Summary 537you would be willing to pay as much as $120 for it. Thus, you can buy it
now (for a profit of $120 $100 $20) or wait until next week, when
the price will be reduced to $75 if the coat is still available. The chances
of its being available next week are 2/3. If it is available in week 2, you
can buy or wait until week 3. There is a 1/2 chance it will be sold
between weeks two and three and a 1/2 chance it will be available at a
reduced price of $60. Finally, if it is available in week 3, you can buy or
wait until week 4. There is a 1/4 chance it still will be available, at a price
of $50 (and a 3/4 chance it will be sold in the meantime). Week 4 is your
last chance to buy before the coat is withdrawn.
a. How long should you wait before buying? Illustrate via a decision tree.
b. Filene’s has 120 of these winter coats for sale. What is its expected
total revenue from the pricing scheme in part (a)? (One-third
of the coats sell in the first week, one-half of the remaining coats
in the second week, and so on. All coats in week 4 are sold
for $50.)
c. Alternatively, Filene’s can set a single price for all coats. Its demand
curve is P 180 Q. Would it prefer a common-price method or the
price-reduction method in part (b)? Explain.- Consider once again the dilemma facing Consolidated Edison’s system
operator. To keep things simple, we focus on one of the decisions before
him: to shed or not to shed load. Suppose his choices are to shed
50 percent of the load (which will “solve” the problem at the cost of
blacking out 50 percent of New York City) or maintain full load (risking
the chance of a total blackout).
a. The operator envisions three possible scenarios by which the system
might weather the demand–supply imbalance at full load. The first
scenario he considers “improbable,” the second is a “long shot,” and
the third is “somewhat likely.” How might he translate these verbal
assessments into a round-number estimate of the probability that
100 percent load can be maintained? What probability estimate
would you use?
b. Consider the three outcomes: 100 percent power, 50 percent power,
and 0 percent power (i.e., a total blackout). It is generally agreed that
0 percent power is “more than twice as bad” as 50 percent power.
(With 50 percent power, some semblance of essential services, police,
fire, hospitals, and subways, can be maintained; moreover, with a
deliberate 50 percent blackout, it is much easier to restore power
later.) What does this imply about the utility associated with 50
percent power? (For convenience, assign 100 percent power a utility
of 100 and 0 percent power a utility of 0.)
c. Construct a decision tree incorporating your probability estimate
from part (a) and your utility values from part (b). What is the
operator’s best course of action? Explain.
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