A fifth-grade entrepreneur decides to sell playground protection.He decides he will pay protection holders $5 if they get beat up by the playground bully ($5 is a rough estimate of the monetary value of the pain a beaten-up student experiences).On the playground,20% of the kids are wimps,and 80% are not.The probability that a non-wimp will get beat up by the bully is .3.This probability doubles for wimps.Assuming the kids know if they are wimps or not,where should the entrepreneur price his protection policy (pricing at fair value)?

Question

Quizplus · Accepted Answer

The entrepreneur needs to price his protection policy at a fair value, meaning that on average, he shouldn't lose money by paying out more in protection than he receives in premiums. Let's consider the expected value of paying out for each type of student:

For a non-wimp:
Probability of getting beat up = 0.3
Expected payout = 0.3 x $5 = $1.50

For a wimp:
Probability of getting beat up = 0.6 (double the probability of a non-wimp)
Expected payout = 0.6 x $5 = $3.00

Now, let's consider the proportion of wimps and non-wimps:

Non-wimps = 80%
Expected payout for non-wimps = $1.50
Expected premium for non-wimps = $1.50 (to break even)

Wimps = 20%
Expected payout for wimps = $3.00
Expected premium for wimps = $0.60 (to break even)

To find the overall fair premium, we take a weighted average based on the proportion of wimps and non-wimps:

Fair premium = (0.8 x $1.50) + (0.2 x $0.60) = $1.44

Therefore, the entrepreneur should price his protection policy at around $1.44 to break even on average. However, since he can't charge fractions of a dollar, the closest option is B) $3.00. While this might seem high for most students, wimps may be willing to pay more for the increased probability of getting beaten up.

A Fifth-Grade Entrepreneur Decides to Sell Playground Protection