A bank faces a pool of high and low risk borrowers with measure one in two successive periods. In each period, each borrower wishes to borrow 1 from the bank. A low-risk borrower's project returns G = 2 with probability pg = 0.8 and high- risk borrower's project yields B = 3 with probability p = 0.2 in each period. If a project is unsuccessful, it yields zero. The bank knows that the proportion of low-risk borrowers is y = 0.5. However, the bank is unable to distinguish between low and high-risk borrowers, i.e. it doesn't have an appropriate screening technology. Consider a bank which operates as a monopoly and wants to attract both types of borrowers in the first period.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
=
A bank faces a pool of high and low risk borrowers with measure one in two successive periods. In each period, each
borrower wishes to borrow 1 from the bank. A low-risk borrower's project returns G = 2 with probability pg 0.8 and high-
risk borrower's project yields B : 3 with probability pb = 0.2 in each period. If a project is unsuccessful, it yields zero. The
bank knows that the proportion of low-risk borrowers is y 0.5. However, the bank is unable to distinguish between low
and high-risk borrowers, i.e. it doesn't have an appropriate screening technology.
=
Question 1
Consider a bank which operates as a monopoly and wants to attract both types of borrowers in the first period.
What's the repayment R(¹) that the bank will charge in the first period? Compute the bank's first period profit
π(1)
i.
ii.
Calculate the posterior probabilities of a borrower being low risk given that the project was successful and also
when the project failed after the first period (i.e. Pr(G|S), Pr(G|F), respectively).
iii.
How much will the bank charge to successful and failed borrowers in the second period (R3), R)? Calculate
the bank's second period profit (²). What's the total profit across the two periods ((1) +ñ π(²))?
Transcribed Image Text:= A bank faces a pool of high and low risk borrowers with measure one in two successive periods. In each period, each borrower wishes to borrow 1 from the bank. A low-risk borrower's project returns G = 2 with probability pg 0.8 and high- risk borrower's project yields B : 3 with probability pb = 0.2 in each period. If a project is unsuccessful, it yields zero. The bank knows that the proportion of low-risk borrowers is y 0.5. However, the bank is unable to distinguish between low and high-risk borrowers, i.e. it doesn't have an appropriate screening technology. = Question 1 Consider a bank which operates as a monopoly and wants to attract both types of borrowers in the first period. What's the repayment R(¹) that the bank will charge in the first period? Compute the bank's first period profit π(1) i. ii. Calculate the posterior probabilities of a borrower being low risk given that the project was successful and also when the project failed after the first period (i.e. Pr(G|S), Pr(G|F), respectively). iii. How much will the bank charge to successful and failed borrowers in the second period (R3), R)? Calculate the bank's second period profit (²). What's the total profit across the two periods ((1) +ñ π(²))?
Expert Solution
steps

Step by step

Solved in 5 steps with 12 images

Blurred answer
Knowledge Booster
Skilled Labors
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education