A new toll road was built in Southern California between San Juan Capistrano and Costa Mesa. On average, drivers save 10 minutes taking this road as opposed to the old road. The toll is $2; the fine for not paying the toll is $76. The probability of catching and fining someone who does not pay the toll is 90%. Individuals who take the road and pay the toll must therefore value 10 minutes at a minimum:
A) between $1.80 and $68.40.
B) between $2 and $68.40.
C) $1.80.
D) between $1.80 and $76.
E) more than $76.

Question

Quizplus · Accepted Answer

If a driver takes the new toll road and saves 10 minutes, then they must value their time at least $0.20 per minute ($2 toll / 10 minutes saved).

The fine for not paying the toll is $76, but the probability of getting caught is quite high at 90%. Thus, the expected cost of not paying the toll is: 
(0.9 x $76) + (0.1 x $2) = $68.80

Therefore, individuals who take the road and pay the toll must value 10 minutes at least $0.20 per minute, which means they value the total time saved at least $2.

So the minimum amount they would be willing to pay is the toll of $2 in order to save the 10 minutes. Therefore, the answer is B: between $2 and $68.40.

A New Toll Road Was Built in Southern California Between