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Key West Fisheries
Teaching Note
A decision tree describing Harry Morgan’s basic problem is shown below. If
Morgan rejects the contract, his monetary position at the end of the year
depends on the price of tuna and the size of his catch. The expected value of
this option is $49,500 after averaging over the four equally likely outcomes.
If Morgan accepts the contract, he locks in a fixed price for 150,000 pounds
of his catch, but the profit from his domestic sales is still uncertain. Thus, he
faces the same chance branches as in the reject decision. After learning about
the type of season(s) and the going price of tuna, he decides how to ship the
fish. Thus, there is a decision square at the end of each of the four chance
branches. He is free to make different shipping decisions in different types of
seasons.1 (This decision is simple since it is made after all uncertainty has
been resolved.)
The decision tree shows that his most profitable shipping decision depends
on the price of tuna. If the going price is $.80 or $1.00 (when the Pacific
catch is small), hiring the freighter is the more profitable option. If the going
price is $.50 or $.70 (when the Pacific catch is large), using his own boat
more profitable. There is an easy intuitive explanation for this result. When
domestic prices are high, the opportunity cost of using his own boat exceeds
the explicit cost of hiring the freighter. Accordingly the freighter is the better
option. Conversely, when domestic prices are low, doing it yourself costs
little and is the better option.
Comparing the expected values of the alternatives, we see that a risk-neutral
decision maker should reject the contract.
11 We have not shown one possible shipping option: transporting half the
catch by freighter and half by one's own boat. The value of this option
always lies midway between the values of shipping all by freighter and all
by own boat. Thus, it is always worse than one of the “all or none”
alternatives and can be eliminated from consideration.
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Freighter
Freighter
Freighter
Freighter
Boat
Boat
Boat
Boat
24
40
69
55
12
22
39
25
42.5
49.5
$.50
.25
$.80
.25
$.70
.25
$1.0 0
.25
0
90
18
90
Reject
Accept
40
69
22
39
$.50
.25
$.80
.25
$.70
.25
$1.0 0
.25
49.5
The following questions are typical vehicles for leading a class discussion of
this decision:
1. What are Morgan’s options? What are the associated risks? If he
accepts the contract, does he face an additional decision?
2. How does one use the answers above to draw the outline of Morgan’s
decision tree? At what point in the tree does the shipping decision occur?
(This last question is important since many students incorrectly put the
shipping decision “up front” – the same time the contract is signed.)
3. What are the monetary values to be listed at the branch tips?
4. Where should Morgan begin solving the tree? (This is another
important question. The analysis of any tree should begin with the last
decision -- that is, the tree should be solved from right to left. Students
who forget this point are inclined to begin with the first decision.)
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Additional Questions:
1. The option to postpone effectively gives Morgan perfect information
about price and catch before having to make the contract decision. The
appropriate decision tree is shown below. From the tree, we see that if the
domestic price is $.80 or $1.00 (when the Pacific catch is small), Morgan
should reject the contract. If the domestic price is $.50 or $.70 (when the
Pacific catch is large), Morgan should accept the contract and use his own
boat. The overall expected value is $60,500. Therefore, the expected value
afforded by this additional information is 60,500 - 49,500 = $11,000.
Freighter
Boat
Reject
Freighter
Boat
Reject
Freighter
Boat
Reject
Freighter
Boat
Reject
40
90
22
40
$.50
.25
$.80
.25
$.70
.25
$1.0 0
.25
60 .5
Delay
signing
24
40
0
69
55
90
12
18
39
25
90
22
2. The decision tree below shows the situation when Morgan can acquire
perfect information about the Pacific catch (from a marine biologist)
before making his contract decision. Knowing that the Pacific catch is
large, Morgan should accept the contract and use his own boat. Knowing
that it is small, he should reject the contract. The expected value is
$60,500. This is exactly the same expected value as in question 1. After a
little reflection this should be no surprise. It happens that Morgan’s best
course of action depends only the Pacific season (and the resulting prices).
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Knowing the Atlantic outcome as well (as in additional question 1) makes
no difference. Since the same decisions are made in either case, Morgan
obtains the same expected value.
31
Freighter
9
Atlantic Large
0
18
.5
Atlantic Small
.5
31
Reject
Accept
60.5
Marine
Biologist
.5
Pacific
Large
Pacific
90
.5
Small
54
90
Accept
Reject
22
24
40
Boat
40
Freighter
Boat
12
22
.5
.5
Atlantic Large
Atl. Small
39
69
69
Boat
55
Freighter
Boat
39
25
.5
.5
Atlantic Large
Atl. Small
Freighter
Atlantic Large
90
90
.5
Atlantic Small
.5
31
Extra Point. For different amounts of information, Morgan’s expected
values are:
--- --- $49,500
Atl --- $54,250
--- Pac $60,500
Atl Pac $60,500
Knowing the Pacific outcome, Morgan obtains no additional benefit from
also knowing the Atlantic. But what if Morgan does not know the Pacific
outcome? In this case, would information on the Atlantic outcome be of
any value? The answer is yes. As the tree below shows, Morgan’s
expected value is $54,250 (which is greater than $49,500).
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31
Freighter
54.5
45
0
.5
.5
54.5
Reject
Accept
54.25
Marine
Biologist
.5
Atlantic
Large
Atlantic
.5
Small
Accept
Reject
24
40
Boat
40
Freighter
Boat
.5
.5
69
Boat
55
Freighter
Boat
39
25
.5
.5
Freighter
90
.5
.5
Pacific Large
Pac. Small
69
69
55
90
Pacific Large
Pacific Small
54
54
30.5
Pacific Large
Pac. Small
Pacific Large
Pacific Small
22
39
18
This demonstrates an important point explored in Chapter Thirteen. The
value of additional information depends in part on the amount of
information a manager starts with.
3. Set U(0) = 0 and U(90) = 100. Then, Morgan’s certainty equivalents
for the 50-50 gambles establish the following utility values:
U(24) = 50, U(52) = 75, U(6) = 25, U(69) = 87.5, U(35) = 62.5,
U(13) = 37.5.
In the graph below, we have drawn free hand a smooth utility curve going
through these points. Then, we have reproduced the original decision tree
with utility values at the end points (as read roughly from the graph).
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The decision tree shows that accepting the contract delivers the higher
expected utility. For the risk-averse Morgan, this is the better course of
action. By reading from vertical axis to horizontal axis on the graph, we
find the certainty equivalent of accepting the contract to be about $40,000.
(Because rejecting the contract is very risky, its certainty equivalent is
lower than the CE of accepting the contract, even though its expected
value is higher.)
Utility 10 0
010 20 30 40 50 60 70 80 90
75
50
25
0
Wealth ($ Thousands)
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Freighter
Freighter
Freighter
Freighter
Boat
Boat
Boat
Boat
24 (50 )
40 (67)
69 (87.5)
55 (77)
12 (36)
22 (48)
39 (66)
25 (51)
67.1
61
$.50
.25
$.80
.25
$.70
.25
$1.0 0
.25
0 (0 )
90 (10 0 )
18 (44)
90 (10 0 )
Reject
Accept
67
87.5
48
66
$.50
.25
$.80
.25
$.70
.25
$1.0 0
.25
CE = $40 K
CE = $34 K
IV. Quips and Quotes
I was expecting this but not so soon. (Written on a Tombstone in Boot Hill)
You can get more with a kind word and a gun than you can get with a kind
word. (Gangster Al Capone on the virtues of diversification)
If at first you don't succeed, try, try again. Then stop. No use being a damn
fool about it. (W.C. Fields)
If you start to take Vienna, take Vienna. (Napoleon Bonaparte)
What men really want is not knowledge but certainty.
If Hell is paved with good intentions, it is largely because of the impossibility
of foreseeing consequences. (Aldous Huxley)
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So far indeed are men in business from knowing the conditions on which
future prices and profits depend that they are often ignorant after the event of
the causes of their past profit and losses. (Thomas Leslie)
They couldn’t hit an elephant from this dis-. . . (The dying words of Civil
War General, John Sedgewick)
Ready, fire, aim. (A confused sequential decision?)
A man jumps from a skyscraper. As he passes the 20th floor, “So far, I don’t
see any problems.”
What do you do when you see a banker jumping out the window? Follow
him. There must be money to be made down there.
The contempt of risk and the presumptuous hope of success are in no period
of life more active than at the age at which young people choose their
professions. (Adam Smith)
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