Chapter 12 - The Economics of Information
Chapter 12: Answers to Questions and Problems
1.
1
4
6
4
a. The expected value of option 1 is 16 (150) + 16 (300) + 16 (750) + 16 (300) +
1
16
1
5
1
1
5
5
(150) = 450. The expected value of option 2 is (120) + (255) +
1
1
5
5
(1,500) + (255) + (120) = 450.
1
4
6
b. The variance of option 1 is16 (150 − 450)2 + 16 (300 − 450)2 + 16 (750 −
4
1
450)2 + 16 (300 − 450)2 + 16 (150 − 450)2 = 56,250. Similarly, the variance
of option 2 is 279,270. The standard deviation of option 1 is 237.17. The standard
deviation of option 2 is 528.46.
c. Option 2 is riskier since both have the same mean but option 2 has greater
variance.
2.
a. Risk loving.
b. Risk averse.
c. Risk neutral.
3.
a. The reservation price is the price where the expected benefits of search equal the
cost of search. According to the graph, $5 is the reservation price.
b. She will purchase the item, since your price is less than her reservation price.
c. Now, the reservation price is $6, since this is where expected benefits of search
equal the new cost of search. Therefore, the most you can charge is $6.
d. She will continue to search, since the price exceeds her reservation price (which is
now $2).
4.
a. E(Price) = 0.7($200) + 0.3($600) = $320.
b. Set E(Price) = MC to get 320 = 2 + 6Q. Solve for Q to find your profitmaximizing output, Q = 53 units.
c. Your expected profits are (E(Price))Q – C(Q) = $320(53) – (2(53) + 3(53)2) =
$8,427.
5.
a. The expected value, which is $50.
b. The maximum value, which is $100.
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Chapter 12 - The Economics of Information
6.
a. With only two bidders, n = 2. The lowest possible valuation is L = $1,500, and
your own valuation is v = $4,000. Thus, your optimal sealed bid is 𝑏 = 𝑣 −
𝑣−𝐿
$4,000−$1,500
= $4,000 −
= $2,750.
𝑛
2
b. With ten bidders, n = 10. The lowest possible valuation is L = $1,500, and your
𝑣−𝐿
own valuation is v = $4,000. Thus, your optimal sealed bid is 𝑏 = 𝑣 − 𝑛 =
$4,000−$1,500
$4,000 −
= $3,750.
10
c. With one hundred bidders, n = 100. The lowest possible valuation is L = $1,500,
and your own valuation is v = $4,000. Thus, your optimal sealed bid is 𝑏 = 𝑣 −
𝑣−𝐿
$4,000−$1,500
= $4,000 −
= $3,975.
𝑛
100
7.
a. With 5 bidders, n = 5. The lowest possible valuation is L = $10,000, and your
𝑣−𝐿
own valuation is v = $30,000. Thus, your optimal sealed bid is 𝑏 − 𝑣 − 𝑛 =
$22,000−$10,000
$22,000 −
= $19,600.
5
b. A Dutch auction is strategically equivalent to a first-price sealed bid auction (see
part (a)). Thus, you should let the auctioneer continue to lower the price until it
reaches $19,600, and then yell “Mine!”
c. $22,000, since it is a dominant strategy to bid your true valuation in a secondprice, sealed-bid auction.
d. Remain active until the price exceeds $22,000; then drop out.
8.
a. Hidden actions lead to moral hazard; hidden characteristics lead to adverse
selection.
b. Incentive contracts can solve moral hazard problems; screening and sorting can
solve adverse selection problems.
9.
The discounted price is most likely due to asymmetric information. The seller has
better information about the car’s condition than the buyer. The buyer cannot tell
whether the low price is due to poor unobservable car characteristics or, e.g., due to
the seller needing cash fast and thus being willing to offer a low price. Thus, an
adverse selection situation is present.
10.
Life insurance policies that will not pay claims arising from suicide are designed to
protect the company from the adverse selection problem. Eliminating this clause will
likely reduce a life insurance company’s bottom line, since individuals who are
contemplating suicide will purchase policies just prior to their death.
11.
Since this is a common value auction, bidders will not bid their own private estimates
because doing so would lead to the winner’s curse. Thus, there will be an additional
incentive for bidders to shade their bids below their estimated valuations. The English
auction format provides bidders the most information (therefore allowing them to
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© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution
in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 12 - The Economics of Information
pool information to some extent), mitigating this problem. For this reason, the
English auction would generate the highest expected revenues in this case.
12.
Your expected inverse demand is E(P) = .6(300,000 – 400Q) + .4(500,000 – 275Q) =
380,000 – 350Q. Therefore, your expected marginal revenue is E(MR) = 380,000 –
700Q. Your marginal cost is MC = $240,000. Setting E(MR) = MC yields 380,000 –
700Q = 240,000. Solving, Q = 200. The price you expect is thus E(P) = 380,000 –
350(200) = $310,000. Your profits are thus ($310,000 -$240,000)(200) - $140,000 =
$13,860,000.
13.
One would expect higher premiums on credit life, thanks to adverse selection. People
who cannot pass physicals will select toward this type of insurance, resulting in
higher premiums. Furthermore, people who are healthy and can pass a physical will
be unwilling to pay the higher premiums, thus exacerbating this effect.
14.
The expected benefit from an additional search are 0.10($100,000 - $70,000) =
$3,000, while the cost of another search is $5,800. Therefore, make her an offer.
15.
In the absence of "guaranteed issue," an insurance company could choose to insure
only those employees with a very low risk structure. In this case they offer lower
rates because they experience fewer claims. But this leaves those workers with
greater risk factors without insurance. By requiring insurers to offer coverage to all
employees, the insurance company must take on employees that are less healthy and a
greater risk. Why the controversy? By insuring those with greater health risks, the
expected number of claims rises, thus increasing the cost of coverage. The workers
with existing health problems benefit at the expense of healthy workers, who pay
higher prices with "guaranteed issue." If the price rises high enough and healthy
workers are free to drop coverage, this can result in adverse selection: The only
people willing to pay the higher premiums are those in poor health.
16.
Brownstown Steel has better information about its financial situation than does its
lenders, and is attempting to use this information advantage to enhance its bargaining
position. If lenders gained full information about the financial situation of
Brownstown Steel Corp., they would be in a position to squeeze the maximum
amount from Brownstown Steel without fear of pushing it into bankruptcy. Absent
the information, lenders will be more generous, since taking too much would increase
the risk that Brownstown Steel goes bankrupt.
17.
The 30-day warranty and 10-point inspection. This not only reduces buyer risk from
being duped by a used car dealer, but provides a costly signal about the quality of the
used cars sold. An unscrupulous dealer would find it costly to mimic this strategy.
Recognizing both of these facts, rational buyers will be more willing to purchase cars
from the dealer.
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 12 - The Economics of Information
18.
Offer two plans for customers with more than $1.5 million in assets. One plan
(perhaps called the “Free Trade” Account) has an annual maintenance fee of $20,000
good for up to 500 “free” transactions (computed as $20,000/$40) per year (each
additional transaction is priced at $40 each). The other plan (perhaps called the “Free
Service” Account) has no annual maintenance fee but charges $120 per transaction.
Given these two options, investors will sort themselves into the plans based on their
individual characteristics.
19.
With 4 other bidders, n = 5. The lowest possible valuation is L = $8,000, and your
own valuation is v = $16,000. Thus, your optimal first-price, sealed-bid is 𝑏 = 𝑣 −
𝑣−𝐿
$16,000−$8,000
=
$16,000
−
= $14,400.
𝑛
5
A risk-neutral Oracle’s bid of $7 billion may seem low since the expected value of the
20.
present value of the stream of profits is $7.6 billion (= 0.7×10 + 0.3×2). The public
bidding process described most resembles a common values auction, since each
company is forming different forecasts for a good that has, essentially, the same value
for both bidders. Therefore, it is prudent to bid less than your forecasted value to
avoid the winner’s curse. However, with new information about SAP’s expected
value of the present value of the stream of profits being $8.4 billion (= 0.8×10 +
0.2×2), this should make you a bit more optimistic about the “true” value of the
company, and so you should consider raising your bid.
21.
The expected value of aggregate ten-year profits of a McDonald’s franchise is
0.25($16) + 0.50($8) + 0.25(-$1.6) = $7.6 million. Similarly, the expected value of a
Penn Station East Coast Subs’ franchise is 0.025($48) + 0.95($8) + 0.025($-48) =
$7.6 million. The variance and standard deviation of owning a McDonald’s franchise
2
is 𝜎𝑀𝑐𝐷𝑜𝑛𝑎𝑙𝑑𝑠
= 0.25(16 − 7.6)2 + 0.50(8 − 7.6)2 + 0.25(−1.6 − 7.6)2 = 38.88
2
and 𝜎𝑀𝑐𝐷𝑜𝑛𝑎𝑙𝑑𝑠 = √𝜎𝑀𝑐𝐷𝑜𝑛𝑎𝑙𝑑𝑠
= √38.88 = 6.23538, respectively. Similarly, the
2
variance and standard deviation for Penn Station East Coast Subs’ is 𝜎𝑃𝑒𝑛𝑛
=
2
2
2
0.025(48 − 7.6) + 0.95(8 − 7.6) + 0.025(−48 − 7.6) = 118.24 and 𝜎𝑃𝑒𝑛𝑛 =
2
√𝜎𝑃𝑒𝑛𝑛
= √118.24 = 10.8738, respectively. Since the expected values are the same
we can compare the standard deviations to determine the most risky investment. Since
σPenn > σMcDonalds there is more risk associated with a Penn Station East Coast Subs’
franchise.
22.
There are several things for a student to consider in deciding to enroll in a traditional
MBA program or an online MBA program. It is likely that students with a spouse and
family will be more attracted to online MBA programs, since these individuals tend to
value stability and have others relying on them for income. In contrast, traditional
MBA programs are more likely to attract singles who are willing to bear the
opportunity cost associated with this form of education. Thus, online MBA programs
can serve as a screen, helping potential employers learn more about candidates from
each type of program. If they need a more flexible employees (e.g., one that might be
willing to travel or move frequently), these are more likely to be found in a traditional
MBA program. If they are looking for more stable employees, these are more likely
to be found in an online MBA program.
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 12 - The Economics of Information
23.
Market collapse is likely when individuals are allowed to engage in insider trading.
This is because “outsiders” will be unwilling to participate in equity (or other)
markets since they know “insiders” will only sell a stock when they know the price is
too high. Similarly, insiders will only buy when the price of a stock is known to be
low. This is a losing proposition for outsiders, who would rationally choose not to
participate in the market. This is an example of a adverse selection and is one of the
primary reasons the SEC exists.
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.