Assume that there are two groups of borrowers in the economy: i = {g, b). The groups are of the same size. To start a project, borrowers need to take a loan of size 1. The return to the borrower's project depends on the borrower's type: it is R'+z, with probability 1/2 and R'-r, otherwise, where I < 1. So, for instance, in good states type g project earns (R' + xg) x 1. The lender cannot observe the borrower's type, so all borrowers get charged the interest rate r (so the gross interest rate is 1+r). Suppose, there is a maximum interest rate ri that g type borrowers would agree to pay. Show under what conditions the lender would choose not to charge a higher interest rate than r and motivate your answer. Do those conditions always hold? Interpret them.
Assume that there are two groups of borrowers in the economy: i = {g, b). The groups are of the same size. To start a project, borrowers need to take a loan of size 1. The return to the borrower's project depends on the borrower's type: it is R'+z, with probability 1/2 and R'-r, otherwise, where I < 1. So, for instance, in good states type g project earns (R' + xg) x 1. The lender cannot observe the borrower's type, so all borrowers get charged the interest rate r (so the gross interest rate is 1+r). Suppose, there is a maximum interest rate ri that g type borrowers would agree to pay. Show under what conditions the lender would choose not to charge a higher interest rate than r and motivate your answer. Do those conditions always hold? Interpret them.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:Assume that there are two groups of borrowers in the economy: i € {g, b}. The groups are of the same size.
To start a project, borrowers need to take a loan of size 1. The return to the borrower's project depends
on the borrower's type: it is R'+ri with probability 1/2 and R' - r; otherwise, where rg < I. So, for
instance, in good states type g project earns (R'+r,) x 1. The lender cannot observe the borrower's type,
so all borrowers get charged the interest rate ri (so the gross interest rate is 1+ ri). Suppose, there is a
maximum interest rate ri that g type borrowers would agree to pay. Show under what conditions the lender
would choose not to charge a higher interest rate than rị and motivate your answer. Do those conditions
always hold? Interpret them.
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