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Solutions to Chapter 13 Exercises
S12. (a) If Oceania only offers a contract designed for the low-cost type of firm, then we have no
To find the optimal levels of Q and M for this contract, we maximize the public benefit from this
contract:
2
2 0.1
b Q M
Q Q
= -
= -
To maximize, we take the derivative and set it equal to zero:
0.5
(2)(0.5) 0.1
1
0 0.1
100
0.1(100) 10
db Q
dM
Q
Q
M
-
= -
= -
=
= =
This gives benefit of
b=2 100 -10 =10
when the firm accepts the contract. Notice that we have the
(c) The expected net benefit is 0.4 times the benefit from purchasing from the low-cost firm:
0.4(2 )
0.4(2[10] 10)
4
B Q M= -
= -
=
(d) We proceed as in part (a). The high-cost firm will be just barely willing to accept a
contract (its participation constraint will be just barely satisfied) when M – 0.16Q = 0, or M = 0.16Q. The
benefit from offering this contract will be
2
2 0.16 .
b Q M
Q Q
= -
= -
This benefit will be maximized by setting its derivative equal to zero:
0.5
(2)(0.5) 0.16
1
0 0.16
39.0625
0.16(39.0625) 6.25
db Q
dM
Q
Q
M
-
= -
= -
=
= =
(e) With Q = 39.0625 and M = 6.25, the low-cost firm would earn a profit of 6.25 –
0.1(39.0625) = 2.34375. So yes, the low-cost firm would accept the contract.
(f) When the firm accepts the contract, the benefit is
2
2 39.0625 6.25
6.25.
b Q M= -
= -
=
Because both low-cost and high-cost firms will accept this contract, the benefit in part (c) will be
realized with probability 1. Thus, the expected net benefit to this contract is B = 6.25. This is less than the
benefit of B = 7 from offering a menu of two contracts, as in Exercise S11, part (j) above.
(g) If Oceania knew BMA’s type and could offer the single best contract based on this
This is larger than the benefits of the other three contracts we have considered: offering an
optimal contract for the low-cost type (B = 4), offering an optimal contract for the high-cost type (B =
UNSOLVED EXERCISES
U1. (a) Asymmetric information can lead to pronounced problems of moral hazard when a broker
sells financial services or products such as stocks, mutual funds, or mortgages. (Recall the simplified
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
To alleviate the moral-hazard problem, investors might screen brokers by investigating what
stocks or investments brokers hold personally. However, it may be difficult to get a truthful answer to this
question, and furthermore, the broker’s own financial needs and risk preferences may genuinely differ
Note that adverse selection was also an important contributing factor to the 2008 mortgage crisis.
When brokers lowered their requirements and allowed home buyers to state their assets and income
(b) Once hired, a realtor may not work as hard to sell your house for as much money as you
would like. A typical real estate contract calls for the seller to pay a 6% commission on the sale of his
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
To counteract this problem, one might consider designing a slightly different contract, where the
seller shares a higher fraction of a higher sale price with the seller’s agent. For example, on a home that
(c) For an extensive overview of the problems of adverse selection and moral hazard in the
medical domain, see the solution to Exercise S11 in Chapter 8.
U2. (a) If MicroStuff sets prices separately, the optimal prices are 80 for WordStuff and 100 for
ExcelStuff. With these prices MicroStuff earns a profit of 260, or $26 billion.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(d) Ingrid and Javiera would buy the applications bundled as in part (c), while Kathy would
(e) Ingrid enjoys a surplus of 20 under separate pricing but only 10 with a single bundled
(f) MicroStuff would like to sell WordStuff to Kathy and—ideally—bundles to Ingrid and
(g) If MicroStuff sells the applications separately and in a bundle, the profit-maximizing
(h) The optimal price for WordStuff under separate pricing only and pricing both separately
and in a bundle is 80, since this extracts as much surplus as possible from Kathy without losing her
U3. (a) Let u0 represent the reservation utility, d the disutility of putting in high effort, pH the
probability of success given high effort, and pL the probability of success given low effort. Further, let x
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
