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).