1 Auto Insurance

Imagine that auto insurers insuring taxi drivers in major U.S. cities because high accident rates lead to massive yearly claims payments-it's very difficult to break even. But one brave insurer remains who will insure them, AllCity. The demand for AllCity auto insurance by taxi driver is given by P (Q) = 4, 000 - 1 Q, meaning they have marginal revenue of MR(Q) = 4, 000 - Q. Their marginal costs are constant and equal to MC(Q) = 2, 000, as are their average total costs, ATC(Q) = 2, 000. Here, Q represents the number of insurance policies in thousands; and P (for now, just) the policy premium.

1. If AllCity charges every taxi driver the same premium, what will that be?

2. Some local governments think the premium you found in the last question is too high. Therefore, they regulate AllCity, making it charge a premium that results in AllCity earning zero profits. What is the premium that coincides with this regulation?

3. What is AllCity's mark-up under this regulation?

4. Certain localities have a even mix of persons for whom being a cab driver is their only job and thus are full-time. The other half only drive part-time to make a little extra money on the weekends. Because the former (latter) group is on the road more (less), they have an increased (decreased) probability of getting in an accident. Because of this, AllCity decides to price discriminate and charge each group a different two-part tariff consisting of a premium, but also the deductible. Which part of the two-part tariff is the fixed fee and which is the variable rate? Explain.

5. For each group, AllCity can set the premium to be "high" or "low." The same is true for the deductible. For full-time drivers, what premium and deductible will AllCity charge them? Why?