B.This Mistake Could Have Been Avoided by Testing the Special First at a Single Location

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 individualsself-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.