《货币经济学》课程文献阅读：Credit Ration with Imperfect Information（Stiglitz and Weiss,1981）

American Economic association Credit Rationing in Markets with Imperfect Information Author(s): Joseph E Stiglitz and Andrew Weiss Source: The American Economic Review, Vol. 71, No. 3(Jun, 1981), pp. 393-410 Published by: American Economic Association StableUrl:http://www.jstor.org/stable/1802787 Accessed:14/07/200910:26 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of se, available at http://www.jstororg/page/info/about/policies/terms.jspJstOr'sTermsandConditionsofUseprovidesinpartthatunless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work, Publisher contact information may be obtained at http://www.jstor.org/action/showpublisher?publishercode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmIssion JStOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the cholarly community to preserve their work and the materials they rely upon, and to build a common research platform that information about JSTOR, please contact suppo American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic revie

American Economic Association Credit Rationing in Markets with Imperfect Information Author(s): Joseph E. Stiglitz and Andrew Weiss Source: The American Economic Review, Vol. 71, No. 3 (Jun., 1981), pp. 393-410 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1802787 Accessed: 14/07/2009 10:26 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org

Credit rationing in Markets with Imperfect Information By JOSEPH E STIGLITZ AND ANDREW WEISS* Why is credit rationed? Perhaps the most they receive on the loan, and the riskiness of basic tenet of economics is that market equi- the loan. However, the interest rate a bank if demand should exceed suang demand; that charges may itself affect the riskiness of the librium entails supply equal rise, decreasing demand and/or increasing borrowers(the adverse selection effect); or 2) supply until demand and supply are equated affecting the actions of borrowers( the incen at the new equilibrium price. So if prices do tive effect). Both effects derive directly from their job, rationing should not exist. How- the residual imperfect information which ver, credit rationing and unemployment do present in loan markets after banks have in fact exist. They seem to imply an excess evaluated loan applications. When the price demand for loanable funds or an excess (interest rate)affects the nature of the trans supply of workers. action, it may not also clear the market One method of "explaining "these condi- The adverse selection aspect of interest tions associates them with short-or long-term rates is a consequence of different borrowers isequilibrium. In the short term they are having different probabilities of repaying viewed as temporary disequilibrium phenom- their loan. The expected return to the bank a; that is, the economy has incurred an obviously depends on the probability of re- xogenous shock, and for reasons not fully payment, so the bank would like to be able explained, there is some stickiness in the to identify borrowers who are more likely to prices of labor or capital (wages and interest repay. It is difficult to identify"good bor rates)so that there is a transitional period rowers, "and to do so requires the bank to during which rationing of jobs or credit use a variety of screening devices. The inter- urs. On the other hand, long-term un- est rate which an individual is willing to pay employment( above some“ natural rate”) may act as one such screening device: the ose credit rationing is explained by governmen- who are willing to pay high interest rates tal constraints such as usury laws or mini- may, on average, be worse risks; they are mum wage legislation willing to borrow at high interest rates be The object of this paper is to show that cause they perceive their probability of re- in equilibrium a loan market may be char- paying the loan to be low. As the interest acterized by credit rationing. Banks making rate rises, the average"riskiness"of those loans are concerned about the interest rate who borrow increases, possibly lowering the bank's profits and Bell Laboratories, Inc, respectively. We Similarly, as the interest rate and other Bell Telephone Laboratories, Inc, and Princeton ms of the contract che the behavior of to thank Bruce Greenwald, Henry Landau, the borrower is likely to change. For in- Rob Porter, and Andy Postlewaite for fruitful cor stance, raising the interest rate decreases the Science Foundation is gratefully acknowledged. An return on projects which succeed. We will version of this paper was presented at the spring how that higher interest rates induce firms 977 meetings of the Mathematics in the Social Science to undertake projects with lower probabili ties of success but higher payoffs whe Indeed, even if markets were not competitive one cessful hopolistic bank to raise In a world with perfect and costless infor the interest rate it charges on loans to the point where mation, the bank would stipulate precisely excess demand for loans was eliminated all the actions which the borrower could

Credit Rationing in Markets with Imperfect Information By JOSEPH E. STIGLITZ AND ANDREW WEISS* Why is credit rationed? Perhaps the most basic tenet of economics is that market equi￾librium entails supply equalling demand; that if demand should exceed supply, prices will rise, decreasing demand and/or increasing supply until demand and supply are equated at the new equilibrium price. So if prices do their job, rationing should not exist. How￾ever, credit rationing and unemployment do in fact exist. They seem to imply an excess demand for loanable funds or an excess supply of workers. One method of "explaining" these condi￾tions associates them with short- or long-term disequilibrium. In the short term they are viewed as temporary disequilibrium phenom￾ena; that is, the economy has incurred an exogenous shock, and for reasons not fully explained, there is some stickiness in the prices of labor or capital (wages and interest rates) so that there is a transitional period during which rationing of jobs or credit oc￾curs. On the other hand, long-term un￾employment (above some "natural rate") or credit rationing is explained by governmen￾tal constraints such as usury laws or mini￾mum wage legislation.' The object of this paper is to show that in equilibrium a loan market may be char￾acterized by credit rationing. Banks making loans are concerned about the interest rate they receive on the loan, and the riskiness of the loan. However, the interest rate a bank charges may itself affect the riskiness of the pool of loans by either: 1) sorting potential borrowers (the adverse selection effect); or 2) affecting the actions of borrowers (the incen￾tive effect). Both effects derive directly from the residual imperfect information which is present in loan markets after banks have evaluated loan applications. When the price (interest rate) affects the nature of the trans￾action, it may not also clear the market. The adverse selection aspect of interest rates is a consequence of different borrowers having different probabilities of repaying their loan. The expected return to the bank obviously depends on the probability of re￾payment, so the bank would like to be able to identify borrowers who are more likely to repay. It is difficult to identify "good bor￾rowers," and to do so requires the bank to use a variety of screening devices. The inter￾est rate which an individual is willing to pay may act as one such screening device: those who are willing to pay high interest rates may, on average, be worse risks; they are willing to borrow at high interest rates be￾cause they perceive their probability of re￾paying the loan to be low. As the interest rate rises, the average "riskiness" of those who borrow increases, possibly lowering the bank's profits. Similarly, as the interest rate and other terms of the contract change, the behavior of the borrower is likely to change. For in￾stance, raising the interest rate decreases the return on projects which succeed. We will show that higher interest rates induce firms to undertake projects with lower probabili￾ties of success but higher payoffs when suc￾cessful. In a world with perfect and costless infor￾mation, the bank would stipulate precisely all the actions which the borrower could *Bell Telephone Laboratories, Inc. and Princeton University, and Bell Laboratories, Inc., respectively. We would like to thank Bruce Greenwald, Henry Landau, Rob Porter, and Andy Postlewaite for fruitful comments and suggestions. Financial support from the National Science Foundation is gratefully acknowledged. An earlier version of this paper was presented at the spring 1977 meetings of the Mathematics in the Social Sciences Board in Squam Lake, New Hampshire. 'Indeed, even if markets were not competitive one would not expect to find rationing; profit maximization would, for instance, lead a monopolistic bank to raise the interest rate it charges on loans to the point where excess demand for loans was eliminated. 393

THEAMERICAN ECONOMIC REVIEW JUNE 1981 no competitive forces leading supply to equal ￥Pz2 demand, and credit is rationed But the interest rate is not the only term of the contract which is important. The amount of the loan and the amount of collateral or quity the bank demands of loan applicants, will also affect both the behavior of bor rowers and the distribution of borrowers in Section Ill, we show that increasing the col- INTEREST RATE lateral requirements of lenders(beyond some point)may decrease the returns to the bank, JRE L THERE EXISTS AN INTEREST RATE WI by either decreasing the average degree of XIMIZES THE EXPECTED RETURN TO THE B/ risk aversion of the pool of borrowers; or in a multiperiod model inducing individual in- vestors to undertake riskier projects Consequently, it may not be profitable to raise the interest rate or collateral require undertake (which might affect the return to ments when a bank has an excess demand the loan). However, the bank is not able to for credit; instead, banks deny loans to bor directly control all the actions of the bor- rowers who are observationally indi rower; therefore, it will formulate the terms tinguishable from those who receive loans of the loan contract in a manner designed to It is not our argument that credit rationing induce the borrower to take actions which will always characterize capital markets, but re in the interest of the bank as well rather that it may occur under not implausi- attract low-risk borrowers ble assumptions concerning borrower and For both these reasons, the expected re- lender behavior turn by the bank may increase less rapidly This paper thus provides the first theoret than the interest rate; and, beyond a point, ical justification of true credit rationing. Pre- may actually decrease, as depicted in Figure vious studies have sought to explain why The interest rate at which the expected each individual faces an upward sloping in- return to the bank is maximized we refer to terest rate schedule. The explanations offered as the "bank-optimal"rate, F* are (a) the probability of default for any Both the demand for loans and the supply particular borrower increases as the amount of funds are functions of the interest rate borrowed increases(see Stiglitz 1970, 1972 (the latter being determined by the expected Marshall Freimer and Myron Gordon; return at P). Clearly, it is conceivable that at Dwight Jaffee; George Stigler), or(b) the P* the demand for funds exceeds the supply mix of borrowers changes adversely (see of funds. Traditional analysis would argue Jaffee and Thomas Russell). In these circum- that, in the presence of an excess demand for stances we would not expect loans of differ loans, unsatisfied borrowers would offer to ent size to pay the same interest rate, any pay a higher interest rate to the bank, bid more than we would expect two borrowers, ding up the interest rate until demand equals one of whom has a reputation for prudence supply. But although supply does not equal and the other a reputation as a bad credit demand at F, it is the equilibrium interest risk, to be able to borrow at the same interest rate! The bank would not lend to an individ- rate ual who offered to pay more than f*. In the We reserve the term credit rationing for bank's judgment, such a loan is likely to be a circumstances in which either (a) among loal worse risk than the average loan at interest applicants who appear to be identical some rate F*, and the expected return to a loan an interest rate above f is actually lower our attention was than the expected return to the loans the drawn to W. Keeton's book In chapter 3 he develops bank is presently making. Hence, there are incentive argument for credit rationing

394 THE AMERICAN ECONOMIC REVIEW JUNE 1981 z m 1Z w I- / 0 a- 2 @ - w w w r INTEREST RATE FIGURE 1. THERE EXISTS AN INTEREST RATE WHICH MAXIMIZES THE EXPECTED RETURN TO THE BANK undertake (which might affect the return to the loan). However, the bank is not able to directly control all the actions of the bor￾rower; therefore, it will formulate the terms of the loan contract in a manner designed to induce the borrower to take actions which are in the interest of the bank, as well as to attract low-risk borrowers. For both these reasons, the expected re￾turn by the bank may increase less rapidly than the interest rate; and, beyond a point, may actually decrease, as depicted in Figure 1. The interest rate at which the expected return to the bank is maximized, we refer to as the "bank-optimal" rate, Pr. Both the demand for loans and the supply of funds are functions of the interest rate (the latter being determined by the expected return at r*). Clearly, it is conceivable that at r the demand for funds exceeds the supply of funds. Traditional analysis would argue that, in the presence of an excess demand for loans, unsatisfied borrowers would offer to pay a higher interest rate to the bank, bid￾ding up the interest rate until demand equals supply. But although supply does not equal demand at r*, it is the equilibrium interest rate! The bank would not lend to an individ￾ual who offered to pay more than r*. In the bank's judgment, such a loan is likely to be a worse risk than the average loan at interest rate P*, and the expected return to a loan at an interest rate above r* is actually lower than the expected return to the loans the bank is presently making. Hence, there are no competitive forces leading supply to equal demand, and credit is rationed. But the interest rate is not the only term of the contract which is important. The amount of the loan, and the amount of collateral or equity the bank demands of loan applicants, will also affect both the behavior of bor￾rowers and the distribution of borrowers. In Section III, we show that increasing the col￾lateral requirements of lenders (beyond some point) may decrease the returns to the bank, by either decreasing the average degree of risk aversion of the pool of borrowers; or in a multiperiod model inducing individual in￾vestors to undertake riskier projects. Consequently, it may not be profitable to raise the interest rate or collateral require￾ments when a bank has an excess demand for credit; instead, banks deny loans to bor￾rowers who are observationally indis￾tinguishable from those who receive loans.2 It is not our argument that credit rationing will always characterize capital markets, but rather that it may occur under not implausi￾ble assumptions concerning borrower and lender behavior. This paper thus provides the first theoret￾ical justification of true credit rationing. Pre￾vious studies have sought to explain why each individual faces an upward sloping in￾terest rate schedule. The explanations offered are (a) the probability of default for any particular borrower increases as the amount borrowed increases (see Stiglitz 1970, 1972; Marshall Freimer and Myron Gordon; Dwight Jaffee; George Stigler), or (b) the mix of borrowers changes adversely (see Jaffee and Thomas Russell). In these circum￾stances we would not expect loans of differ￾ent size to pay the same interest rate, any more than we would expect two borrowers, one of whom has a reputation for prudence and the other a reputation as a bad credit risk, to be able to borrow at the same interest rate. We reserve the term credit rationing for circumstances in which either (a) among loan applicants who appear to be identical some 2After this paper was completed, our attention was drawn to W. Keeton's book. In chapter 3 he develops an incentive argument for credit rationing

VOL. 7I NO. 3 STIGLITZ AND WEISS: CREDIT RATIONING receive a loan and others do not, and the of projects; for each project 0 there is a rejected applicants would not receive a loan probability distribution of(gross)returns R even if they offered to pay a higher interest We assume for the moment that this distri- rate;or(b) there are identifiable groups of bution cannot be altered by the borrower individuals in the population who, with a Different firms have different probability given supply of credit, are unable to obtain distributions of returns. We initially assume loans at any interest rate, even though with a that the bank is able to distinguish projects larger supply of credit, they would. 3 with different mean returns so we will at In our construction of an equilibrium first confine ourselves to the decision prob- model with credit rationing, we describe a lem of a bank facing projects having the market equilibrium in which there are man same mean return however. the bank can- banks and many potential borrowers. Both not ascertain the riskiness of a project. For borrowers and banks seek to maximize prof- simplicity, we write the distribution of re- its, the former through their choice of a turns*as F(R, 0)and the density function as project, the latter through the interest rate f(R, 0), and we assume that greater 0 corre- they charge borrowers and the collateral they sponds to greater risk in the sense of mean require of borrowers(the interest rate re- preserving spreads(see Rothschild-Stiglitz) ceived by depositors is determined by the i.e., for 8,>82,if zero-profit condition). Obviously, we are not discussing a"price-taking"equilibrium. our (1)Rf(R, 1)dR equilibrium notion is competitive in tha R(R, 02)dR banks compete; one means by which they compete is by their choice of a price(interest then for y>0 rate)which maximizes their profits. The reader should notice that in the model pre (2)F(R, )dr> F(R,02)dR the demand for loanable funds equals the supply of loanable funds. However, these are If the individual borrows the amount B, and not, in general, equilibrium interest rates. If, the interst rate is f, then we say the individ at those interest rates, banks could increase ual defaults on his loan if the return R plus their profits by lowering the interest rate the collateral C is insufficient to pay back charged borrowers, they would do so. he promised amount, i. e, if Although these results are presented in the context of credit markets, we show in Section ( 3) C+R≤B(1+P) V that they are applicable to a wide class of principal-agent problems (including those describing the landlord-tenant or employer These are subjective probability distributions; the employee relationship) perceptions on the part of the bank may differ from I. Interest Rate as a Screening device Michael Rothschild and Stiglitz show that condi- tions (1)and(2)imply that project 2 has a greater arance than project 1, although the converse is not In this section we focus on the role of true. That is, the mean preserving spread criterion for interest rates as screening devices for dis- measuring risk is stronger than the increasing varianc tinguishing between good and bad risks. We criterion. They also show that(1)and(2)can be in assume that the bank has identified a group terpreted equally well as: given two projects with equal every risk averter pre I to pro definition. a firm There is another form of rationing which is might be said to be in default if R<B(I+A). Nothing subject of our 1980 paper: banks make the provision however, that if the firm defaults, the bank has first credit in later periods contingent on performance in claim on R+C. The analysis may easily be generalized earlier period; banks may then refuse to lend even when to include bankruptcy costs. However, to simplify the hese later period projects stochastically dominate earlier analysis, we usually shall these projects which are financed this section we assume that the project is the sole project

VOL. 71 NO. 3 STIGLITZ AND WEISS: CREDIT RATIONING 395 receive a loan and others do not, and the rejected applicants would not receive a loan even if they offered to pay a higher interest rate; or (b) there are identifiable groups of individuals in the population who, with a given supply of credit, are unable to obtain loans at any interest rate, even though with a larger supply of credit, they would.3 In our construction of an equilibrium model with credit rationing, we describe a market equilibrium in which there are many banks and many potential borrowers. Both borrowers and banks seek to maximize prof￾its, the former through their choice of a project, the latter through the interest rate they charge borrowers and the collateral they require of borrowers (the interest rate re￾ceived by depositors is determined by the zero-profit condition). Obviously, we are not discussing a "price-taking" equilibrium. Our equilibrium notion is competitive in that banks compete; one means by which they compete is by their choice of a price (interest rate) which maximizes their profits. The reader should notice that in the model pre￾sented below there are interest rates at which the demand for loanable funds equals the supply of loanable funds. However, these are not, in general, equilibrium interest rates. If, at those interest rates, banks could increase their profits by lowering the interest rate charged borrowers, they would do so. Although these results are presented in the context of credit markets, we show in Section V that they are applicable to a wide class of principal-agent problems (including those describing the landlord-tenant or employer￾employee relationship). I. Interest Rate as a Screening Device In this section we focus on the role of interest rates as screening devices for dis￾tinguishing between good and bad risks. We assume that the bank has identified a group of projects; for each project 6 there is a probability distribution of (gross) returns R. We assume for the moment that this distri￾bution cannot be altered by the borrower. Different firms have different probability distributions of returns. We initially assume that- the bank is able to distinguish projects with different mean returns, so we will at first confine ourselves to the decision prob￾lem of a bank facing projects having the same mean return. However, the bank can￾not ascertain the riskiness of a project. For simplicity, we write the distribution of re￾turns4 as F(R, 0) and the density function as f(R, 0), and we assume that greater 6 corre￾sponds to greater risk in the sense of mean preserving spreads5 (see Rothschild-Stiglitz), i.e., for , >2,Jif 00 0 (1) fRf(R, 01) dR= Rf(R, 2) dR then for y O, (2) j F(R,01)dR> jF(R,02)dR If the individual borrows the amount B, and the interst rate is r, then we say the individ￾ual defaults on his loan if the return R plus the collateral C is insufficient to pay back the promised amount,6 i.e., if (3) C+R<B(I +P) 3There is another form of rationing which is the subject of our 1980 paper: banks make the provision of credit in later periods contingent on performance in earlier period; banks may then refuse to lend even when these later period projects stochastically dominate earlier projects which are financed. 4These are subjective probability distributions; the perceptions on the part of the bank may differ from those of the firm. 5Michael Rothschild and Stiglitz show that condi￾tions (I) and (2) imply that project 2 has a greater variance than project 1, although the converse is not true. That is, the mean preserving spread criterion for measuring risk is stronger than the increasing variance criterion. They also show that (I) and (2) can be in￾terpreted equally well as: given two projects with equal means, every risk averter prefers project I to project 2. 6This is not the only possible definition. A firm might be said to be in default if R < B(1 + P). Nothing critical depends on the precise definition. We assume, however, that if the firm defaults, the bank has first claim on R+ C. The analysis may easily be generalized to include bankruptcy costs. However, to simplify the analysis, we usually shall ignore these costs. Throughout this section we assume that the project is the sole project

THEAMERICAN ECONOMIC REVIEW JUNE /98I Thus the net return to the borrower (R, r) an be written as (4a)T(R, A)=max(R-(1+P)B;-c) The return to the bank can be written as (4b)P(R, )=min(R+C; B(1+r)) that is, the borrower must pay back either FIGURE 2a. FIRM PROFITS ARE A CONVEX FUNCTION OF THE RETI N THE PROJECT the promised amount or the maximum he can pay back(R+C) For simplicity, we shall assume that the borrower has a given amount of equity(which he cannot increase), that borrowers and lenders are risk neutral, that the supply of loanable funds available to a bank is unaf fected by the interest rate it charges bor owers, that the cost of the project is fixed, and unless the individual can borrow the difference between his equity and the cost of the project, the project will not be under FIGURE 2b. THE RETURN TO THE BANK IS A CONCAVE taken, that is, projects are not divisible. For FUNCTION OF THE RETURN ON THE PROJEC notational simplicity, we assume the amount borrowed for each project is identical,so that the distribution functions describing the The value of 6 for which expected profits number of loan applications are identical to are zero satisfies those describing the monetary value of loan (5)I(f,6)≡ would make the amount borrowed by each individual a function of the terms of the max[R-(P+1)B;-q]dF(R,6)=0 contract; the quality mix could change not only as a result of a change in the mix of applicants, but also because of a change in interest rates could cause the returns to the the relative size of applications of different bank to decrease with increasing interest rates roups.) hinged on the conjecture that as the interest We shall now prove that the interest rate rate increased e mix of applicants became acts as a screening device; more precisely we worse; or THEOREM 2: As the interest rate increases THEOREM 1: For a given interest rate the critical value of 8, below which individuals there is a critical value 6 such that a firm do not apply for loar ns. Increases borrows from the bank if and only if0>0 This follows immediately upon differenti This follows immediately upon observing ating(5) that profits are a convex function of R, as in Figure 2a. Hence expected profits increase with risk dF(R, 0) (6) 1+P)B-C aI/06 0 undertaken by the firm (individual) and that there is limited liability. The equilibrium extent of liability is derived in Section Ill For each 6, expected profits are decreased

396 THE A MERICAN ECONOMIC REVIEW JUNE 1981 Thus the net return to the borrower 7T(R, r) can be written as (4a) 7(R, r) =max(R-(1 +r)B; -C) The return to the bank can be written as (4b) p(R,fr)=min(R+C; B(1+r)) that is, the borrower must pay back either the promised amount or the maximum he can pay back (R+ C). For simplicity, we shall assume that the borrower has a given amount of equity (which he cannot increase), that borrowers and lenders are risk neutral, that the supply of loanable funds available to a bank is unaf￾fected by the interest rate it charges bor￾rowers, that the cost of the project is fixed, and unless the individual can borrow the difference between his equity and the cost of the project, the project will not be under￾taken, that is, projects are not divisible. For notational simplicity, we assume the amount borrowed for each project is identical, so that the distribution functions describing the number of loan applications are identical to those describing the monetary value of loan applications. (In a more general model, we would make the amount borrowed by each individual a function of the terms of the contract; the quality mix could change not only as a result of a change in the mix of applicants, but also because of a change in the relative size of applications of different groups.) We shall now prove that the interest rate acts as a screening device; more precisely we establish THEOREM 1: For a given interest rate r, there is a critical value 0 such that a firm borrows from the bank if and only if 0>0. This follows immediately upon observing that profits are a convex function of R, as in Figure 2a. Hence expected profits increase with risk. (1+r)B-C / --~R -C FIGURE 2a. FIRM PROFITS ARE A CONVEX FIJNCTION OF THE RETURN ON THE PROJECT C R (1 + r) B -C FIGURE 2b. THE RETURN TO THE BANK IS A CONCAVE FUNCTION OF THE RETURN ON THE PROJECT The value of 0 for which expected profits are zero satisfies (5) r(IA) E f max[R-(r+ 1)B; -C] dF(R, ) 0 Our argument that the adverse selection of interest rates could cause the returns to the bank to decrease with increasing interest rates hinged on the conjecture that as the interest rate increased, the mix of applicants became worse; or THEOREM 2: As the interest rate increases, the critical value of 0, below which individuals do not apply for loans, increases. This follows immediately upon differenti￾ating (5): BJ dF(R,O) (6) do I1 +rP)B- C >0 dr ari/ao For each 0, expected profits are decreased; undertaken by the firm (individual) and that there is limited liability. The equilibrium extent of liability is derived in Section III