## Questions

1. Economists often model businesses as strictly maximizing

profits. However, we also observe many firms

giving money to charity or providing some of their

products to disadvantaged consumers for free or at a

reduced price. Are these acts altruistic? What other

motives might firms have? Use real-world examples to

argue your case.

2. Consider Hong, who is endowed with a number of

tokens. The tokens can be allocated between Hong and

another person. Each unit of Hong’s own consumption,

x1, can be purchased for p1 tokens. Each unit of the

other person’s consumption, x2, can be purchased for

p2 tokens. Consider each of the following sets of

choices. Determine if each violates WARP, SARP, or

GARP.

(a) When endowed with 20 tokens, with p1 =1 and

p2 = 1 Hong chooses x1 =17, x2 = 2.05. When

endowed with 30 tokens, with p1 =0.5,

p2 = 10.5, Hong chooses x1 = 18, x2 =2. When

endowed with 100 tokens, with p1 =1.72,

p2 = 2.9, Hong chooses x1 = 20, x2 = 1.9.

(b) When endowed with 20 tokens, with p1 =1 and

p2 =1 Hong chooses x1 =18, x2 = 2. When

endowed with 30 tokens, with p1 =0.5,

p2 =10.5, Hong chooses x1 =17, x2 =2.05.

(c) When endowed with 20 tokens, with p1 = 1 and

p2 = 1 Hong chooses x1 = 17, x2 =3. When

endowed with 30 tokens, with p1 = 1, p2 =2,

Hong chooses x1 =10, x2 =10. When endowed

with 100 tokens, with p1 = 5, p2 =5, Hong

chooses x1 = 18, x2 = 2.

(d) When endowed with 20 tokens, with p1 =1 and

p2 =1Hong chooses x1 =17, x2 =3.When endowed

with 30 tokens, with p1 = 1, p2 = 2, Hong chooses

x1 =20, x2 = 5. When endowed with 100 tokens,

with p1 = 10, p2 =5, Hong chooses x1 = 5, x2 =10.

3. Consider the prisoner’s dilemma game, in which two

prisoners are accused of a crime. Both are isolated in

the prison. Without a confession, there is not enough

evidence to convict either. Any prisoner who confesses

will be looked upon with lenience. If one prisoner

confesses and the other does not, that prisoner not

confessing will be put away for a much longer sentence.

The payoffs can be represented as pictured in

Figure 14.7 (Player 1’s payoffs are in the upper right,

and Player 2’s are in the lower left).

Prisoner 1

Prisoner 2

Confess

Confess

Don’t confess

Don’t confess

–10

–10

60

60

–100

–100 50

50

FIGURE 14.7

The Prisoner’s Dilemma

(a) Determine the Nash equilibrium strategy for each

player. What would be the result of the game if

both players chose this strategy?

(b) In most experiments involving the prisoner’s

dilemma, we observe that players tend to choose

not to defect a reasonable proportion of the time.

How might this be motivated by altruism?

(c) If a selfish player is playing the prisoner’s dilemma

against an opponent she believes to be altruistic,

what would her strategy be? Is this similar to the

observation in the TIOLI game? Why or why not?

(d) Now suppose that the prisoner’s dilemma is played

three times in sequence by the same two players.

How might a belief that the other player is altruistic

affect the play of a selfish player? Is this

different from your answer to c? What has

changed?