than richer

ones, and that MFIs can offer a different contract for each borrower. We will assume, instead, that all borrowers give ex-ante the same expected profit although they differ in their level of risk.

McIntosh, de Janvry and Sadoulet (2005) present an empirical analysis of the highly competitive microcredit market in Uganda. Studying the location decision of the MFIs, they find a strong tendency towards the creation of clusters of institutions, even though the presence of a competitor in the market increases the level of defaults. Our model provides a possible explanation for this phenomenon.

Our paper is closely related to the work of Navajas, Conning and Gonzales- Vega (2003). They describe the Bolivian microcredit market and its evolution from monopoly to duopolistic competition. They stress that the two main institutions in the market (Bancosol and Caja Los Andes) have specialized in different market niches: they offer different contracts based on different mechanisms that attract different types of borrowers. This pattern seems to be common in microcredit markets. Our paper draws on this observation.

The paper is organized as follows: In Sections 1.2 we introduce the model.

In Section 1.3 we describe the Entrant’s reaction function. In Section 1.4 we analyze the Incumbent’s behavior we show how and when differentiation takes place, taking into account different behavioral assumptions for the Incumbent.

In section 1.5 we conclude.

### 1.2 The Model

Consider a microcredit market initially served by a single MFI (the Incum- bent), and suppose that a second one (the Entrant) is considering entering the market. There is a unit measure of borrowers demanding a loan to finance a new business. The size of the loan is, for simplicity, set to one. There is a fractionβ of safe borrowers characterized by a returnRs and a probability of success ps, and a fraction 1−β of risky borrowers with return Rr and probability of success pr. We assume that piRi =m > 1 and that ps > pr. HenceRs< Rr. This ensures that both types have the same expected return.

Thus MFIs are ex-ante indifferent between serving either type of borrowers.

We also setprRs≥1, so that, even in case of mismatch between contract and borrower type, lending is viable.

MFIs can only serve a fraction α ∈ [0,1) of borrowers. We assume that
α > max{β,1−β} (implying that α ≥ 1/2) so that MFIs are able to serve
at least all the borrowers of a given type. They can offer only one contract,
defined as a pair C = (x, D), in which they specify the repayment D ∈R_{+},

inclusive of principal and interests, and the probabilityx∈[0,1] for a borrower
to be served (or, in other words, the fraction of the demand the MFI is willing
to serve). We denote byC^{I}= (x^{I}, D^{I}), the contract offered by the Incumbent
and withC^{E} = (x^{E}, D^{E}), the contract offered by the Entrant. The borrowers’

type is private information. As a tie-breaking rule, we assume that even when the contract leaves the borrowers with no rent, they still prefer borrowing to not borrowing.

The timing is the following: at timet= 1 the Incumbent sets his contract.

The Entrant observes the market and the Incumbent’s strategy and at time t = 2 she decides whether to enter the market or not. At time t = 3, the borrowers observe both contracts and choose their favorite.

The choice of a particular contract determines the pool of borrowers served.

In this respect their choice results in a commitment: once a contract (and the
underlying mechanism) is chosen, it cannot be changed in the short run. As
argued in the Introduction, this assumption seems quite plausible. Part of the
successes of microfinance is due to the design of innovative mechanisms able
to deal with issues as moral hazard, absence of collateral, adverse selection,
gender specificity and so on. These mechanisms are tailor-made to address the
unique features of the socio-economic environment of the borrowers, and can
therefore be substantially different across MFIs.^{5} The differences in mecha-
nisms are reflected in the management and organization of the MFIs. A clear
evidence of that is that extremely few MFIs use more than one mechanism.

Hence, once a mechanism is designed and implemented, it is reasonable to think that an MFI has to stick to it at least in the short run.

We do not model explicitly any of these mechanisms, but we think the
contracts as being a fundamental part of them. This approach is correct
as long as we can consider the repayment (or in other words the interest
rate) as the main strategic variable of the market. Despite the importance
of the underlying mechanisms, there is clear evidence that borrowers actually
consider the interest rate as a fundamental parameter to base their decision
on.^{6}

We solve the model considering first the Entrant’s optimal reaction for any given choice by the Incumbent, and then proceed by backward induction to specify the optimal choice by the Incumbent.

Note that any contract acceptable by the Safe borrowers attracts also the
Risky ones since R_{s} < R_{r}. Thus, when only one MFI is in the market, she

5For instance, it is extremely common to observe in the same market MFIs adopting only group lending and others using only individual lending.

6See, for instance, Karlan and Zinman (2007).

can only decide on whether to serve the risky or both types. When two MFIs are operating, instead, they can make any choice: should they choose to serve only safe borrowers, the presence of the competitor can help them screen out one type from the other.

Borrowers compare the contracts offered by both the Incumbent and the
Entrant and decide on the MFI at which they want to apply for credit. Bor-
rowers are solely concerned by the monetary outcome of the contract, so the
demand faced by each MFI depends on C^{I} and C^{E}. We define the demand
function as B^{i}(·,·) : (R+×[0,1])×(R+×[0,1]) → [0,1]. It assigns to each
combination of contracts the mass of borrowers preferring MFI i. We can
partition the space of contracts into four cases:

1. Full separation: x^{i}p_{s}(R_{s}−D^{i})> x^{j}p_{s}(R_{s}−D^{j}) and x^{j}p_{r}(R_{r}−D^{j}) ≥
x^{i}pr(Rr−D^{i}), fori6=j∈I, E: in this case the Safe borrowers prefer the
contract offered by firm i, whereas the Risky ones prefer the contract
offered byj. Thus,β borrowers apply for credit to MFIi(B^{i}(C^{i}, C^{j}) =
β), and 1−β to MFI j (B^{j}(C^{i}, C^{j}) = 1−β). If these conditions are
fulfilled the MFIs can screen the borrowers.

2. Full coverage by both: D^{i} ≤Rs;D^{j} ≤Rs;x^{i}ps(Rs−D^{i})> x^{j}ps(Rs−D^{j})
andx^{i}p_{r}(R_{r}−D^{i})> x^{j}p_{r}(R_{r}−D^{j}): in this case all the borrowers prefer
the contract offered by MFIi. ThusB^{i}(C^{I}, C^{E}) = 1 but, because of the
capacity constraint, MFIican at most serve the firstαapplicants. The
remaining 1−α (the residual demand of both types) is served by j, so
thatB^{j}(C^{I}, C^{E}) is bounded below by 1−α.^{7}

3. Partial separation: D^{i} ≤Rs;Rs≤D^{j} ≤Rr;x^{i}ps(Rs−D^{i})> x^{j}ps(Rs−
D^{j}) andx^{i}p_{r}(R_{r}−D^{i})≥x^{j}p_{r}(R_{r}−D^{j}): also in this caseB^{i}(C^{i}, C^{j}) = 1,
so that MFI ican serve up to α borrowers. But MFI j is only able to
attract the residual demand of the Risky borrowers, so thatB^{j}(C^{i}, C^{j})
is bounded below by (1−α)(1−β).

4. Exclusion: R_{s} ≤ D^{i} ≤ R_{r}; R_{s} ≤ D^{j} ≤ R_{r} and x^{i}p_{r}(R_{r} −D^{i}) ≥
x^{j}pr(Rr−D^{j}): in this case both MFIs can attract only the Risky bor-
rowers, who in turn prefer the contract offered by i. We have then
B^{i}(C^{i}, C^{j}) = 1−β and B^{j}(C^{i}, C^{j}) = 0.

7The actual residual demand depends on the mass of borrowers served by the competitor.

MFIs can in principle decide not to use their whole capacity (settingx <1). But given the capacity constraint, the residual demand measuresat least 1−α.

We assume that if both MFIs offer the same contract, they share the
demand equally. Moreover, both types are equally rationed.^{8}

### 1.3 The Entrant Strategy

As mentioned above, at time t = 2 the Entrant chooses her contract upon the observation of the Incumbent’s choice. She has then three different pos- sibilities: (i) Offer a contract that attracts all the borrowers of a specific type; (ii) Target the residual demand of the chosen sector(s); (iii) Offer a non-specialized contract, suited to attract both types. As we will see, the first option is only feasible if the Incumbent has set a contract that allows screening. Let P(·,·) : (R+×[0,1])×(R+×[0,1]) → [0,1] be the function assigning to each combination of contracts the probability of repayment. It takes valuepr,psorpb :=βps+(1−β)pr when the MFI serves respectively the Risky, the Safe or Both types of borrowers. The Entrant faces the following maximization problem:

max

x^{E},D^{E}Π^{E} =X^{E}(C^{E}, C^{I}, α)h

P^{E}(C^{I}, C^{E})D^{E}−1i

whereX^{E}(C^{E}, C^{I}, α) := min{x^{E}B^{E}(C^{I}, C^{E}), α}denotes the mass of borrow-
ers served by the Entrant.

The Entrant’s strategy set is given by the set of all possible contracts (x, D) such that x ∈ [0,1] and D ≥ 1. But the strategy set can be divided in three subsets, each of them identifying a possible intention: serving the Risky, the Safe or Both borrower types. In other words, the choice of a contract determines the group to target to, but also the strategic behavior to adopt with respect to the competitor: a particular contract (xi, Di) determines whether there will be direct competition (both MFIs targeting the same pool of borrowers as in case 2 and 4 of the taxonomy), full separation (each MFI specializing in a particular group as in case 2) or monopolistic behavior on the residual demand (the MFI exploits the capacity constraint of the competitor as in case 3).

Since by assumption 1 > α ≥ max{β,(1 −β)}, whatever the Incum-
bent strategy is, the Entrant can always target the residual demand (1−
x^{I}B^{I}(C^{I}, C^{E})), and impose on it a monopoly price. For the sequel, it is use-
ful to calculate the profit the Entrant earns serving the residual demand of
the Risky types, when the Incumbent faces a demand B^{I}(C^{I}, C^{E}) = 1 (case

8This taxonomy is exhaustive since if the Safe borrowers are indifferent between the contracts, then also the Risky are.

3 in the taxonomy), i.e. serves both markets. The Entrant optimally sets
D^{E} =Rr and x^{E} = 1, extracting the whole surplus from the residual Risky
borrowers and earning:

ΠResR = (1−α)(1−β)(m−1). (1.1)
In the same way we can define the profit the Entrant earns serving the residual
demand of both types. She sets D^{E} =Rs, extracting all the Safe borrower’s
surplus and leaving the Risky ones a rent. She earns:

ΠResB = (1−α)[β(m−1) + (1−β)(prRs−1)] (1.2)
Finally, if the Entrant serves both types, facing a demand B^{E}(C^{I}, C^{E}), her
profit is given by:

Π_{Both}=α(β(m−1) + (1−β)(prRs−1)) (1.3)
Screening borrowers is only possible when competitors coordinate. If an
MFI chooses to specialize in the Risky sector, the screening is easily done by
setting a contract withD > Rs, so that no Safe borrower is willing to apply.

But serving only the Safe borrowers is not so easy. A suitable contract for the Safe type, requires a lower value ofD, and that surely attracts also the Risky borrowers.

In our model, as in a more standard screening problem, MFIs can ration some borrowers in order to make screening possible. By properly adjusting the value of x, they can reduce the expected profitability of the contract designed for the Safe borrowers. At the same time, the Risky ones can be given an informational rent. This idea is quite standard, but we apply it in a particular way: in our model the optimal contracts are the result of a competitive interaction between two different MFIs, each offering one single contract. In what follows, we prove the existence of equilibria in which the MFIs find it profitable to design screening contracts in order to make this differentiation possible.

Screening Strategies: Since the Entrant’s contract is chosen after the ob- servation of the Incumbent’s choice, under some conditions the Incumbent can induce the Entrant to serve one particular market niche and engage in a screening strategy. She can do it by offering a contract that makes it op- timal for the Entrant to target only one type of borrowers. We explain the mechanism in the next two lemmas.

Lemma 1. If the Incumbent chooses a contract such that D^{I}≤Rs and x^{I} <

min{xˆs(D^{I}),1} where xˆs(D^{I}) is defined as:

α(m−1)

m−prD^{I} if ΠResR≥max{ΠResB,ΠBoth}
(1−β)(m−1)−Π_{ResB}

(1−β)pr(Rr−D^{I}) if ΠResB ≥max{ΠResR,ΠBoth}
(1−β)(m−1)−Π_{Both}

(1−β)p_{r}(R_{r}−D^{I}) if Π_{Both}≥max{ΠResR,ΠResB}
then the Entrant’s optimal reaction is to offer a contract (x^{E} = 1;D^{E} =
R_{r}−_{x}^{x}E^{I}(R_{r}−D^{I})), so that screening takes place with the Incumbent serving
the Safe borrowers and the Entrant serving the Risky.

Proof. See Appendix 1.6

When the Incumbent is profit maximizing, the relevant outside option is
Π^{E}_{Both}. The other options matter when the Incumbent is altruistic.

The intuition behind this result is standard: if the Incumbent wants to serve only the safe borrowers, she must exclude some of them. What is less standard is that the number of excluded borrowers depends on the prevailing Entrant’s outside option.

To understand why, remember that, as in any screening model, the level
of rationing is inversely proportional to the informational rent: the higher is
the informational rent given to the Risky borrowers, the lower is the level of
rationing needed to induce self-selection of the contracts. But the Entrant’s
profit (from serving only the Risky) is lowered by the informational rent that
her customers must be given. Thus, the higher is the number of excluded
Safe borrowers, the higher is the Entrant’s profit. In other words, to induce
screening, the Incumbent must exclude a high enough number of customers
(ˆxs(D^{I})) in order to make the Entrant’s profit higher than the outside options.

The Incumbent behaves the way explained above whenever serving the Safe
market niche is her most profitable strategy. Clearly, this is not necessarily the
case. The Incumbent can, in a similar way, decide to specialize in the Risky
market niche, inducing the Entrant to specialize in the Safe one and to make
screening possible. In order to do it, she has to grant the Risky borrowers
an adequate informational rent, allowing the Entrant to ration as few Safe
borrowers as possible. The mechanism is detailed in the next lemma. Define
D^{I}_{min} := ^{Π}^{Res}_{x}E^{−}βp^{x}s^{E}^{β}. This is the minimum value of D^{I} making the Entrant

indifferent between the screening profit and the relevant outside option.^{9}
Lemma 2. If the Incumbent offers a contract(x^{I}, D^{I}) characterized by:

D^{I}_{min}< D^{I}≤Dˆ^{I}(x^{I}) :=Rr− 1

x^{I}x˜^{E}(Rr−D^{I}) (1.4)
where

˜

x^{E} := max

α

1 + (1−β)(p_{r}R_{s}−1)
β(m−1)

, (1−β)(m−1)

β(m−1) + (1−β)(m−p_{r}R_{s})

.

Then the Entrant’s optimal reaction is to offer a contract characterized by
x^{E} <min{x˜^{E},1} andD^{E} =Rs, so that screening takes place with the Incum-
bent serving the Risky borrowers and the Entrant serving the Safe ones.

Proof. See Appendix 1.6.

Also in this case, to attain screening, Risky borrowers must be given better conditions via a reduction of the repayment Dr. At the same time some of the Safe borrowers must be rationed.

An important implication of the two lemmas above is that if specialization is an equilibrium in a microfinance market, then it is an equilibrium withcredit rationing. This rationing is due to the combined effect of adverse selection and oligopolistic competition. Different than in Stiglitz and Weiss (1981), where rationing is merely a consequence of the presence of ‘bad’ types in the market, in our model the value ofxsis also determined by the best option the competi- tor has with respect to the screening strategy. In Lemma 1, the Incumbent chooses the level of rationing in order to make the screening strategy optimal for the Entrant. In Lemma 2, the Incumbent increases the information rent offered to the Risky borrowers in order to reduce rationing of the Safe ones and increase the Entrant’s profit. This an explanation for rationing in mar- kets with a limited availability of contract types and oligopolistic competition that, to our knowledge, has not been explored before.

Non-screening Strategies: When the conditions stated in Lemmas 1 and 2 are not fulfilled screening is not possible. As illustrated in Figure 1.1, there are two cases to consider.

9The thresholdD^{I}_{min}is important since, as shown in the Appendix, as long asD^{I}> Rs

the Incumbent can raise the Entrant’s profit from screening by setting a lower D^{I}. But
if D^{I} < Rs the Entrant’s profit might decrease because a lower D^{E} (necessary to have
screening) is only in part compensated by a higherx^{E}.

*D *^{I}*x *^{I}

*0* *R*_{s}^{^}*D *^{I}*(1)*

*1 *

*^**x *^{I}_{s}

*^**x *^{I}_{r}

*A*
*B*

*C*

*R**r*

*D*

*Risky*
*Screening*

*Safe*
*Screening*

*Risky or both*
*No Screening*

*Both*
*No screening*

*E*

Figure 1.1: Entrant strategies as a function of the Incumbent strategies
In the first case, the Incumbent sets a contract with D^{I}≤Rs, butx^{I} ≥xˆ^{I}_{s}
(region ˆx^{I}_{s}AD1). By choosing such a contract the Incumbent indicates that her
preferred strategy is to serve both types. The Entrant can then either undercut
the Incumbent’s price, or she can simply decide to serve the residual demand.

More precisely, the Entrant knows that by serving the residual demand she can earn:

ΠRes = max{Π^{E}_{ResR}; Π^{E}_{ResB}}. (1.5)
Alternatively she can earn:

ΠU ndct=α[β(psD^{I}−1) + (1−β)(prD^{I}−1)] (1.6)
(where x^{E} = α). The choice clearly depends on the value D^{I} set by the
Incumbent.

In the second case, the Incumbent sets a contract lying in the region RsRrECB. This is a contract that only suits the Risky borrowers but does not fulfill the condition of Lemma 2. The Entrant has two possible strategies:

(a) undercut the Incumbent’s price. (b) offer a contract with x^{E} = α and
D^{E} = Rs. In this last case she serves a fraction α of both borrowers’ type,
making a profit:

Π^{E}_{Both} =α{β(m−1) + (1−β)(p_{r}R_{s}−1)} (1.7)

and leaving the Incumbent with the residual demand on the risky borrowers.

### 1.4 The Incumbent Strategy

We have now all the elements to analyze the Incumbent’s optimal strategy. In order to better describe the special features of microfinance markets, we will consider three different behavioral assumptions: profit maximization, naive altruism and smart altruism. This will help us to understand more features of a highly heterogeneous phenomenon, and to provide some policy advice via the comparison of the effects on welfare of different conducts.

1.4.1 The Profit maximizing Incumbent (PM Model)

We start by assuming that the Incumbent MFI is profit maximizing. Despite the presence of many socially motivated institutions the biggest and more influential MFIs do claim to be able to make significant profits, and consider this ability as the result of a careful and business oriented management. This has remarkable implications: if microfinance showed to be effective in poverty reduction, then this result could be attainable in a costless or even profitable way.

Thiswin-to-win promise has generated mixed reactions. On the one hand there has been a huge (and probably naive) wave of enthusiasm by a number of NGOs that glimpse in microcredit the ultimate solution to their financial problems. On the other hand a number of researchers and practitioners showed quite some skepticism. Indeed the profitability of some MFIs seems to be quite sensible to the definition itself of profit, since in some cases unorthodox accountancy methods are used.

Anyway, the advocates of a pure profit maximizing behavior seem to be the most numerous and the most influential, so that more and more MFIs are trying to follow their advice. In order to get a better theoretical understanding of the problems involved in this debate, we now examine a model describing a scenario in which the Incumbent behaves as a profit maximizer.

LetC^{E}(C^{I}) be the Entrant’s reaction function to the Incumbent’s strategy.

The Incumbent faces this maximization problem:

max

x^{I},D^{I}Π^{I}=X^{I}(C^{I}, C^{E}(C^{I}), α)

P(C^{I}, C^{E}(C^{I}))D^{I}−1

The Incumbent, just like the Entrant, can choose whether to specialize in a particular sector or to target both types of borrowers. In the first case she needs to induce the Entrant to offer an incentive compatible contract as

showed in Lemma 1 and 2. In what follows we describe her optimal behavior for each possible case.

Incumbent serves the Safe borrowers: If the Incumbent wants to at-
tract all the Safe borrowers she needs to offer a contract satisfying the condi-
tions in Lemma 1, inducing the Entrant to target the Risky borrowers and to
offer an incentive compatible contract. When the Incumbent is profit maxi-
mizing the Entrant’s dominant outside option is to undercut the Incumbent’s
contract setting x^{E} = 1 and D^{E} =D^{I}. Thus the relevant value of ˆx_{s}(D^{I}) is
the last in Lemma 1. In fact, since ˆxs(D^{I}) is increasing inD^{I}, the Incumbent
will choose D^{I} as big as possible, taking into account the constraintD≤Rs.
This leads toD^{I} =R_{s}. As a consequence, serving the residual demand would
give a strictly smaller profit. If the constraint in Lemma 1 is not binding, then
the Incumbent just set x^{I} <1.

Under these conditions B^{I}(C^{I}, C^{E}) = β, and the Incumbent’s expected
profit is:

Π^{I}_{sr} =βxˆs(Rs)(m−1). (1.8)
Incumbent serves the Risky borrowers: If the Incumbent wants to serve
all the Risky borrowers she can either induce the Entrant to serve the Safe
ones only (and engage in a screening strategy) or she can offer a non targeted
contract.

In the first case the findings of Lemma 2 apply. ˆD^{I}(see (1.4)) is increasing
inx^{I}, so the Incumbent chooses x^{I} = 1, and D^{I} = ˆD^{I}(1). This gives her the
expected profit:

Π^{I}_{rs} = (1−β)(prDˆ^{I}−1) (1.9)
In the second case her profit is nil if the Entrant chooses the Risky sector,
too. Otherwise she earns ΠResR= (1−α)(1−β)(m−1)

Incumbent serves both types: The Incumbent knows that when she chooses this strategy, the Entrant reacts targeting either the Risky or Both borrowers. It follows that the unique Incumbent’s concern is the danger of price competition by the Entrant. This reasoning implies the following simple result:

Lemma 3. In any equilibrium with no screening in which the Incumbent serves both types, her profit is given by:

Π^{I}_{b} = ΠRes = max{ΠResR,ΠResB} (1.10)

Proof. See Appendix 1.6.

### β Π

Π^{ResR}
Π^{rs}
Π^{ResB}
Π ^{sr}

Figure 1.2: Incumbent Profit: Example 1.

In order to choose her optimal strategy, the Incumbent has then to compare equations (1.8), (1.9) and (1.10). Not surprisingly, the ranking depends on the values of the parameters. Let Θ be the set of parameters such that an equilibrium with screening prevails. More formally

Θ ={α, β, pr, ps, Rr, Rs|Π^{I}_{sr}≥max{Π^{I}_{rs},Π^{I}_{b}} ∨Π^{I}_{rs} ≥max{Π^{I}_{sr},Π^{I}_{b}}}.
We prove that Θ is always non-empty and that under some general conditions
has a strictly positive measure.

Proposition 1. The set Θ is always non-empty. Moreover it has a strictly positive measure if one of the following conditions is satisfied:

α > ^{m}^{−}_{m}^{p}_{−1}^{r}^{R}^{s} or α < ^{p}^{r}_{m}^{R}_{−1}^{s}^{−1} or α > _{2m}_{−}^{m}_{p}^{−1}

rRs−1

The first condition applies when the incumbent serves the Risky borrowers
and ΠResB ≥ΠResR. The second one applies when the Incumbent serves the
Safe borrowers and ΠResB ≥ΠResR. Finally, the last condition applies when
the Incumbent serves the Safe borrowers and Π_{ResR}≥Π_{ResB}.

The first two conditions are easier to satisfy whenprRsis big or, in other words when the level of heterogeneity of the borrowers is low. The third

### β Π

ΠResR

Πrs

ΠResB

Πsr

Figure 1.3: Incumbent Profit: Example 2.

condition, instead, is satisfied when prRs is small, so that heterogeneity is large.

Given the observations above, the third condition is the easiest to inter-
pret (and to satisfy). Indeed, when heterogeneity is large, then the condition
Π_{ResR} ≥ Π_{ResB} is easily satisfied. Moreover, this is the situation in which
the opportunity cost from serving the wrong type is the highest. So there are
clear incentives to engage in a screening strategy.

The first two situations are somewhat less intuitive. When heterogeneity is low, then the Entrant’s outside option is larger, so that it is more difficult for the Incumbent to induce screening. On the other hand, also the Incumbent outside option is larger (they are actually the same). But the Incumbent profit also increases whenprRsincreases, so that screening is possible when prRs is quite big.

The conditions above ensure that either Π^{I}_{sr} or Π^{I}_{rs} intersects Π^{I}_{B} twice, as
showed in Figure 1.2 and 1.3. Since Π^{I}_{sr} and Π^{I}_{rs} are concave, this is enough
to show that the set Θ has a strictly positive measure. The three functions
have a common intersection point in β = β^{c}. The conditions in Proposition
1 make sure that the second intersection point lies in the right region, to the
left or to the right of β^{c} depending on whether ΠResR is bigger or smaller
than ΠResB. Note that the three thresholds are well defined since they always
belong to [0,1].

This result shows that in a microfinance market the special kind of prod-

uct differentiation we described is not a singularity. This is in line with the empirical findings of Navajas et Al. (2003).

Welfare Anaysis: We can now examine the results above in order to un- derstand the consequences of competition for the profitability of MFIs and the welfare of the borrowers. As a first conclusion, competition is always better than monopoly in terms of total welfare.

Proposition 2. When two MFIs are operating in the market, the total welfare is higher than it would be under a monopolistic regime.

Proof. See Appendix 1.6

It must be stressed that this result depends mostly on the fact that, since α≤1, the presence of two MFIs ensures a larger outreach. Still, we claim that competition is not necessarily the best scenario for poor borrowers. Indeed, if we consider borrower welfare as a good proxy for poverty reduction, than the effects of increasing competition are ambiguous when one takes into account the bias given by the capacity constraint. Indeed, it is easy to show that competition can make borrowers worse off if compared to a monopoly with no capacity constraint.

Proposition 3. If the parameters are such that a monopolist with no capacity constraint would serve both types, then in equilibria with screening the Risky borrowers enjoy less rent and the Safe ones are more rationed.

Proof. See Appendix 1.6

The result is due to the fact that, in a competitive equilibrium, the MFI serving the Risky borrowers is able to extract a higher rent than a monopo- list who does not want to exclude the Safe borrowers. Clearly the reverse is true if a monopolist prefers serving the Risky borrowers only. In such a case competition can only have positive effects. This observation has important policy implications since, very often, the capacity constraint of MFIs is deter- mined by socially motivated investors or donors (like The World Bank etc.).

If their goal is to maximize borrower welfare, then there are instances in which financing only one monopolist can be better than financing two competitive MFIs.

It is also worth noticing that the Entrant is always guaranteed the profit ΠBoth. As a consequence, in all the cases in which a monopolist would target both types, the Entrant earns the same profit she would earn if she were without competition. That provides one more possible explanation for the

puzzling behavior of MFIs described by McIntosh, de Janvry and Sadoulet (2005), who report that MFIs prefer to locate where other MFI are already active despite the possible negative effect of competition.

1.4.2 The Altruistic Incumbent (AI Model)

We now turn to consider a different behavioral assumption concerning the Incumbent MFI. Microfinance has been invented for humanitarian reasons. It was thought as a possible poverty reducing tool, based on the idea that poor people have a relevant but unexplored amount of entrepreneurial skills that ought to be used: poor must be helped to help themselves.

This is probably the reason why microfinance markets are characterized by a heterogeneous population of institutions, spanning from small volun- teer based humanitarian projects to big international financial institution and banks. A critical analysis of the real motivations inducing international banks to downscale to microfinance is beyond the scope of this paper. Nonethe- less, an economic theory on microfinance cannot put aside the fact that some important players in the game may not be merely profit maximizing.

Indeed, empirical evidence shows that in many cases the very first MFIs entering, or even creating the market were not profit-maximizing institutions.

Their first, declared goal was to make their customers better off. It seems therefore appropriate to consider in our model also MFIs striving for an effi- cient way to properly serve their clients without incurring substantial capital losses.

Some of these benevolent MFIs did a pretty good job, and their success attracted the attention of other institutions, with completely different goals and often profit maximizing behavior.

In this section we model a situation in which a socially motivated Incum- bent is followed by a profit maximizing Entrant. Our goal is to understand how and if the presence of an altruistic firm influences the Entrant’s strategy, the borrower welfare and the market equilibrium.

There are different possible ways to model altruistic behavior. We consider two instances. First, we assume that the Incumbent’s altruism leads to the maximization of the sum of his clients utility, subject to a non-bankruptcy constraint (NBC). We label this behavior asNaive Altruism, since the Incum- bent takes into account only the direct effects his strategy has on his own clients. This assumption is useful to describe small project-based programs, endowed with less resources and technical knowledge. Second, we consider a different form of altruism that we label asSmart Altruism. This is the behav- ior of an MFI that takes into account also the effect her strategy has on the

Entrant’s clients. Therefore, a smart MFI maximizes the sum of the utilities of all the borrowers in the market. This second behavioral assumption fits better a market in which the Incumbent MFI is a larger institution running a well structured program.

Naive Altruism: Consider first a naive altruistic Incumbent. She solves the following problem:

max

D^{I},x^{I}X^{I}(C^{I}, C^{E}(C^{I}), α)[m−P(C^{I}, C^{E}(C^{I}))D^{I}] (1.11)
subject to:

B^{I}(C^{I}, C^{E}(C^{I}))x^{I}[P(C^{I}, C^{E}(C^{I}))D^{I}−1]≥0 N BC

The Entrant’s behavior is the same described in Section 1.3 and, as before, the altruistic Incumbent takes into account her reaction when she chooses her best strategy.

The solution of this problem is quite simple. Suppose for a moment that the Incumbent MFI has complete information about the borrower types, so that she can screen them. Whatever her preferred sector is, she sets her contract so as to leave her customers the highest possible utility while taking into account the NBC. The maximal utility she can give to her customers without going bankrupt is (1−β)(m−1) if she serves the Risky, β(m−1) if she serves the Safe, and α(m−1) if she serves Both types. By assumption α >max{β,1−β}, which implies that a perfectly informed Incumbentalways prefers to serve both types.

If the Incumbent’s information is incomplete, she can still ensure his cus-
tomers the payoffα(m−1) serving both types. This is simply done by setting
D^{I} = _{βp} ^{1}

s+(1−β)pr. It is the value that makes her NBC binding. There are no other screening issues to deal with. Moreover, the Entrant cannot under- cut the Incumbent’s offer, or she would make negative profits. On the other hand, the borrower welfare attainable serving only Risky or only Safe clients is surely smaller than (1−β)(m−1) andβ(m−1), since to make screening possible some information rent has to be given to the Risky types, and some Safe borrowers are necessarily rationed. We can then conclude that targeting Both types is a strictly dominating strategy for a Naive Altruistic Incumbent.

This simple model shows that an MFI concerned only with her customers’

welfare has no incentive whatsoever to engage in a screening strategy. Trying to differentiate her offer from that of the Entrant can only decrease her pos- itive impact on borrowers. Depending on the values of the parameters, the

Entrant’s reaction is either to serve the residual demand of the Risky types or the residual demand of Both types.

In general the benefits of such behavior for the market considered as a
whole, are not necessarily higher than the benefits the same market would
have if the Incumbent maximized her profit. This is particularly true when the
lending capacityαis relatively small. In fact, when the Incumbent serves Both
types, the Entrant can behave as a monopolist on the residual demand. This
clearly reduces the welfare of the residual clients. But more importantly, this
behavior reduces the Entrant’s profit, potentially hampering the development
of a competitive sector and reducing outreach.^{10}

In what follows we examine a slightly more sophisticated type of altruism, leading the MFI to consider the effects of her strategy on the welfare of the whole pool of borrowers. We discuss the advantages and disadvantages of such an assumption, together with the implications in terms of policy.

Smart Altruism: The second possible type of altruism we consider consists in the maximization of the total borrower welfare. As sketched above, a smart altruistic MFI is concerned with the welfare of her clientsand with the welfare of the customers served by her competitor. In other words, she takes into account the consequences her strategy has on the Entrant’s behavior and on her customers. As we will see, this different perspective can lead to different types of equilibria, in which MFIs specialize in different market niches.

A smart altruistic Incumbent faces the maximization problem:

max

D^{I},x^{I}X^{I}(C^{I}, C^{E}(C^{I}), α)[m−P(C^{I}, C^{E}(C^{I}))D^{I}]+ (1.12)
X^{E}(C^{I}, C^{E}(C^{I}), α)[m−P(C^{E}(C^{I}), C^{I})D^{E}(C^{I})]

subject to:

B^{I}(C^{I}, C^{E}(C^{I}))x^{I}[P(C^{I}, C^{E}(C^{I}))D^{I}−1]≥0 N BC

The Incumbent has again three options: serve the Safe borrowers (inducing screening), serve the Risky ones (also inducing screening), or target both

10We could speculate that this reduction has negative consequences in terms of total welfare, especially because lower profits might discourage potential investors from entering the market. But in the model we have no such things as fixed entry cost, so that no formal arguments can be given. Still we can conjecture that the presence of entry costs would only make our result non valid forsome values of the parameters, not adding any intuition. For specific values the Incumbent could blockade entry, and the analysis would be trivial. For some others, she would accommodate, and our results would apply