HW XXXXXXXXXXElectoral Competition

XXXXXXXXXXCandidates Adams and Bu

are running for public office. To campaign,

each makes a binding promise regarding the level of effort ???? ≥ 0 or ???? ≥ 0 that

he will exert if elected. Voter utility is increasing in the effort exerted by the

winning candidate. That candidate receives a benefit of 100 representing the

perks of office (e.g. fame, influence, salary, etc.), and also bears a cost of ???? = ????2

or ???? = ????2 which increases (increasingly) in the effort he commits to exert.

What voter behavior and what candidate behavior do you predict will occur in

equili

ium, and why?

XXXXXXXXXXIn a certainty pool of politicians, half are high types (??) and half are low

types (??). An incumbent is drawn randomly from this pool and must implement

a policy ?? ∈ {??, ??}. A random variable ?? ∈ {??,??} denotes the right thing to do: if

?? = ?? and ?? = ?? or ?? = ?? and ?? = ?? then voters each receive utility 1;

otherwise, they receive utility 0.

Voters do not know what the right thing to do is (that is, they do not observe ??),

ut they think that ?? is more likely: ??(?? = ??) = .6 and ??(?? = ??) = .4. The

incumbent is better informed, because she observes a signal ?? ∈ {??,??} that is

informative of ??. If she is a high-type then her signal is accurate with probability

???? = 1. That is, ??(?? = ??|?? = ??) = ??(?? = ??|?? = ??) = 1. If she is a low-type

then her signal is only accurate with probability ??(??|??) = ??(??|??) = ???? = .8. In

that case, ??(??|??) = ??(??|??) = 1 − ???? = .2.

The notion of pandering is that the incumbent might implement policy ?? even

when she believes that the right thing to do is probably ??, so that voters will

elieve she is a high-type and reelect her. To explore this possibility, suppose

that voters believe the incumbent is doing what she honestly thinks is best (i.e.,

implementing ?? = ?? when she observes ?? = ?? and implementing ?? = ?? when

she observes ?? = ??), and answer the following.

a. (+4) If the incumbent is a high type, how likely is it that she will

implement policy ?? = ??? How likely is it that she will implement policy

?? = ???

. (+2) If the incumbent is a low type, how likely is it that she will

implement policy ?? = ??? ?? = ???

c. (+5) If voters observe that the incumbent implemented policy ?? = ??,

how likely is it that she was a high type? A low type?

d. (+2) If voters observe that the incumbent implemented policy ?? = ??,

how likely is it that she was a high type? A low type?

e. (+2) At the next election, voters can retain the incumbent or elect a

challenger, who will be high or low type with equal probability. If they

seek to maximize the probability of electing a high type, and the

incumbent implements ?? = ??, should they reelect her, or elect a

challenger? What if she implements ?? = ???

HW XXXXXXXXXXElectoral Competition

Answered Same DayMar 08, 2022

Q1

In equili

ium the voter’s utility equals the candidate benefit.(e2A or e2A)

Maximum benefit that a voter can give with his effort is 100

e2A =CA = 100

eA = 50

Equili

ium is (100, 50)

Q2

a)

If incumbent is high type the likelihood of implementing the policy a is qH/x=a =0.6/1 =0.6

If incumbent is high type the likelihood of implementing the policy b is qH/x=b =0.4/1= 0.4

)

If incumbent is low type...

In equili

ium the voter’s utility equals the candidate benefit.(e2A or e2A)

Maximum benefit that a voter can give with his effort is 100

e2A =CA = 100

eA = 50

Equili

ium is (100, 50)

Q2

a)

If incumbent is high type the likelihood of implementing the policy a is qH/x=a =0.6/1 =0.6

If incumbent is high type the likelihood of implementing the policy b is qH/x=b =0.4/1= 0.4

)

If incumbent is low type...

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