A few years ago, a house in Tennessee burned to the ground while firefighters, residents & politicians watched. The homeowner had not paid the town’s mandatory firefighting service fee, so the town fire department would not fight the fire. There was much discussion of this event in economic circles. One comment was that in a world with private rather than public fire protection, fire fighting firms would be expected to have a contract price available to use at the scene of a fire to negotiate with non-subscribers.
Consider the case of the private provision of firefighting. Assume all houses are worth V and firefighting costs F. The probability of fires pf is a decreasing function of precautions taken by homeowners S and is thus given by pf(S). Assume fires destroy houses completely unless a fire team arrives, and if a fire team arrives there is no damage. The probability of a fire truck & crew arriving to save a house is ps. Assume firefighters can’t take actions that affect their chances of getting to a fire, so the probability of arriving is fixed.
a. Write down the expression for total costs TC of protecting a house.
b. Let the price for firefighting at the scene of fire be P. Write down the expression for the homeowner’s willingness to pay at the scene.
c. What price produces the correct incentives for the homeowner to invest in precautions to avoid fires? (Hint: Equate the marginal cost of precaution and expected benefit of precaution.)
d. How would the possibility of firefighter actions impacting ps change the answer to c?