Question

In: Economics

Hogg, who is risk-neutral over votes, is running for office with 500,000 sure voters. To add...

Hogg, who is risk-neutral over votes, is running for office with 500,000 sure voters. To add voters, he wants to choose n, the number of negative campaign ads to run, where 0 n 4. The ads will backfire with probability n/5 and give him no extra votes. Otherwise, the ads will work and give him 100,000 + 40,000n extra votes. So n = 0 implies a total of 600,000 votes. He should choose n = :

a. 0.

b. 1.

c. 2.

d. 3.

e. 4.

Can someone explain how the answer is B

Solutions

Expert Solution

When n= 0:

Sure votes = 500000

Backfire probability = 0/5=0

Extra votes = 100000

Hence, total votes = 600000

When n=1

Sure votes = 500000

Backfire probability = 1/5*500000 = 100000

Extra votes = 100000 + 40000

Hence, total votes = 500000-100000+140000=540000

When n=2

Sure votes = 500000

Backfire probability = 2/5*500000 = 200000

Extra votes = 100000 + 80000

Hence, total votes = 500000-200000+180000=480000

When n=3

Sure votes = 500000

Backfire probability = 3/5*500000 = 300000

Extra votes = 100000 + 120000

Hence, total votes = 500000-300000+220000=420000

When n=4

Sure votes = 500000

Backfire probability = 4/5*500000 = 400000

Extra votes = 100000 + 160000

Hence, total votes = 500000-400000+260000=360000

As clearly evident, when the person is risk-neutral over votes and given that he would like to choose n, number of negative campaign to add voters, that means he would choose n>0

It is only when n=1, total votes = 540000 > 500000

For other values of n, total votes < 500000

Thus, the person would choose n=1

Hence, answer is B

Rahul Sunny answered 11 months ago
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