c. Calculate her Expected Utility EUwork if she works hard. (hint: this will be afunction of the interest i).d. Calculate her Expected Utility EUshirks if she shirks. (hint: this will be a functionof the interest i).e. Write down the condition under which the borrower will work hard.f. No-shirking condition: Manipulating the condition you found in e, find themaximum i for which the borrower is going to work hard. Call this interest i"1.NOTE: i', will be a number. Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project.The entrepreneurOnce the entrepreneur undertakes the project, she decides either to work hard or to shirk.• If she works hard, then she earns a high return R=$500 with probability p=0.75 and earnsnothing with probability (1-p)=0.25.• If she shirks, she earns a high return with probability q=0.25 and earns nothing withprobability (1-q)=0.75.The borrower has ex-post utility u(y)=y-D if she works hard and u(y)=y if she does not workhard, where y is her income (after loan payments) carned from the project. Assume D=125.The bank:A bank is willing to finance the project and lend $200 to the borrower. The bank charges theagent an interest rate of i on the loan.The borrower always repays the loan when she succeeds. If she fails, she is protected by limitedliability: she repays nothing to the bank.Finally, assume that the bank could also purchase $200 in risk-free bonds with a return ofr=0.10, and that the financial markets are perfectly competitive.Section A1: No collateral1. The borrowerSuppose the borrower takes a loan of $200 from the bank. Supposethat the interest rate charged on the loan is i (we'll find i later).a. What is her ex post income yail if she fails? NOTE: I'm asking for realizedincome, NOT utility!b. What is her ex post income ysuceed if she succeeds? (hint: this will be a function ofthe interest i).

The entrepreneur seeks to finance a venture costing $200, where success yields a high return while…

a. What is her ex post income yfail if she fails? NOTE: I'm asking for realized income, NOT utility! b. What is her ex post income ysucceed if she succeeds? (hint: this will be a function of the interest i).

a. What is her ex post income yfail if she fails? NOTE: I'm asking for realized income, NOT utility! b. What is her ex post income ysucceed if she succeeds? (hint: this will be a function of the interest i).

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

c. Calculate her Expected Utility EUwork if she works hard. (hint: this will be a
function of the interest i).
d. Calculate her Expected Utility EUshirks if she shirks. (hint: this will be a function
of the interest i).
e. Write down the condition under which the borrower will work hard.
f. No-shirking condition: Manipulating the condition you found in e, find the
maximum i for which the borrower is going to work hard. Call this interest i"1.
NOTE: i', will be a number.

Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200
to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project.
The entrepreneur
Once the entrepreneur undertakes the project, she decides either to work hard or to shirk.
• If she works hard, then she earns a high return R=$500 with probability p=0.75 and earns
nothing with probability (1-p)=0.25.
• If she shirks, she earns a high return with probability q=0.25 and earns nothing with
probability (1-q)=0.75.
The borrower has ex-post utility u(y)=y-D if she works hard and u(y)=y if she does not work
hard, where y is her income (after loan payments) carned from the project. Assume D=125.
The bank:
A bank is willing to finance the project and lend $200 to the borrower. The bank charges the
agent an interest rate of i on the loan.
The borrower always repays the loan when she succeeds. If she fails, she is protected by limited
liability: she repays nothing to the bank.
Finally, assume that the bank could also purchase $200 in risk-free bonds with a return of
r=0.10, and that the financial markets are perfectly competitive.
Section A1: No collateral
1. The borrower
Suppose the borrower takes a loan of $200 from the bank. Suppose
that the interest rate charged on the loan is i (we'll find i later).
a. What is her ex post income yail if she fails? NOTE: I'm asking for realized
income, NOT utility!
b. What is her ex post income ysuceed if she succeeds? (hint: this will be a function of
the interest i).

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