In: Economics
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
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