Manufacturers of gas furnaces for homes know that in rare instances, a furnace w

Question

Manufacturers of gas furnaces for homes know that in rare instances, a furnace will develop a gas leak that leads to an explosion. The manufacturers can take precautions, in the form of costly changes to the manufacturing process, to lower the probability of such explosions. Assume that this is a “unilateral precaution” situation, in that only manufacturers can take actions to affect the probability of these explosions.

Let x stand for the amount of money per furnace spent on these precautionary steps by the manufacturer.

Let the probability that a furnace explodes, which is a function of x, be given by

P(x) = 1/100x

Let the average social cost of a furnace explosion of this type be A.

So, the cost of precaution plus the expected social cost of explosions is a function of x, and is given by

x + P(x)*A = x + A/100x

Suppose that the state, after years with a common law rule of no liability for the power company for outage related losses, passed a statute giving full liability to power companies in the event of power failures, as in part c.

a. What does economic theory predict will happen to the price of electricity in Storm City? Explain.

b. What would happen to premiums on homeowners’ insurance sold to residents of Storm City? (homeowners’ insurance typically covers losses due to power failures).

Explanation / Answer

a. Thus far there were no liability on the power companies due to loss of power in the city. However, with the new rule, the liability is on the power companies. This means the power companies will need to make sure that incidents of power failure and resultant losses to consumers is at the minimum.

Given from the case, we know that the additional cost of precautionary expense is, x + A/100x. In order to make sure that the incidents are low, power companies will add this expense while ordering furnaces. This will increase the cost of the furnace by x + A/100x. In return the price of electricity will increase in the area.

Economic theory predicts that as the power companies are forced to mitigate risk with more expensive materials, the price of electricity will rise in the city.

b. The homeowners insurance covers many losses. One of these losses are loss due to power failure. With the liability of loss due to power failure shifting completely on the power companies, the insurance company (ethically) can omit the power failure losses from the coverage. This means the number of incidents covered will reduced and the premium will reduce.

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