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 projectVOL. 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