Skydiving – jumping out of an airplane with a parachute – is incredibly fun, but also dangerous. The risk of dying in a skydiving accident is actually very small – for this problem, we will assume it is zero. However, there is a substantial risk of other injuries.

There are standard precautions a skydive operator can take – such as using more modern equipment, hiring experienced instructors, and taking extra care in packing the parachutes – to reduce this risk. The cost of running a skydiving business is $150 per customer without these precautions; these precautions cost an additional $100 per customer, and reduce the probability of injury from 1 in 100 to 1 in 300. The average skydiving injury does $30,000 worth of harm to the customer.

There are five potential customers, each with one opportunity to skydive; the joy each one would get from skydiving is worth $500, $400, $300, $200, and $100, respectively. (That is, the most enthusiastic customer would get a benefit of $500, the second-most-enthusiastic $400, and so on.)

(a) What is the efficient level of precaution for skydive operators to take (high or low)?

(b) Given this precaution level, what is the efficient level of activity? (That is, how many customers are there for whom the benefits of skydiving outweigh the total costs?)

Suppose there is perfect competition in the skydiving industry – there are many skydive operators, with identical costs, so the price of skydiving is driven down to marginal cost plus expected liability payments (if any).

For parts (c)-(f), assume that customers correctly perceive and consider the risk of injury when deciding whether to skydive, and can observe the level of precaution taken by each skydive operator.

(c) Under a rule of no liability, what level of precaution will operators take? Why?

(d) Under perfect competition (assumed throughout this problem), what will be the price of skydiving?

(e) What will customers perceive as the total cost of skydiving? How many customers will choose to skydive?

(f) Are precaution and activity higher, lower, or equal to the efficient levels?

For parts (g)-(j), assume instead that customers are unaware of the risk of injury, and completely ignore it when deciding whether or not to skydive – they simply weigh the financial price against the benefit. Continue to assume the skydiving industry is perfectly competitive.

(g) Under a rule of strict liability, what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(h) Under a rule of simple negligence (where anything less than the efficient level of precaution is considered negligent), what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(i) Under a rule of no liability, what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(j) Which of these rules is the most efficient?

Recall the skydiving scenario described in Question 1 – precaution costs the skydive operator $100 per customer, and reduces the chance of a $30,000 injury from 1 in 100 to 1 in 300.

But now, suppose there is just one skydive operator, and he has only $9,000 in assets. After paying $9,000, he would be bankrupt, and thus avoid paying further damages. This is referred to as being judgment-proof. Suppose customers cannot observe the level of precaution taken, and do not suspect the operator is judgment-proof.

(a) Calculate the damages the operator expects to pay per customer under a strict liability rule if he takes precaution, and if he does not. What level of precaution would a strict liability rule lead to?

(b) Calculate the damages the operator expects to pay per customer under a simple negligence rule if he takes precaution, and if he does not. (Assume that anything less than the efficient level of precaution would constitute negligence.) What level of precaution would a simple negligence rule lead to?

(c) A different way to encourage precaution is through safety regulation. Imagine a government agency which calculates the efficient level of precaution for skydiving operators, conducts periodic inspections, and assesses substantial fines (say, $3,000) when these precautions are not being taken. Explain the following passage from Cooter and Ulen:

“In those industries where undercapitalized firms risk bankruptcy, safety regulations have an advantage over liability. By collecting fines before an accident occurs, officials can force an undercapitalized firm to comply with safety standards that it would violate if the only sanction were liability.”

There are standard precautions a skydive operator can take – such as using more modern equipment, hiring experienced instructors, and taking extra care in packing the parachutes – to reduce this risk. The cost of running a skydiving business is $150 per customer without these precautions; these precautions cost an additional $100 per customer, and reduce the probability of injury from 1 in 100 to 1 in 300. The average skydiving injury does $30,000 worth of harm to the customer.

There are five potential customers, each with one opportunity to skydive; the joy each one would get from skydiving is worth $500, $400, $300, $200, and $100, respectively. (That is, the most enthusiastic customer would get a benefit of $500, the second-most-enthusiastic $400, and so on.)

(a) What is the efficient level of precaution for skydive operators to take (high or low)?

(b) Given this precaution level, what is the efficient level of activity? (That is, how many customers are there for whom the benefits of skydiving outweigh the total costs?)

Suppose there is perfect competition in the skydiving industry – there are many skydive operators, with identical costs, so the price of skydiving is driven down to marginal cost plus expected liability payments (if any).

For parts (c)-(f), assume that customers correctly perceive and consider the risk of injury when deciding whether to skydive, and can observe the level of precaution taken by each skydive operator.

(c) Under a rule of no liability, what level of precaution will operators take? Why?

(d) Under perfect competition (assumed throughout this problem), what will be the price of skydiving?

(e) What will customers perceive as the total cost of skydiving? How many customers will choose to skydive?

(f) Are precaution and activity higher, lower, or equal to the efficient levels?

For parts (g)-(j), assume instead that customers are unaware of the risk of injury, and completely ignore it when deciding whether or not to skydive – they simply weigh the financial price against the benefit. Continue to assume the skydiving industry is perfectly competitive.

(g) Under a rule of strict liability, what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(h) Under a rule of simple negligence (where anything less than the efficient level of precaution is considered negligent), what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(i) Under a rule of no liability, what level of precaution will operators take? What will be the price of skydiving? How many customers will choose to skydive?

(j) Which of these rules is the most efficient?

Recall the skydiving scenario described in Question 1 – precaution costs the skydive operator $100 per customer, and reduces the chance of a $30,000 injury from 1 in 100 to 1 in 300.

But now, suppose there is just one skydive operator, and he has only $9,000 in assets. After paying $9,000, he would be bankrupt, and thus avoid paying further damages. This is referred to as being judgment-proof. Suppose customers cannot observe the level of precaution taken, and do not suspect the operator is judgment-proof.

(a) Calculate the damages the operator expects to pay per customer under a strict liability rule if he takes precaution, and if he does not. What level of precaution would a strict liability rule lead to?

(b) Calculate the damages the operator expects to pay per customer under a simple negligence rule if he takes precaution, and if he does not. (Assume that anything less than the efficient level of precaution would constitute negligence.) What level of precaution would a simple negligence rule lead to?

(c) A different way to encourage precaution is through safety regulation. Imagine a government agency which calculates the efficient level of precaution for skydiving operators, conducts periodic inspections, and assesses substantial fines (say, $3,000) when these precautions are not being taken. Explain the following passage from Cooter and Ulen:

“In those industries where undercapitalized firms risk bankruptcy, safety regulations have an advantage over liability. By collecting fines before an accident occurs, officials can force an undercapitalized firm to comply with safety standards that it would violate if the only sanction were liability.”

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