Question

Consider a corrupt provincial government in which each housing inspector examines two newly built structures each week. All the builders in the province are unethical and want to increase their profits by using substandard construction materials, but they can’t do that unless they can bribe a housing inspector into approving a substandard building.

a. If bribes cost \(1,000 each, how much will a housing inspector make each year in bribes? (Assume that each inspector works 52 weeks a year and gets bribed for every house he or she inspects.)

b. There is a provincial construction supervisor who gets to hire all of the housing inspectors. He himself is corrupt and expects his housing inspectors to share their bribes with him. Suppose that 20 inspectors work for him and that each passes along half the bribes collected from builders. How much will the construction supervisor collect each year?

c. Corrupt officials may have an incentive to reduce the provision of government services to help line their own pockets. Suppose that the provincial construction supervisor decides to cut the total number of housing inspectors from 20 to 10 in order to decrease the supply of new housing permits. This decrease in the supply of permits raises the equilibrium bribe from \)1,000 to \(2,500. How much per year will the construction supervisor now receive if he is still getting half of all the bribes collected by the 10 inspectors? How much more is the construction supervisor getting now than when he had 20 inspectors working in part b? Will he personally be happy with the reduction in government services?

d. What would happen if reducing the number of inspectors from 20 to 10 only increased the equilibrium bribe from \)1,000 to $1,500? In this case, how much per year would the construction supervisor collect from his 10 inspectors? How much less is the construction supervisor getting than when he had 20 inspectors working in part b? In this case, will the construction supervisor be happy with the reduction in government services? Will he want to go back to using 20 inspectors?

Short answer

a. A housing inspector makes $104,000 in bribes each year.

b. The supervisor collects $1,040,000 as bribes every year.

c. The supervisor will receive $1,300,000 as a bribe every year.

The supervisor is getting $260,000 more every year compared to when he had 20 inspectors, and the bribe was $1000.

The supervisor will be happy with the reduction in services of the government.

d. The supervisor will receive $780,000 as a bribe every year.

The supervisor is getting $260,000 less every year compared to when he had 20 inspectors, and the bribe was $1000.

The supervisor will not be happy with the reduction in services of the government.

They will want to return to using 20 inspectors.

Step-by-step solution

Explanation for part (a)

It is given that an inspector gets $1000 as a bribe for every house they inspect, and the total number of inspections is two every week.

The total number of inspections per year will be 104 (=52 weeks ×2 per week) and accordingly, the total bribe amount every year is $104,000 (=104 inspection×$1000).

Explanation for part (b)

If the supervisor has 20 housing inspectors working under them, then the total bribe amount every year is $2,080,000 (20 inspectors ×104,000 bribe of each inspector).

If the supervisor gets half of the total bribe every year, then they will collect $1,040,000 (=$2,080,000/2) every year.

Explanation for part (c)

There are only ten housing inspectors, and the bribe amount is $2500/inspection.

• An inspector conducts 104 inspections every year and gets $260,000 (=104 inspection×$2500) as the total bribe amount every year.
• $2,600,000 (10 inspectors ×$260,000 bribe of each inspector) is the total bribe amount of 10 housing inspectors every year.
• The supervisor will get $1,300,000 (=$2,600,000/2) as a bribe every year.

The supervisor is getting $260,000 (=$1,300,000-$1,040,000) more every year as a bribe if they reduce the number of inspectors and increase the bribe amount to $2500.The supervisor will be happy with the reduction in services of the government.

Explanation for part (d)

There are only ten housing inspectors, and the bribe amount is $1500/inspection.

• An inspector will get$156,000 (=104 inspection×$1500) as the total bribe amount every year.
• $1,560,000 (10 inspectors ×$156,000 bribe of each inspector) is the total bribe amount of 10 housing inspectors every year.
• The supervisor will get $780,000 (=$1,560,000/2) as a bribe every year.

The supervisor is getting $260,000 (=$1,040,000-$780,000) less every year as a bribe if they reduce the number of inspectors and increase the bribe amount to $1500.The supervisor will not be happy with the reduction in services of the government, and they will try to get back 20 inspectors.