Question

Frequent power outages trouble the residents of Storm City. Located in the center of the storm belt, the city experiences periodic windstorms that down trees and power lines. The tables below give some data about the likelihood of power outages and the consequences. (For example, the “more inspections” row of the table indicates that if the Power company chooses to do tree trimming and more inspections, the probability of an outage will be .2, and the marginal reduction in the probability of an outage due to “more inspections” is .1). As you can see there are actions that the power company can take to reduce the probability of an outage, and actions that households can take to reduce the costs of the outage.

Additional

Action taken              Actor                          probability     marginal cost of

                                                                        of outage         additional action

none                            power company                       0.4                   $0       

tree trimming               power company                       0.3                   $150   

more inspections         power company                       0.2                   $250

better transformers      power company                       0.1                   $350   

Additional

Action taken              Actor                          costs of           marginal cost of

                                                                        outage             additional action

none                            households                  $5,000             $0                               

candles, flashlights      households                  $4,000             $150

eliminate freezer         households                  $3,000             $200

replace electric heat    households                  $2,000             $300

back-up generators      households                  $0                    $1,000                                    

Society would like to minimize the total cost of this tort situation, where total cost = (cost of power company actions) + (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 actions will be taken by each party? 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 actions will be taken by each party? Compute the total costs of this situation. Is this an improvement over the situation in part a?

c. Suppose that there is a simple negligence rule that assigns liability to the power company only for failure to trim trees. What actions will be taken by each party?

Compute the total costs 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.

Answer 1

Answer: The first thing that is most important here is the understanding of cost minimization. The total cost in this case comprises of three factors: 1. Cost of Power company actions 2. Cost of the household's actions 3. The probability of outage multiplied with the cost of that outage i.e. E(x) where x is the outage If one wants to minimize the total cost, then one should minimize all the three factors. Now, as this is a linear equation between the total cost and the three factors. What we can do is consider all of them individually a. One approach that comes in mind is that we hold two factors constant and change the third one. For example, we can minimize (put them to zero) all the costs incurred (one for the power company and the other for households) and see what can we get as total cost and then increase these costs together and see the changes to the total cost. In the above case, Total Cost 0+00.4*5000 $2000

Considering this way, every possible condition, we can conclude that the Power Company should choose 'better transformers' and households should choose to 'replace electric heat'. That way the total cost comes up to be $850, the least b. By strict liability, it means Power Company would choose to minimize its cost and hence that variable would become 0. Now the total cost is totally dependent on the households. In that case, the power company would choose to do 'no actions' and the household would choose to 'replace electric heat' actionagain. That way the total cost comes up to be $1100. Hence it is no improvement over the last situatiorn. c. If the liability is assigned only for failure to trim trees then power company will choose 'tree trimming' and households will again choose to 'replace electric heat'. This way the total cost would become $1050 and hence this is an improvement over the situation in Part b but not in part al