# Guido's EZ Loan Company (based on practice exercise 9)

If you borrow \$100 from Guido's EZ loan and pay it back at his standard rate of interest, Guido is \$20 richer. If you don't pay, he not only loses his \$100 capital, he must pay Mick's Rent-a-Thug \$20 to break your legs.
 For purposes of analysis, we will assume that Guido starts with \$130 of working capital that he is considering putting at risk by lending \$100 to you. If you default, this \$130 is reduced to \$10; if you pay, the amount becomes \$150, and if he denies your loan application the capital remains at \$130. This informaition given Guido the payoff matrix at the right: Guido's wealth if you pay Guido's wealth  if you get your  legs broken Guido approves  your application \$150 \$10 Guido denies  your application;  you borrow from  someone else \$130 \$130

A. What is Guido's decision by the maximin criterion?
B. What is Guido's decision by the maximax criterion?
C. What is Guido's decision by the Laplace-Bayes criterion?
D. What is Guido's decision by the minimax regret criterion?

Guido likes your face. On the basis of this information, he estimates that there's a 90% probability you'll pay.
E. What is Guido's decision by the EMV criterion?
F. What is the EVPI?

If Guido crosses her palm with silver, Madame Blivitski will read your horoscope. Out of all the people who will pay, 80% were born under a reliable star, while 70% of the people who default were born under a crooked star.

G. If Madame Blivitski saye you were born under a reliable star, what is Guido's EMV of lending to you?
H. If Madame Blivitski saye you were born under a crooked star, what is Guido's EMV of lending to you?
I. How wide can Madame Blivitski make her palm? (In other words, what is EVSI?)

Guido is a sentimental soul. Although breaking people's legs is an essential part of his business to set the proper example for future customers, he really hates to see it. In other words, Guido is risk averse. Due to his tender heart, Guido would consider getting \$37.50 cash without breaking anybody's legs to be just as good as a 50-50 lottery between (a) \$150 without breaking anybody's legs and (b) \$10 together with the mental anguish (to Guido) of seeing you hobble around on crutches.
The exponential model of Guido's utility function is Ue(x)=1.09574(1-e0.01625x) but we can approximate this by the much simpler function Up(x)= with the inverse function CME(u) = 150u2.

J. If it takes \$5 worth of silver to cross Madame Blivitski's palm, and Guido takes his risk aversion into accuont, should he loan you the money on the basis of your face, cross Madame Blivitski's palm, or just sit on his money?