JOURNA OF ECONOIC DEVEOPENT 59 Volume 35, Numer 1, arch 2010 ON TE PROVIION OF ICRO OAN - ICROFINANCE INTITUTION AND TRADITIONA BANK RUBANA AJABEEN * Truman tate Unversty Ths aer emloys a utlty maxmzng model to answer two questons: () what are the cost-related factors that determne the suly of a loan y tradtonal anks and mcrofnance nsttutons (FIs)?; and () why s the suly of mcro loan zero under a ank s maxmzaton rolem whle t s ostve under the maxmzaton rolem of an FI? We fnd that costs assocated wth default, nformaton asymmetry and lalty determne the suly of a loan y a fnancal nsttuton. Furthermore, we show that under certan condtons (that we derve) a ank may make a loss f t rovdes mcro loan. As a result, t does not suly mcro loan. Keywords: Bank, Grou endng, crofnance Insttutons, Jont alty, cro oans JE classfcaton: D24, G21 1. INTRODUCTION It has now een estalshed n the lterature that fnancal develoment enhances economc growth (e.g., studes y Alfaro et al. (2004) and evne (2005)). owever, most of the less develoed countres (DCs) have thn fnancal system. For examle, domestc credt rovded y the ankng sector n the less develoed countres such as Chad and Tanzana s as low as 17 ercent of GDP. Ths comares wth 173 ercent for the develoed countres, such as the U.. and Jaan (World Bank (2008)). Furthermore, n most DCs, the oor do not have access to credt from formal fnancal nsttutons. There are at least three reasons why anks n DCs do not rovde credt to these domestc resdents. Frst, t s dffcult for anks to evaluate the credt worthness of entrereneurs - n most DCs, there are no agences that track credt hstory. econd, most of the eole lve on susstence and do not have any assets to serve as collateral. * I gratefully acknowledge valuale comments from an anonymous referee and from Elzaeth Asedu.
60 RUBANA AJABEEN Thrd, the sze of loan may e so small - t may not cover the cost ncurred y the ank n rocessng the loan. In resonse to ths credt rolem a new tye of fnancal nsttuton, known as mcrofnance nsttuton (FI) has emerged worldwde. FIs rovde credt to entrereneurs who do not have access to formal ank credt. The loans are small and known as mcro-credt. The World Bank stulates that there are aout 7,000 FIs oeratng worldwde. For examle, over the last two decades the numer of FIs n Bangladesh has ncreased from less than 50 to nearly 1,000, an ncrease of aout 1,900% (CDF (2005)). Currently, FIs n Bangladesh serve aout 11 mllon households. The 2006 Noel Peace Prze was awarded to uhammad Yunus for oneerng the dea of mcrocredt and settng u the Grameen Bank, a mcrofnance nsttuton of Bangladesh. The mortance of mcrofnance s also evdent n the fact that The Unted Natons declared the year 2005 as the Year of crocredt. FIs engage n oth ndvdual lendng and grou lendng n rovdng loans. owever, the mostly used method s grou lendng; orrowers form grous to otan loans. 1 The dea s that wthn grous there s no nformaton asymmetry - each memer of a grou has nformaton aout the erformance of the roject undertaken y the other memers of the grou as well as the credt worthness of the other memers. Furthermore, wthn a grou all memers are jontly lale for each loan and defaultng on a loan can lead to non-refnancng n the future. As a result there s an ncentve for memers to montor each other. Ths reduces the costs of the FIs assocated wth lendng, such as gatherng nformaton, montorng rojects or audtng orrowers. In addton the jont lalty feature ovates the need for collateral, ecause each memer serves as collateral for other memers. The growng numer of FIs n DCs and ther success has romted the rofessonals, racttoners and researchers to concentrate on the ssue of commercalzaton of mcrofnance. 2 Countres n atn Amerca and Afrca have develoed legal structure and secfc regulatons for sustanale growth of mcrofnance ndustry. any FIs have started concentratng on usng market-ased rncles n ther oeratons whle mantanng fnancal self-suffcency. For examle, FIs n Inda and Camoda rely mostly on deosts and commercally rced sources for fundng. Exerence of FIs, lke, AA n Bangladesh dects that t s ossle to attan hgh effcency (or low cost) whle servng oor clents. Gven ths scenaro t s mortant to conduct a rgorous economc analyss that comares the two tyes of nsttutons: tradtonal anks and FIs. Ths aer rovdes an analyss of the cost structure of FIs and tradtonal commercal anks. There s a vast lterature on FIs (see Brau and Woller (2004), for a lterature revew). ost of the aers on FIs, (e.g., Ghatak (1999), affont (2003)) 1 For detals aout grou formaton see Ghatak (1999). 2 Ths necessarly mles the alcaton of market-ased rncles to mcrofnance.
ON TE PROVIION OF ICRO OAN 61 attrute the lack of lendng to oor entrereneurs - to a lack of collateral and/or nformaton asymmetry. We however note that anks may e reluctant to lend f the cost of rocessng a loan s very hgh. Ths argument s artcularly relevant for the oor. The reason s that tycally, the amount of loan requests from oor households tend to e small and the costs of rocessng the loan (whch ncludes nformaton gatherng, aer work, etc.) tend to e hgh. Indeed, the name, mcro-credt s a clear ndcaton that the loan sze s ertnent to any analyss of FIs. Ths aer constructs a utlty maxmzng model to answer two questons. Frst, what are the cost-related factors that determne the suly of a loan y tradtonal anks and FIs? econd, why s the suly of mcro loan zero under a ank s maxmzaton rolem whle t s ostve under the maxmzaton rolem of an FI? We fnd that costs assocated wth default, nformaton asymmetry and lalty determne the suly of a loan y a fnancal nsttuton. Furthermore, we show that under certan condtons (that we derve) a ank may make a loss f t rovdes mcro loan. As a result, t does not suly mcro loan. The aer s organzed as follows. ecton 2 derves the models that cature the ehavor of commercal anks and FIs and ecton 3 rovdes a summary of our fndngs and concluson. 2. TE ODE There are two general aroaches to modelng tradtonal anks: structural and non-structural. The nonstructural aroach focuses on acheved erformance and s measured y a varety of fnancal ratos, such as return-on-asset, return-on-equty, or the rato of fxed costs to total costs, and the structural aroach reles on the economcs of cost mnmzaton or roft maxmzaton (ughes and ester, 2008). We follow the structural aroach, however, we devate from the lterature n ths area (e.g., studes y ughes et al., 2000; and ughes et al., 2001) y forgong the agency rolem (ank manager s ehavor) and focusng on ank s ortfolo choce of asset allocaton (rovson of varous loans). One mortant contruton of ths aer s that we extend the exstng lterature y alyng the structural aroach n analyzng the ehavor of a new tye of fnancal nsttuton: FIs. Recall that one of our goals s to determne the otmzed ortfolo choce of asset allocatons of FI and tradtonal anks. For the model we assume that oth fnancal nsttutons have a CE utlty functon. One advantage of the CE functon s that t enhances the modelng rocess y aggregatng the dfferent knds of assets (or loans) nto one equaton. We however note that generally, the CE utlty functon s used to model the ehavor of fnancal nsttutons n a comutale general equlrum (CGE) model, and s rarely emloyed n a artal equlrum analyss of fnancal nsttutons. 3 3 For examle, see Decaluwe and Nsengyumva (1994) and Naastead (2002). Unlke these studes our
62 RUBANA AJABEEN Thus, one of the contrutons of ths aer s that t adds to the scant lterature that emloys CE utlty functon to study fnancal nsttutons n a artal equlrum settng. Furthermore, to the est of our knowledge, t s the frst study to utlze a CE utlty functon to analyze FIs. As onted out earler, the nalty of oor entrereneurs to otan loans from the formal ankng system may e artly due to the costs related to rovdng loans to these orrowers. Therefore, n modelng the otmzaton rolems of commercal anks and FIs, we wll focus on ther cost structure. Two asects of the cost structure are vtal for our analyss. Frst, the transacton cost of rocessng nformaton aout the orrowers, for examle, the cost of audtng a orrower. In ths case, we follow the costly state verfcaton set u gven y Townsend (1979). 4 The second asect ertans to the management cost of rovdng the fnancal servces. Ths s reresented y a ank s technology. We assume that fnancal nsttutons ehave lke any other otmzng agent. 5 Usually, loans suled y a fnancal nsttuton are consdered as ts assets whle deosts ket y the savers n a fnancal nsttuton are consdered as ts laltes. We assume a comettve fnancal market where the ank and the FI earn zero rofts. 6 Gven ths set u, n ecton 2.1 we construct a model to analyze the ehavor of tradtonal anks and n ecton 2.2 we derve the model of FIs. 2.1. A Commercal Bank We assume that, the loans rovded y a commercal ank can e dvded nto two tyes of loans: short-term loan and long term loan. hort term loans are for the urose of workng catal and can e ether large () or mcro () n sze. ong-term loans () are for the urose of nvestment exendtures, consumton, house uldng, etc. For smlcty we assume that, the commercal ank otans ts resources only from deosts of households. It then uses these funds to rovde three dfferent loans. aer has ntroduced roalty of default and the cost of audtng a defaulted orrower n the otmzaton rolem of a fnancal nsttuton. 4 Accordng to Townsend s (1979) costly state verfcaton, a orrower wll e audted when he/she fals to meet contractual olgatons. 5 Our models of the fnancal nsttutons evolve around the deas gven y Bernanke et al. (1999), Ghatak (1999), Ghatak and Gunnane (1999) and ughes and ester (1994). 6 The zero rofts of FIs are assumed to ncororate the sustanalty ssue, namely, fnancal self-suffcency of FIs. oreover, n countres lke, Bangladesh and exco FIs oerate n comettve framework. Daley-arrs, drector of crocredt ummt Camagn, asserts that, y studyng the case of Bangladesh, the world s most saturated mcrofnance market, t would e ossle to redct what could haen n other cases f FIs are constructed wth the same care as n Bangladesh (Daley-arrs, Polln and ontgomery (2007)).
ON TE PROVIION OF ICRO OAN 63 A orrower s characterzed y the roalty of default. It s assumed, that assocated wth loan of tye a orrower has a roalty of default (0,1) where =,,. If the orrower makes reayment, ank gets ( 1 ) r A where, r s the nterest rate on loan and A s the amount of loan. But, f the orrower defaults, the ank audts hs/her roject and lqudates the roject. We assume that the amount lqudated s equal to β A, where, β s the roorton of defaulted loan recovered y the commercal ank. At the same tme, the ank ears a cost of audtng μ β A, where, μ s the cost coeffcent of audtng defaulted loan. Therefore, the varale cost of rovdng loan s μ β A and the ank receves a return of ( ) r A β A + 1. A ank also ears a fxed cost of oeraton and mantenance, FC and costs of lalty, namely, nterest ( r D ) ad on deosts ( D ). We assume that, the ank maxmzes a constant elastcty of susttuton (CE) tye of utlty functon suject to two constrants. The frst constrant, gven n Equaton (1), s the udget constrant or the zero roft functon. Proft of the commercal ank s the returns from defaulted and non-defaulted loans mnus cost of audtng defaulted loans, nterest ayments on deosts and fxed costs. β + ( 1 ) r + β + ( 1 ) r + β + ( 1 ) μ β μ β μ β r D D FC = 0. r (1) The second constrant, Equaton (2), reresents the cost of rocessng a small sze loan. Ths ncludes cost of nformaton gatherng, aer work, etc. The admnstratve cost of a loan, lke, ook-keeng cost, s an mortant art of the cost structure of a ank. When makng a decson aout a mcro loan a ank tres to cover the cost of rocessng the loan y the earnng from that loan. The cost of oeratng the loan should not exceed a threshold level. 7 In our model ths level s reresented y K. Ths mles: μ β K. (2) Gven Equatons (1) and (2) the ank s ojectve s to choose the comnaton of three loans that would maxmze ts utlty: 7 As there s a maxmum, usually, set y the central ank, on the nterest rate that could e charged and to maxmze the net nterest margn, every ank has a mnmum loan level elow whch t would never go. For examle, tradtonal anks would not lend out a small loan of $500 as t would not cover the cost. For such a mcro sze loan, ether the orrower s suggested y commercal anks to use ones credt card or the orrower has to fnd a non-nsttutonal source, lke, relatves, frends and moneylenders.
64 RUBANA AJABEEN ax U 1 σ σ σ σ [ δ ( ) + δ ( ) + δ ( ) ] =, (3) where, δ s the CE dstruton arameters n ank s ortfolo ( =, and ) and σ s the susttuton arameter n ank s utlty functon. The rolem of the ank can e rewrtten as: σ σ σ [ δ ( ) + δ ( ) + δ ( ) ] ax F = μ β + μ β + λ + ρ [ K μ β ], 1 σ ( 1 ) r β ( 1 ) r β ( 1 ) + μ β + rd D + FC + β (4) r where, λ s the margnal value of ank s roft, and ρ margnal eneft from relaxng the constrant on the varale cost of mcro loans or margnal cost from tghtenng that constrant. The frst constrant s a ndng constrant and λ s therefore, ostve. As the second constrant s an nequalty constrant, therefore, ρ could e ether zero or ostve. We now turn our attenton to the mcro loan. Note that under the ank s rolem, the suly of mcro loan,, wll e zero f the frst order condton wth resect to s negatve: 8 [ μ β β ( 1 ) r ] ρ [ μ β ] 0, F : λ < or, λ ( C R ) ρ ( C ) < 0, (5) where, R = β + ( 1 ) r s the margnal revenue earned y the ank from mcro loan, C = μ β s the margnal cost orn y the ank on mcro loan and π = R C s the margnal roft of the ank on mcro loan. Two scenaros can arse from Equaton (5). cenaro 1. If margnal value of the ank s roft s ostve and the margnal eneft of relaxng the constrant on the varale cost of mcro loans s also ostve then the margnal revenue from mcro loan could e ether greater than or equal to or less than the margnal cost of mcro loan. Proof. ee Aendx A. 8 The Kuhn-Tucker condtons for the rolem of the ank are F < 0, = 0 and F = 0.
ON TE PROVIION OF ICRO OAN 65 cenaro 1 mles that there s a osslty that the margnal cost of mcro loan could exceed the margnal eneft of mcro loan. Therefore, accordng to ths cost-eneft analyss the osslty of negatve margnal roft rohts the ank from sulyng mcro loan. As a utlty otmzer, t s economcally ratonal for a ank not to suly a roduct, namely, mcro loan, as there s a osslty of makng a loss y dong so. cenaro 2. If margnal value of the ank s roft s ostve and the margnal eneft of relaxng the constrant on the varale cost of mcro loans s zero then the margnal revenue from mcro loan would e greater than the margnal cost of rovdng that loan. Proof. ee Aendx A. Postve margnal roft otaned from mcro loan does not justfy why commercal anks do not suly ths loan. Therefore, we gnore ths osslty. oluton to the ank s rolem yelds (see Aendx A for detals): [ r D FC ] = 1 D +, (6) T = 0, (7) ψ ψ = B X, (8) T r where, = [ β + ( 1 ) μ β] + [ β + ( 1 ) μ β ] [ β + ( 1 ) r μ β ] δ 1 B =, X = and, ψ = [ β + ( 1 ) r μ β ] δ 1 + σ susttuton n ank s utlty functon. r B ψ X ψ s the elastcty of Our results may e summarzed as follows: Result 1. The suly of ank loans deends on the nterest rates charged on dfferent loans ( r ), cost coeffcent of audtng defaulted loans ( μ ), orrower s default roalty ( ), roorton of defaulted loans recovered ( β ), fxed cost ( FC ) and lalty cost ( r D D ). Result 2. It s not always otmal for a ank, usng ts tradtonal framework, to rovde a certan tye of loan, n ths case the mcro loan. 9, 9 In recent tme erod some tradtonal anks are actve n the mcrocredt market. owever, they usually
66 RUBANA AJABEEN 2.2. A crofnance Insttuton Behavor of a FI can e exlaned under a smlar setu as that of a commercal ank. We assume that the loans suled y a FI can e dvded nto two tyes of loans: mcro loan () for the urose of workng catal and small housng loan (). 10 mlar to the commercal ank, for smlcty we assume that, the FI otans ts funds through deosts of households only. 11 We assume that, FIs use grou-lendng method to rovde loans. For smlcty, we assume a grou sze of two and that the grou memers are alke. 12 owever, two memers receve two searate ut dentcal loans. Grou memers are characterzed y ther roalty of default. For examle, n case of loan, each memer n a grou has a roalty of default of j (0,1) where =, and j = 1,2. Whenever one memer of the grou defaults, the non-defaultng artner has to make a ayment of c where 0 < c < 1. It s a fracton of A, the amount of loan. If the memer decdes to reay the loan then he/she has to ay the followng two amounts: ayment for own loan, ( 1 1 ) r A where, r s the nterest rate charged on loan and ayment for jont lalty c 2( 1 1) A f hs/her artner defaults. When oth memers default, the FI audts the roject and lqudates the roject. We assume that the amount lqudated s equal to 1 2 β A, where, β s the roorton of defaulted loan recovered y the FI. Note that under ths scenaro, the frequency of audtng a loan (or a orrower) decreases relatve to the ank s rolem. 13 As a consequence, the overall cost of audtng s less under the rolem of FI. Nevertheless, the FI may stll ncur some audtng cost, whch s μ 1 2β A where, μ s the cost coeffcent of audtng defaulted loan. Therefore, the varale cost of rovdng loan to one memer of the grou s μ 1 2β A and the FI gets a return of 1 2β A + ( 1 1) r A + c 2( 1 1) A. mlar to the ank, the FI also ncurs some general costs such as fxed costs of have searate sectons or ranches that oerate n ths market. These ranches have smlar structure as the FIs. 10 Though not all, ut many of the FIs rovde loans, other than mcro loan, for dfferent uroses to ther customers. mall housng loan s used as a reresentatve of these dfferent urosed loans. 11 any of the FIs have started concentratng on deosts y savers, equtes sold, loans from other fnancal nsttutons as ther sources of funds. Accordng to crobankng Bulletn (crofnance Informaton Exchange (2007)), even though some funds are susdzed, y the end of 2006 almost 70 ercent of the fundng of a FI came through commercal orrowng and deosts. 12 Ths small sze of the grou would cature the man essence of the model. arger grou sze would manly, make comutatons comlex rather than changng any results. 13 The reason s that under the FI audtng occurs only when all the memers of a grou defaults. In contrast, the ank audts each orrower that defaults.
ON TE PROVIION OF ICRO OAN 67 oeraton and mantenance, deosts ( D ). FC and lalty costs, namely, nterest ( r D ) ad on The FI maxmzes a CE utlty functon suject to ts udget constrant. The zero roft functon s the udget constrant of the FI. Proft of the FI s the returns from defaulted and non-defaulted loans lus jont lalty ayment mnus cost of audtng defaulted orrowers, nterest ayments on deosts and fxed costs. It s gven n Equaton (9). 1 + c 2 2β + ( 1 1) r + c 2( 1 1) + 1 2β + ( 1 1) r ( 1 ) μ β μ β r D FC = 0. 1 1 2 1 2 D (9) Unlke the tradtonal commercal ank, the FI does not face any addtonal constrant on the varale cost of mcro loan. ecfcally, one of the man functons of FIs s the rovson of mcro loans. Rather than one large loan FIs rovde a numer of small loans, n ths case two mcro loans. Gven Equaton (9) the FI chooses the comnaton of the two loans that would maxmze ts utlty: 14 1 σ [ ] σ σ ax U δ + ( 1 δ ) =, (10) where, δ s the share of mcro loan n the ortfolo of the FI and σ s the susttuton arameter n the CE utlty functon of the FI. oluton to the FI s rolem yelds (see Aendx B for detals): [ r D FC ] = 1 D +, (11) T ψ ψ = J V, (12) where, T = [ 1 2β + ( 1 1) r + c 2( 1 1) μ 1 2β ] ψ ψ [ β + ( 1 ) r + c ( 1 ) μ β ] J V, + 1 2 1 2 1 1 2 14 Usually, outreach, reachng the maxmum numer of orrowers, s regarded as one of the goals of FIs. We tred to cature that asect through loans nstead of clents.
68 RUBANA AJABEEN [ 1 2β + ( 1 1) r + c 2( 1 1) μ 1 2β ] [ β + ( 1 ) r + c ( 1 ) μ β ] J =, ψ 1 1 = 1 + σ 2 1 2 1 1 2 s the elastcty of susttuton n FI s utlty functon. ( 1 δ ) V = and, δ Our results may e summarzed as follows: Result 3. The suly of loans y a FI deends on the nterest rates charged on dfferent loans ( r ), cost coeffcent of audtng defaulted loans ( μ ), orrower s own default roalty ( 1 ), default roalty of other memer of the same grou ( 2 ), roorton of defaulted loan recovered ( β ), jont lalty ayment ( c ), fxed cost FC ) and lalty cost ( r D D ). ( Result 4. Unlke a tradtonal ank t s otmal for a FI to rovde mcro loan to ts orrowers. As a utlty otmzer, t s economcally ratonal for a FI to suly mcro loan, as t s ossle to make ostve margnal roft y dong so. 2.3. Dscusson of Results Our results show that suly of each tye of loan s determned y the returns from the loan as well as the costs of rovdng the loan. Note that Results 1 and 3 hghlght the dfference etween tradtonal anks and FIs. ecfcally, FIs dffer from commercal anks wth resect to the cost of default (default roalty of other memer of the grou and jont lalty ayment) and the cost of nformaton (frequency of audtng the defaulted loan and cost of rocessng mcro loan). All other costs, namely, fxed costs, nterest ayment on deosts, nterest charged on dfferent loans and orrower s own roalty of default exst for oth commercal anks and FIs. Thus our results ndcate that the cost structure of a fnancal nsttuton lays an mortant role n the suly of the varous tyes of loans. Our results also suggest that one reason why tradtonal anks do not rovde loans to mcro entrereneurs s that they want to mnmze rsk and cost. A natural queston that arses s ths: why don't tradtonal anks adot jont lalty lendng to mtgate the cost and rsk assocated wth mcro lendng? 15 A lausle exlanaton s that among other factors the organzatonal structure of a ank deends on the envronment under whch t oerates, namely, roerty rghts, legal set u, charterng rules and government 15 ometmes when collateral s nsuffcent to avod rsk or costs, anks use co-sgnng rncle whch s dfferent from the jont lalty lendng. Under the jont lalty lendng all the grou memers are jontly lale for all loans whle under co-sgner method only the co-sgner s lale for the loan alcant ut the loan alcant s not lale for the co-sgner (Gangoadhyay and ensnk (2009)).
ON TE PROVIION OF ICRO OAN 69 regulatons (ughes and ester (2008)). 16 Adoton of jont lalty lendng y the tradtonal anks requres some change n the exstng envronment. Intatng a change of the aove-mentoned factors s hghly costly and outsde the scoe of a tradtonal ank. Evdently, anks do not attemt to serve the mcro loan orrowers (through jont lalty lendng) as the relatve contrutons such a movement wll make to roft are smaller than f they serve the large loan orrowers. 3. CONCUION crofnance nsttutons (FIs) have ecome ncreasngly mortant n DCs. An mortant dfference etween FIs and commercal anks s that FIs rovde mcro credt, ut anks, under the tradtonal framework, generally do not. Ths aer constructs a utlty maxmzaton model to analyze the cost structure of FIs and tradtonal commercal anks. It also derves the condtons under whch a ank wll not ssue mcro loans. Frst, we fnd that the costs assocated wth default, nformaton asymmetry and lalty determne the suly of a loan y a fnancal nsttuton. econd, f the margnal value of the ank s roft s ostve and the margnal eneft of relaxng the constrant on the varale cost of mcro loans s also ostve then there s a osslty that the margnal revenue from mcro loan could e less than the margnal cost of mcro loan. As a consequence no mcro loan s ssued. Aendx A. odel of a Commercal Bank The rolem of the ank can e rewrtten as: ax F = σ σ σ [ δ ( ) + δ ( ) + δ ( ) ] μ β + μ β + λ + ρ [ K μ β ]. + μ 1 σ β + rd D + FC β r ( 1 ) r β ( 1 ) r β ( 1 ) (A.1) Our am s to fnd out the condtons, under whch a commercal ank sules ostve amounts of and and zero amount of. ettng the frst order condtons 16 Dscussons on these ssues are eyond the scoe of ths aer.
70 RUBANA AJABEEN wth resect to and equal to zero, we have: ( 1+ 1 )[ ( ) ( ) σ 1+ σ Z δ A ] = λ [ β + ( 1 ) r μ β ] or, U λ ( R C ) = λ π =, (A.2) σ σ σ where, Z = δ ( ) + δ ( ) + δ ( ), ( ) ( ) + ( ) ( 1+ σ ) U = Z σ δ A margnal utlty derved y the ank from loan tye, R = + ( 1 ) r, [ ] 1 1 s the β s the margnal revenue earned y the ank from loan tye, C = μ β s the margnal cost orn y the ank on loan tye and π = R C s the margnal roft of the ank on loan tye ( = and ). We assume that, U, R, C and π are ostve. Gven ostve margnal utlty and a ostve λ, Eequaton (A.2) mles that, the ank would choose to suly ostve amount of (or ) f the margnal revenue from (or ) were greater than the margnal cost of rovdng (or ). Now for the suly of mcro loan to e zero, frst order condton wth resect to needs to e negatve. The frst order condton would then change to the followng form: F : [ μ β β ( 1 ) r ] ρ [ μ β ] < 0 or, ( ) ( ) 0 λ, λ C R ρ C <. (A.3) cenaro 1. If margnal value of the ank s roft s ostve and the margnal eneft of relaxng the constrant on the varale cost of mcro loans s also ostve then the margnal revenue from mcro loan could e ether greater than or equal to or less than the margnal cost of mcro loan. Proof of cenaro 1. If oth the agrange multlers λ and ρ, and margnal cost and margnal revenue of mcro loan are ostve then the second term of Equaton (A.3), ( ) C ρ wll e ostve. The frst term ( C R ) ostve, zero or negatve deendng on whether than R. [ λ C R ρ C Now, Equaton (A.3), ( ) ( )] λ can e ether C s greater than, equal to or less wll e negatve, f ρ ( C )] s ostve and, If C < R so that [ λ ( C R )] s negatve or, If C = R so that [ λ ( C R )] s zero or, If C > R so that λ ( C R )] s ostve. [ [
ON TE PROVIION OF ICRO OAN 71 The thrd oton mles that, there s a osslty that the margnal cost of mcro loan could exceed the margnal eneft of mcro loan. cenaro 2. If margnal value of the ank s roft s ostve and margnal eneft of relaxng the constrant on the varale cost of mcro loans s zero then the margnal revenue from mcro loan would e greater than the margnal cost of rovdng that loan. Proof of cenaro 2. If ρ = 0 then the second term n Equaton (A.3), ( C ) ρ ecomes zero. Wth > 0 negatve s f R > C. B. odel of a FI λ the only way ( C R ) λ can e The rolem of the FI can e rewrtten as: ax F = + λ σ σ [ δ + (1 δ ) ] μ 1 β + μ 1 σ β + r + FC 1 2β ( 1 1) r c 2( 1 1) 1 2β ( ) ( ) 1 r c 1 1 2 2 1 1 2 D D (B.1) As the FI faces a ndng constrant, λ s ostve. To fnd out the condtons under whch the FI rovdes ostve amount of and we set the frst order condtons wth resect to and equal to zero. Z 1 1 + σ [ ( ) ( 1+ σ ) δ A ] = λ [ β + ( 1 ) r + c ( 1 ) μ β ] 1 2 or, ( ) 1 U = λ R C = λ π, (B.2) σ where, Z = δ + 1 δ ) U = Z σ δ A s the margnal utlty derved y the FI from loan tye, R = 1 2β + ( 1 1) r + c s the margnal revenue earned y the FI from loan tye, C ( ) 2 1 1 μ 1 2 σ (, ( ) + 1 1 ( ) ( 1+ σ ) 2 1 1 2 [ ] = β s the margnal cost orn y the FI on loan tye and π = R C s the margnal roft of the FI on loan tye ( = and ). We, 17 17 In case of, δ s relaced y 1 δ ) (.
72 RUBANA AJABEEN assume that, U, R, C and π are ostve. Therefore, gven the ostve margnal utlty and a ostve λ Equaton (B.2) mles that, the FI would suly ostve amount of loan (or ), f margnal revenue from (or ) were greater than margnal cost of rovdng (or ). REFERENCE Alfaro,., A. Chanda,. Kaleml-Ozcan, and. ayek (2004), FDI and Economc Growth: The Role of ocal Fnancal arkets, Journal of Internatonal Economcs, 64, 89-112. Bernanke, B.,. Gertler, and. Glchrst (1999), The Fnancal Accelerator n a Quanttatve Busness Cycle Framework, n Taylor, T.B., and. Woodford, eds., andook of acroeconomcs 1, North-olland, Amsterdam. Brau, J.C., and G.. Woller (2004), crofnance Insttutons: A Comrehensve Revew of the Exstng terature and an Outlne for Future Research, Journal of Entrereneural Fnance and Busness Ventures, 9, 1-26. Credt and Develoment Forum (2005), CDF tatstcs: crofnance Data Bank of FI-NGOs, Credt and Develoment Forum, Bangladesh. Daley-arrs,., R. Polln, and F. ontgomery (2007), Deate on crocredt, Foregn Polcy n Focus, Washngton D.C. Decaluwe, B., and F. Nsengyumva (1994), Polcy Imact under Credt Ratonng: A Real and Fnancal CGE of Rwanda, Journal of Afrcan Economes, 3, 262-308. Gangoadhyay,., and R. ensnk (2009), Co-gned oans versus Jont alty endng n an Adverse electon odel, Research Paer, 09/05, Centre for Analytcal Fnance, Indan chool of Busness, Inda. Ghatak,. (1999), Grou endng, ocal Informaton and Peer electon, Journal of Develoment Economcs, 60, 27-50. Ghatak,., and T.W. Gunnane (1999), The Economcs of endng wth Jont alty: Theory and Practce, Journal of Develoment Economcs, 60, 195-228. ughes, J.P., W. ang,.j. ester, and C.-G. oon (2000), Recoverng Rsky Technologes Usng the Almost Ideal Demand ystem: An Alcaton to U.. Bankng, Journal of Fnancal ervces Research, 18, 5-27. ughes, J.P., and.j. ester (2008), Effcency n Bankng: Theory, Practce and Evdence, Workng Paer, 08/01, Federal Reserve Bank of Phladelha, Pennsylvana. (1994), Bank anagers Ojectves, Workng Paer, 94/08, Federal Reserve Bank of Phladelha, Pennsylvana. ughes, J.P.,.J. ester, and C.-G. oon (2001), Are cale Economes n Bankng
ON TE PROVIION OF ICRO OAN 73 Elusve or Illusve? Evdence Otaned y Incororatng Catal tructure and Rsk-Takng nto odels of Bank Producton, Journal of Bankng and Fnance, 25, 2169-2208. affont, J.J. (2003), Colluson and Grou endng wth Adverse electon, Journal of Develoment Economcs, 70, 329-348. evne, R. (2005), Fnance and Growth: Theory and Evdence, n Aghon, P., and.n. Durlauf, eds., andook of Economc Growth 1, Elsever, North-olland. crofnance Informaton Exchange, Inc. (2007), crobankng Bulletn, 15, Washngton D.C. Naastead, C.W.. (2002), Effectve uly Falures and tructural Adjustment: A Real-Fnancal odel wth Reference to Inda, Camrdge Journal of Economcs, 26, 637-657. Townsend, R.. (1979), Otmal Contracts and Comettve arkets wth Costly tate Verfcaton, Journal of Economc Theory, 21, 265-293. The World Bank (2008), World Develoment Indcators, The World Bank, Washngton D.C. alng Address: 100 E Normal treet, Deartment of Economcs, Truman tate Unversty, Krksvlle, O 63501, UA. E-mal: mruana@truman.edu. Receved Arl 1, 2008, Revsed etemer 21, 2009, Acceted Novemer 21, 2009.