Frequent power outages trouble the residents of Stormville. Located in the center of the storm belt, the
Question:
Frequent power outages trouble the residents of Stormville. Located in the center of the storm belt, the town experiences periodic windstorms that down trees and power lines, causing power outages. The Stormville Power Company can take precautionary actions to lower the annual probability of a power outage. Table A lists levels of annual precautionary spending that the Power Company can choose, the annual probability of a power outage associated with each level of precaution, and the annual cost of maintaining each level.
A. Possible Power Company Precaution Levels (annual basis)
“Level” of precaution chosen | Annual Probability of outage at this level | Total cost per year of this level of precaution |
Zero | .9 | 0 |
One | .75 | 20,000 |
Two | .6 | 100,000 |
Three | .45 | 190,000 |
There are 1,000 households in Stormville that are served by the Power Company, and that suffer damage if there is an outage. Table B lists actions that the households of Stormville can take to lower the size of their loss in the event of a power outage. It also lists the total cost of the outage associated with each level of precaution, and the marginal cost of each additional action. So, the “Small Generator” line of the table indicates that if each household buys flashlights and a small generator, each household will lose $120 if there is an outage, for a total social loss of 120X1000=$120,000. The annual cost for a household of having flashlights and a small generator is $75, for a total social cost of 75X1000 = $75000, and the marginal cost to a household of adding a small generator as a precaution is $60.
Table B: Possible Household Precautions and their Costs on an Annual Basis
Additional Precautionary Action Taken | Total losses from outage (all households) | Cost of outage for each household | Total Annual Cost of Precaution (All Households) | Total annual cost of precaution for each household | Marginal annual cost of additional precaution for each household |
None | 200,000 | 200 | 0 | 0 | 0 |
flashlights | 160,000 | 160 | 15,000 | 15 | 15 |
Small generator | 120,000 | 120 | 75,000 | 75 | 60 |
Large generator | 80,000 | 80 | 150,000 | 150 | 75 |
As discussed in class, society would like to minimize the total cost of this tort situation, where total cost = (cost of power company precaution) + (cost of household actions) + (probability of outage*costs of outage)
a. Suppose that the Power company has no liability for damages due to power outages. What level of precaution will the power company choose, and what action will be taken by the households? Compute the total costs of this situation.
b. Suppose, on the other hand, that the power company is strictly liable for all outage-related damages. What level of precaution will the power company choose, and what action will be taken by the households? Compute the total cost of this situation.
c. Suppose that there is a simple negligence rule that allows the power company to escape liability by adopting precautionary level 2. What level of precaution will the power company choose, and what action will be taken by the households? Compute the total cost of this situation. Is this an improvement over the situation in parts a and b?
d. Propose a negligence rule that will bring about the efficient set of actions, that is, the set of actions by the power company and the households that minimizes the total cost of this tort situation.
Expert Answer:
a As discussed in class the power company will choose the level of precaution that minimizes its costs whose cost at each level of precaution are given in the Table A In other words the power company ... View the full answer
