Some time this summer, I will revise my Price Theory Problems e-book. Here is a new problem I will add.
My goal in posting this is to highlight how different firms are affected by the same economic shock and to show how the use of past econometric models that no longer hold create profit opportunities. I do not actively own any stock in any insurance companies and I do not consult for them.
Every driver is required to buy car insurance. The historical probability of experiencing an accident can be expressed by the function: prob(accident) = f(Miles_i) where Miles_i is the count of miles person i drives per year.
ASSUME: that the price of the premium is set as a function of this historical accident function and the insurance firm is risk neutral.
The profits of the insurance firm will rise in the short run due to COVID-19. True, False, Uncertain explain.
My tentative answer is : True
In the typical insurance model, the aggregate economic activity where the person is driving is taken as given. So, in the prob(accident) = f(Miles_i) there is a KEY omitted variable. The true accident production function can be written as; prob(accident) =f(Miles_i, Aggregate Miles) where Aggregate Miles are all of the other vehicle miles being driven by all of the other vehicles in the area where you drive.
Since COVID-19 is a macro shock that effectively shrinks Aggregate Miles to zero, your probability of having an accident per mile of driving falls sharply and this means that holding your premium price constant, that short run insurance profits rise.
Now, where is perfect competition here? Are the insurance companies updating their models and offering discounts now that driving per mile is safer?
Note that there is no "price gouging" here. The price of insurance does not rise. My point is that this price does not fall as the risk declines.
After writing out this problem, I see that the news is reporting that car insurance sellers profits are up.