Questions 1-2 are related.
1. The value of Second Corp.àstock depends on the success of a
new
product, the online self-help course “You don have to put yourself ³t
to be a winner!” Until yesterday, analysts believed there is a 60% chance
that the course will succeed, and a 40% chance that it will fail. In case of
success, Second Corp.àshares are worth $18; in case of failure, the shares are
worth $12. Today, analysts learned that initial subscriptions to the course
are strong. For launches of this type of course, initial subscriptions are strong
50% of the time. However, for courses that turn out to be successful in the
end, initial subscriptions are strong 75% of the time. What is the updated
probability that the course will succeed, after the positive news about initial
subscriptions?
2. By how much money does the expected value of Second Corp.àstock
increase as a result of the positive news?
Questions 3-4 are related.
3. Seven salespeople want to reorganize the Bay Area districts they cover.
Currently, the assignments are: Alameda (Onur), Berkeley (Dooley), Castro
Valley (Rita), Danville (Fiora), Emeryville (Ivy), Fremont (Ziggy), Gilroy
(Silvester). However, preferences are as follows (current assignments marked
in bold):
#
1
2
3
4
5
6
7
Onur
Dooley
Berkeley
Fremont
Fremont
Gilroy
Emeryv.
Alameda
Alameda Berkeley
Danville
Danville
Gilroy
Castro V.
Castro V. Emeryv.
Rita
Fiora
Ivy
Ziggy
Silvester
Alameda
Berkeley
Danville
Gilroy
Castro V.
Berkeley
Gilroy
Gilroy
Berkeley Alameda
Emeryv.
Danville Berkeley Castro V.
Gilroy
Castro V. Fremont Emeryv. Danville
Berkeley
Fremont
Castro V. Alameda Fremont Emeryv.
Gilroy
Emeryv.
Fremont Alameda
Danville
Danville
Alameda Castro V. Emeryv.
Fremont
What are the assignments under the Top Trading Cycle algorithm? Show
your steps in deriving them.
1
4. What would Onuràtop choice need to be so that everyone would be
assigned their top choices under the Top Trading Cycle algorithm?
Questions 5-6 are related.
5. Consider the function f (x) = 2x 12 x2 . At which x does the function
have a maximum, and what is the value of the function at the maximum?
6. Consider the function f (x; y) = 2x + y 12 x2 , where x + y = 2. At
which x and y does the function have a maximum, and what is the value of
the function at the maximum?
Questions 7-8 are related.
7. A consumeràpreferences for combinations of goods x and y are described by the utility function: u = x + 1:5y 2=3 . Prices are px = 10 and
py = 5. The consumer has wealth w = 100. What are the optimal quantities of x and y to consume? Is the individual risk-loving, risk-neutral, or
risk-averse at these quantities?
8. Suppose wealth decreases to w = 20. What are the optimal quantities
of x and y to consume? Is the individual risk-loving, risk-neutral, or riskaverse at these quantities?
Questions 9-10 are related.
9. Consider the following money utility functions:
v1 = 2w1=2
v2 = 3w1=3
Calculate the associated coe#ients of risk aversion. Which money utility
function is more risk averse?
10. What is the certainty equivalent of a lottery that pays $729 with
50% probability, and $64 otherwise, under each money utility function?
2

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