BEM/Ec 146
HW #1 Key
1.a.
Red Lobster probably made the mistake of underestimating how much crab the
average customer could eat, by not taking adverse selection into account. “Average”
customer is in fact probably misleading, and this promotion apparently drew in heavy
eaters who wanted to take advantage of this all-you-can-eat special, as shown by the
weblogs boasting 18 pounds of crab in one sitting. Light eaters would be far less likely to
indulge in the special, worried they wouldn’t get their money’s worth. Adverse selection
mandates that the average all-you-can-eat eater has a much greater appetite than the
average customer. Also, once you’ve paid the upfront fee, the marginal cost of ordering
more crab is zero.
b.
This mistake could have been avoided by testing the special first at a single
location, only advertising the special within the restaurant so as not to attract big eaters,
restricting the hours and nights, providing unlimited amounts of cheap stuff like bread
and soda, adding a small surcharge after 2 plates, etc.
2.a.
In theory, adverse selection tells us that the most likely drivers to buy the
insurance are the most dangerous drivers; therefore, the expected damage to a car with
insurance is much greater than the expected damage to any given car.
Furthermore, moral hazard tells us that once drivers get insurance, they will be
inclined to drive more recklessly, even if they are ordinarily good drivers, because they
are not responsible for damage to the car. Therefore, theoretically, the expected damage
to a car with insurance should go up even higher.
b.
Moral hazard does not lead to more accidents because, even though drivers are
immune from monetary damage to the car, they still fear personal injury or death. No
reasonable person tries to get into an accident, no matter how good their insurance is.
Adverse selection likely does not lead to more accidents partly because of self-serving
bias. People like to believe they are better drivers than they really are. Poor drivers often
have poor judgment, so they may think they are great drivers, and that they don’t need
insurance. Finally, it is possible that some drivers who get into frequent accidents are
risk-loving, and therefore enjoy gambling by not buying insurance, even if they know
they are risky drivers. Good drivers on the other hand are more likely to be risk-averse
and so will be more likely to buy insurance.
3.
Attribution theory tells us that if something positive happens in a company, the
company will take credit for it, i.e. attribute an internal source. But if something negative
happens, the company will pin it on a scapegoat who was “most” responsible for the
negative event, i.e. attribute it to an external source. In reality, the company’s incentives
were most likely out of line and encouraged bad behavior.
Evidence suggests that people in the West are more likely to accept the “bad
apples” explanation because people here are more worried about their stock options and
about placing blame on an individual in order to clear the name of the larger entity, as
opposed to the East where there is more of a team mentality and the focus is more on
fixing the problem and moving on, rather than pointing fingers.
4.
A positive externality that affects me personally is when my roommates bring
their band over to our house and jam out. A negative externality that affects me is when
the neighbors call the police/security because of said jamming.
The positive externality is not internalized because we are all friends and there is
no need to make payments for externalities that benefit us all, and besides, they are
jamming because they want to.
The negative externality is not internalized because according to the law we are
allowed to be reasonably loud during the daytime, and the neighbors are unwilling to
come over and talk to us about ways to compensate/deal with their discomfort.
5.a.
Let 1 be oldest, and 5 be youngest pirate
If Pirate 5 is the last one alive, he will give himself all the gold. (-∞, -∞, -∞, -∞, 100)
If only Pirates 4 and 5 are alive, 4 will propose giving himself all the gold, knowing that
his own vote will satisfy the weak majority, and 5 cannot kill him. (-∞, -∞, -∞, 100, 0)
If only 3, 4, and 5 are alive, 3 need only propose a division which will improve either 4’s
payoff from 100 or 5’s payoff from 0 (we know that 5 has no power to kill 4, so he
cannot possibly get 100). So 3 will propose (-∞, -∞, 99, 0, 1), which will pass.
If only 2, 3, 4, and 5 are alive, 2 only needs to improve 3, 4, or 5’s payoff from (99, 0, 1),
to get the 50% weak majority, so he will propose (-∞, 99, 0, 1, 0), which will pass.
If all pirates are alive, 1 can get away with improving only 2 of the remaining pirates’
payoffs from (99, 0, 1, 0), so he will propose (98, 0, 1, 0, 1), which will pass.
Thus, the subgame perfect equilibrium is (98, 0, 1, 0, 1). 1, 3, and 5 approve, and 2 and 4
reject.
b.
By extending this chain of subgame equilibria, we can determine that the payoffs
will be (101-n/2, 0, 1, 0, 1, ..., 0, 1, 0) for an even n ≤ 200 number of pirates.
Thus, the payoff for the oldest pirate is 101 - (88/2) = 57
c.
ui(X)=xi – α/(n-1)Σk=1n [xk–xi]0 –β/(n-1)Σk=1n [xi –xk]0
with
α = 1, β = 0
=> ui(X)=xi – 1/(n-1)Σk=1n [xk–xi]0
For n = 1, there is no envy. Payoffs are (-∞, -∞, -∞, -∞, 100).
For n = 2, i’s utility = xi – [xj – xi]0
5 will vote Nay if 4 proposes giving anything not greater than 100 to 5. 4 cannot propose
anything greater than 100 to 5, so 4 dies, 5 takes all. (-∞, -∞, -∞, -∞, 100)
For n = 3, 3 can offer whatever he wants; he can win 4’s vote with anything, because 4
knows he will die next if he votes Nay. The money distribution is (100, 0, 0) between 3,
4, and 5, and the payoffs for all 5 pirates are (-∞, -∞, 100, -50, -50).
For n = 4, 2 needs to win 2 out of the 3 remaining votes. So he needs to ensure 4 and 5
have payoffs of greater than -50. Giving himself a payment of 100 and the others nothing
provides payoffs of (-∞, 100, -33.3, -33.3, -33.3), so he wins the votes of 4 and 5.
When all 5 pirates are still alive, 1 can give himself all 100; he will win the votes of 3, 4,
and 5.
Thus, the money received is (100, 0, 0, 0, 0),
and the payoffs are (100, -25, -25, -25, -25)
6. Chris’s strategy – Pat’s strategy
Obey-Obey (C if pro-C, P if pro-P)
Disobey-Disobey (P if pro-C, C if pro-P)
Big-Little (C regardless)
Little-Big (P regardless)
Mixed-Mixed (M if pro-C, M if pro-C) ,
(M if pro-P, M if pro-P),
(M regardless, M regardless)
7.
x1 = 0 and 1
If x2 ≤ ½ and x3 ≥ ½, u3 = ½(1 + x3) – ½(x2 + x3) = ½(1 – x2)
If x2 ≥ ½ and x3 ≤ ½, u3 = ½(x2 + x3) – ½ x3 = ½ x2
Thus, the third firm’s utility is maximized regardless of its location, as long as it locates
on the “fat” side of the circle (i.e. the side opposite firm 2)
Therefore, firm 3 will locate itself halfway between firm 1 and firm 2 on the circle, on the
fat side:
x3 = ½(1 + x2) if x2 ≤ ½,
x3 = ½ x2 if x2 ≥ ½
u2 = ½(1 – x3) if x3 ≤ ½ and x2 ≥ ½
u2 = ½ x3 if x3 ≥ ½ and x2 ≤ ½
Combining these with the equations relating x2 and x3,
u2 = ¼(1 + x2) if x2 ≤ ½
u2 = ½(1 – ½ x2) if x2 ≥ ½
Thus, we can easily see that Firm 2 will maximize its utility by choosing x2 = ½
Since the circle is symmetrical, Firm 3 will choose x3 = ¼ or x3 = ¾
Then X = (0 and 1, ½, ¼) or X = (0 and 1, ½, ¾)
u2 = ¼(1 + x2) = ¼(1 + ½) = 3/8. u1 = u2 = 3/8 by symmetry about the circle.
u3 = ½ x2 = ½ * ½ = ¼
U = (3/8, 3/8, ¼)
8.
Prices are likely to be higher in the communities where the homeowners control
the zoning boards. While the property developers will want to build whatever price level
of house that will sell quickly, the homeowners will want to be surrounded by expensive
houses, as this will increase their own property value.
9.
One reason the members of the club may play golf more frequently is that it is
“free” for them to play after they have paid the sunk membership cost. Thus, a member
gains immediate utility u0 when he plays golf, while a non-member gains utility u0 – 100,
so there is a greater incentive for a member to play.
More importantly, only avid golfers will ever go for the membership and so these
individuals are likely to play golf more often, holding costs constant. This is an example
of selection, since people who become members think they’re going to get their money’s
worth, and so should play more golf than those who just play casually.
10.a.
Property rights are the rights to use, restrict the use of, and sell property. For
example, if you own a car, you can use the car when you like, you can let your friends
drive it but lock out others, and you can sell it when you are tired of it.
b.
Partial equilibrium analysis – As opposed to a general equilibrium analysis, a
partial equilibrium analysis does not take all reactions and counterreactions of all agents
into consideration. It assumes that some agents do not react to a change, or are not
behaving optimally. For example, if we study the stock market, but assume that some
people are investing randomly.
c.
Adverse selection / Hidden information – When individuals self-select in a way
that takes advantage of another party. For example, having a reverse auction to complete
a job: Often, the lowest bidders will do the worst job, hence why they are willing to work
for so low.
d.
Moral Hazard / Hidden Action – When a party behaves in a self-serving way after
it is too late for the other party to do anything about it. For example, I had my car
shipped to me from home. After we had paid them 300 dollars up front, they didn’t pick
the car up until a week after they were supposed to.