FIGURE 8.2

The interest rate and expected profit

FIGURE 8.2

The interest rate and expected profit

return given by the loan rate less the cost of raising deposits on the money market. This analysis is set out more formally in Box 8.1.

Each of these two components has an attached probability. For very small loans the probability of default is virtually zero. As the loan size increases after a certain point the probability of default rises so that the profit on the loan starts to decrease such that the loan offer curve bends backwards. This is demonstrated in Figure 8.3.

In the range A, loans are small and risk-free. In this range L < //(1 + S), the project yields the minimum outcome discounted by the interest cost of funds. In the range B, the probability of default rises with loan size. The maximum loan size is given by L*. When the demand for loans is D2, the equilibrium rate of interest is r*2 and loan supply is the region B with no excess demand. When the demand for loans is given by Di the rate of interest is ri and the loan offered is L*, which is less than the demand at the rate of interest ri. At Di the size of the loan demanded would always exceed the maximum offered, so that credit rationing occurs.

Even if the demand curve lies between Di and D2 and does intersect the loan offer curve but at a higher interest rate than ri, the loan offered will still be L*. The Hodgman Model is able to explain the possibility of type i rationing but is unable to explain type 2 rationing. There is a group demand for credit but at a group interest rate.

Models of limited loan rate differentiation were developed in an attempt to extend the Hodgman analysis, but ended up raising more questions than answers. In Jaffee and Modigliani (i969) a monopolistic bank is assumed to face rigidities in

BOX 8.1 | ||

The Hodgman Model |

A risk-neutral bank is assumed to make a one-period loan to a firm. The firm's investment project provides outcome {x}, which has a minimum {/} and maximum {u} value;so / < x < u. The probability distribution function of x is described by f (x). The contracted repayment is (1 + r)L, where L is the loan and r is the rate of interest. The bank obtains funds in the deposit market at a cost S. Expected profit is given by the following function:

If default occurs (x < (1 + r)L) the bank receives x. The first term is the income the bank receives if x < (1 + r)L; that is, if there is a default. The second term represents bank income if the loan is repaid. The first two terms represent the weighted average of expected revenue from the loan. The weights are probabilistic outcomes. The third term is the bank's cost of funds.

the setting of differential loan rates. The question that arises in such models is: When is it optimal for a bank to set a rate of interest such that the demand exceeds supply, as in the case of D? The problem is that by assuming constraints to setting interest rates it should not be surprising that a nonmarket clearing outcome for the credit market could arise. The more interesting issue is the reasoning and origin for the constraints.

The origin of the practice of limited loan rate differentiation is to do with custom and practice, goodwill, legal constraints (such as usury laws), and

FIGURE 8.3 | ||

Type 1 rationing |

institutional rigidities. Interest rates are kept at below market rates as a preferential price to blue-chip customers, emphasizing the customerâ€”loan relationship. Such explanations recognize the fundamental nature of the loan market as being made up of heterogeneous customers. The lender is a price setter and the borrower is a price taker. Different borrowers have different quality characteristics. If the lender is a perfectly discriminating monopolist, it would lend according to the borrower's quality characteristics; hence, there would be no rationing. But the underpinnings of this approach remain ad hoc and not founded in theory.

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