1.Suppose that optimal deterrence of a particular crime requires setting the exp

Question

1.Suppose that optimal deterrence of a particular crime requires setting the expected punishment equal to $2,000. Assume the probability of apprehension is fixed at .20.

(a)Suppose an offender has wealth of $5,000 and incurs a cost of $1,000 per month in prison. What combination of fine and prison term achieves optimal deterrence at the lowest cost?

(b)Another offender has wealth of $7,000. What fine and prison term achieves optimal deterrence for this offender? (Assume he incurs the same cost of time in prison.)

(c)Considerations of fairness dictate that offenders must face the same prison term for the same offense. Given this constraint, what fine and prison term must be used to achieve optimal deterrence for the above two offenders? In what sense does this create a trade-off between fairness and efficiency?

Explanation / Answer

a) expected punishment= 2000

Optimal combination requires to charge a fine equal to maximum wealth of offender.

Let number of months in prison be x

0.2(5000 + 1000x) = 2000

x= 5

Optimal combination- fine of 5000 and prison of 5 months

b)0.2( 7000 + 1000x) = 2000

x=3

Optimal combination= 7000 fine and 3 months in prison.

c) when same prison term must be charged, prison term should be 5 months and both will be charged 5000.

There is a trade-off between fairness and efficiency as efficiency has to be sacrificed for fairness. Second offender is charged 5000 and he is still left with 2000, which reduces the chances of not committing the crime.

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