a. Suppose the goal is to limit the number of speeders to 500. What actual fine, f, and what probability of apprehension, p, minimizes the cost of achieving this goal? b. Suppose the actual fine for speeding is statutorily capped at $100. What now is the minimum expenditure on enforcement that achieves the goal of 500 speeders?

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1. Suppose the following information has been gathered on the enforcement of a speed limit on a
particular highway over a holiday weekend
Expenditure on
enforcement
$1,000
Probability of
apprehension (p)
Expected fine
(pf)
Number of
speeders
.1
1,000
10,000
100,000
.5
50
500
.9
1,000
5
a. Suppose the goal is to limit the number of speeders to 500. What actual fine, f, and
what probability of apprehension, p, minimizes the cost of achieving this goal?
b. Suppose the actual fine for speeding is statutorily capped at $100. What now is the
minimum expenditure on enforcement that achieves the goal of 500 speeders?
Transcribed Image Text:1. Suppose the following information has been gathered on the enforcement of a speed limit on a particular highway over a holiday weekend Expenditure on enforcement $1,000 Probability of apprehension (p) Expected fine (pf) Number of speeders .1 1,000 10,000 100,000 .5 50 500 .9 1,000 5 a. Suppose the goal is to limit the number of speeders to 500. What actual fine, f, and what probability of apprehension, p, minimizes the cost of achieving this goal? b. Suppose the actual fine for speeding is statutorily capped at $100. What now is the minimum expenditure on enforcement that achieves the goal of 500 speeders?
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