
Problem assignments from: The Economics of Microfinance, Armendariz and Morduch, 2nd edition
 Chapter 1  Probs: 11, 12, 15, 17, 110.
 Chapter 2  Prob: 27.
 Chapter 4  Prob: 48.
 Chapter 5  Prob. 56 and 57.
Listening/Reading Assignments
Please read/watch/hear the following three items:
 Topic: Financial Lives of Poor Households
Podcast Portfolios of the Poor (62 min)
 Topic: Profit and Performance: Competing Models of Microfinance
Webcast, “Profiting from the Poor? A Discussion on Microfinance IPOs” Debate between Yunus and Akula (75 min, debate starts 10 min in)
 Topic: Institutional Innovations in Microfinance
Interview, Director of KGFS
Read any one of these two:
 Topic: Measuring the Impact of Microfinance
Planet Money PodcastPoor Economics (27 minutes)
 Guardian PodcastDoes Microfinance Help Poor People Escape Poverty (29 minutes)
And any one of these:
 Topic: Crisis in Indian MF 
6 MF crises the sector does not want to remember
 BBC PodcastIndia’s microcredit meltdown (25 min)
 BBC PodcastThe Bankers and the Bottom Billion (40 min)
Write brief (at least 200 words) descriptions of what you hear/read/see.
This will be a total of five reports. Email them to me by March 1.
Posttrip reports:
Write three reports in all. You can use your blogs to write these reports. These reports will be of two types and will be, primarily, about microfinance, although the general report can touch on other issues, as well:
 one, a general report on the trip; this report will relate the
lessons learned from the visit to the issues brought up and discussed
during the Fall term. The length of this report may be from 2 to
4 pages.
 two, specialized reports on any two visits, about one to two pages. . You can choose from among the following
 the IFMR oneday workshop,
 Auroville and the visits to Svaram (the musical instruments company) and Wellpaper.
 Pondicherry  the Sarvam presentation on microfinance and village development, as well as Sharanam, the building project.
 Thanjavur  the presentations at the KGFS office, as well as the site visits to the branch in Mathur village plus the visits to a) the women's selfhelp group or b) the visit to the petty shop started by the woman whose deceased husband was a client of KGFS.
 Kancheepuram  the presentations at the HandinHand office, as well as the visits to the microfinance clients, the weaving operation, the bakery, and the beauty parlor.
 Mahabalipuram  the visit to GLIM, management education, Karmayoga, and the children's visit.
Here’s what I would like you to keep in mind when writing your reports:
 What did you see in India that confirmed what you had read in the text book or in other assigned materials or in other readings related to microfinance?
What did you see that contradicted what you had read?
How did your ideas change as a result of these contradictory/confirming observations?
 Give examples of what you saw that related to what you had been taught in class/read in the book etc.
 How did the trip complement or reiterate class readings/discussions..
 Would you go back to India? If so, why? Would you travel elsewhere, as a result of your India trip? Again, the focus should be on microfinance.
 A lot of the course had to do with why microfinance is not just simply making small loans; we talked about externalities, agency problems, and how microfinance structures try to ameliorate these issues. What did you see/hear during the trip that speaks to these issues?
You can put general thoughts on poverty, development etc in the paper, but put it in the general report; most of the report should be about microfinance.
Solutions:
Problem 1:1
The issue seems to be why microfinance has spread in poorer countries, but not in richer countries, even though poor households in relatively richer countries also lack access to financial services at reasonable prices. One possibility is that the costs of serving these poor households is greater in richer countries because providing such services could be labor intensive, which is more expensive in richer countries. Microfinance solutions don't have to have group cohesion, but group cohesion and the ability for borrowers to be able to influence their fellow borrowers definitely enhances group lending contracts. Such cohesion seems to be less common, sociologically speaking.
Problem 1:2
Lack of good financial and legal institutions might raise the probability of not getting paid back in a country like Bolivia or Kenya; information might also be difficult to get on potential borrowers. In addition, these risks might be correlated across loans  as, for example, if there were political unrest. The risks are not just project risks, which is typically the case in a welltodo country. Also, in firstworld countries, the risks across loans are less correlated, allowing for more diversification.
Problem 1:5
The principle of diminishing returns to capital assumes that the amount of other inputs is kept constant. It may very well be that poorer individuals are also less educated, less financial savvy and less able to seek out innovative solutions to their problems. Hence, since these inputs are not being kept constant, a larger project in a more welltodo environment may have higher returns than a small project in a less welltodo environment.
Problem 1:7
Suppose the required investment in I. Then the expected payoff in Russia is 0.5(200)  I. In Belgium, the payoff would be 110I. Clearly, investing in Belgium is better, since 100I < 110I.
Problem 1:10
 The social payoff from project A is 1200(0.8)1000 < 0, while the social payoff from project B is 11001000 = $100 > 0. Hence project B is preferable socially.
 The payoff from borrower A to the bank is (12001000)(0.8)(0.5) = $80; the borrower also gets an expected payoff of $80. The payoff from borrower B is (11001000)(0.1) = $10; the borrower's payoff is $90. Hence the manager will prefer to finance A, rather than B, since he's making more from B than from A. He ignores the social cost of $1000 for both projects. The point is that if the bank manager and the borrowers ignore the social cost, project A yields $160, while project A only yields $100. Hence the borrower for project A should be able to outbid the project B entrepreneur for loans.
 If the government does not give incentives to the bank manager to consider social costs, then the bank manager could make the wrong decision. In other situations, using profit as a gauge of bank efficiency works, but not in this case.
Problem 2:7
 It is socially efficient for both types to access loans. Since the social cost of the loan is $1.45 per dollar of loan, we need 0.9(230)145 > 52, and 0.5(420)145>55, both of which are true.
 If the bank can observe types, then it would charge the first type 0.9R = 1.45 or R=1.6111. At this interest rate, the entrepreneur would accept the loan because 0.9(230161.11) > 52. The second type would be charged an interest rate of 0.5R = 1.45 or R = 2.9. At this rate, the entrepreneur would accept the loan because 0.5(420290) > 55.
 If the bank couldn't observe the types, then it would be repaid (0.9(0.6) + 0.4(0.5)) or 74% of the time. Hence breakeven R would have to be 0.74R = 1.45 or R = 1.9595.
At this interest rate, type 2 will accept the loan because
0.5(420195.95) > 55, but type 1 wouldn't because 0.9(230195.95) < 52. Hence this setup would not be an equilibrium one. In equilibrium, the bank would charge R = 2.9 and only type 2 entrepreneurs would accept the loan.
 If banks cannot distinguish between project types, then the market might collapse and socially desirable projects might not be undertaken.
Problem 48
 Suppose the bank believes that investors will exert effort. Then it will charge an interest rate of R=1.5, since all projects are riskless. Remember, the gross cost of the loan is 1.5, so if the bank wants to cover costs, it has to charge at least R=1.5. At this interest rate, exerting effort yields (3001508040) or $30, while shirking yields 0.75(300150)80 = 32.5; so the borrower will shirk. So this is not an equilibrium.
If the bank believes that investors will not exert effort, then it will charge an interest rate of 1.5/0.75 or 2.0. At this rate, though, taking the loan yields 0.75(300200)80 or $5, so there will be no takers. Hence the bank will simply not lend any money in this economy.
 Suppose there is monitoring (which induces returnmaximizing effort) and joint liability lending, as well as limited liability for entrepreneurs. In this case, the bank will charge R=1.5, once again. Now, however, for each investor, the payoff from expending effort is (3001508040) = $30 less monitoring costs of $20 for a net of $10. (Since both parties will expend effort, there is no need for bailing out one's partner.)
However, if the parties decide to shirk (but monitor), then the payoff for each will be (300150)8020 or $50 with probability (0.75)^{2}. It will be 0.5{(3002(150)))8020 or 100 with probability 2(0.75)(0.25) (i.e. if whether his project succeeds or his partner's, all of the payoffs from the project have to be turned over to the bank. It will be 08020 = $100 if both parties are unlucky, which happens with probability (0.25)^{2}. The expected payoff, then, is 50((0.75)^{2})100(1(0.75)^{2}) = $15.625. Hence both parties will end up finding it optimal not to shirk. Consequently, this is a viable equilibrium solution.
This situation is also desirable from a social point of view because each entrepreneur generates a net profit of $10,whereas if only individual loans can be made, no loans will be made at all and there will be no gain to society.
This assumes that the bank wants to break even. However, if the bank wants to charge the highest possible interest rate, consistent with forcing the borrowers to not shirk, we have the condition (300R804020) > (300R8020) (0.75)^{2} + (0.5{0}8020)2(0.75)(0.25) + (8020)(0.25)^{2}. In other words, R < 208.57. So the max R will be 208.57.
It is not clear, however, what the role of monitoring is, because we can see from the analysis that even with no monitoring, there would be optimal expenditure of effort.
However, if we now ignore the ability of the borrowers to shirk when there's monitoring and just assume that there will be no shirking (as the problem states), we have another issue to take into account. The parties can only pay as much as they make. That is, if there is no competition for the bank, it can extract all the surplus. In this case, what will the interest rate be? Since each borrower will make 300R804020, we see that the interest rate cannot be more than R = 160.
 In this case, since the groups are selfselected, it makes sense to assume that both parties will think similarly, and hence we can assume that borrowers monitor each other simultaneously. The other possibility  that borrowers will not monitor each other  can be ruled out because as we have seen, in this case, there will be no loans made.
Problem 56
a. The interest rate charged to the hightype borrowers will be R =1.1. The bank needs to recover $20 on a $200 loan, and according to the information in the problem, there are no borrowing costs for the bank.
For the others, we have to see what the repayment rates will be. Since the borrowers know their types, there will be assortative matching. All type 2s will pair with other type 2s, while all type 3s will pair with type 3s. All the type 2 pairs will repay all the time. The type 3 groups will pay 1(0.25)^{2} or 93.75% proportion of the time, assuming that the interest rate is low enough for the one lucky borrower to pay for the unlucky borrower. If so, then the expected return to the bank will (0.9375)R per borrower from the type 3 groups and R per borrower from the type 2 groups. Hence the total return will be 0.5(1.9375R). This has to be enough to recoup $130; solving 130 = 0.5(1.9375R), we get $134.19. That is, R = 1.3419, which in fact is sufficient for the type 3 groups to repay 93.75% of the time, as assumed.
b. In this part, we're assuming (for some reason), that there are mixed pairs. The high type borrowers will pay 100% of the time because they will always have enough money. The group with two type 3 borrowers will also pay in full. However, the mixed groups will not be able to pay fully, since the type 2 borrower only gets a return of $200, which is not sufficient to make the required payment of 200(1.3419) or $268.38. If the bank had taken this sort of irrational behavior by borrowers, then it probably would have charged a higher interest rate.
Problem 57
a. If the borrower repays at time 1, he pays R to the bank, but he gets y; he also gets a further loan of 1, which has to be invested immediately (so it's a net wash), plus dy, which is the discounted value from the second period payoff. If he doesn't repay, then he gets y, which he keeps. So he would repay if yR+dy > y, i.e. if dy>R. Of course, the bank needs to cover its costs, so the lower limit is K, i.e. the range is K<R<dy.
b. If I=100, y=200, K=150, d=0.9, then we have the requirement 0.9(2) > R or R<1.8 for borrowing to take place. Since the cost of funds is effectively 1.5 plus 1.5 from the second loan, there would not be any borrowing and lending.
If y = $360, then the restriction would be 3.6(0.9) > R and R can be even larger  as large as 3.24; so in this case, there can be borrowing because the bank can recoup the cost of both loans.

