# We developed our first graphical model of adverse selection in the context of car insurance in section

## Question:

We developed our first graphical model of adverse selection in the context of car insurance in section 22A.2 where we assumed that the marginal cost MC1 of providing car insurance to unsafe drivers of type 1 is greater than the MC2 of providing insurance to safe drivers of type 2.
A: Continue with the assumption that MC1 > MC2. In this exercise, we will investigate how our conclusions in the text are affected by altering our assumption that D1 = D2 —i.e. our assumption that the demand (and marginal willingness to pay) curves for our two driver types are the same.
(a) Suppose demand curves continue to be linear with slope α — but the vertical intercept for type 1 drivers is A1 while the intercept for type 2 drivers is A2. Suppose first that A1 > A2 > MC1 >MC2. Illustrate the equilibrium. Would p∗ —the price that emerges in the asymmetric equilibrium—still be halfway betweenMC1 and MC2 as was the case in the text?
(c) What is the equilibrium if instead A2 > A1 > MC1 > MC2? How does p∗ compare to what you depicted in (a)?
(d) Identify again the deadweight loss from asymmetric information.
(e) What would have to be true about the relationship of A1, A2, MC1 and MC2 for safe drivers not to buy insurance in equilibrium?
(f) What would have to be true about the relationship of A1, A2, MC1 and MC2 for unsafe drivers not to buy insurance in equilibrium?
B: In our model of Section B, we assumed that the same consumption/utility relationship u(x) can be used for high cost θ and low cost δ types to represent their tastes over risky gambles with an expected utility function.
(a) Did this assumption imply that tastes over risky gambles were the same for the two types?
(b) Illustrate the actuarially fair insurance contracts in a graph with x2 —the consumption in the good state—on the horizontal and x1 —the consumption in the bad state—on the vertical. Then illustrate the choice set created by a set of insurance contracts that all satisfy the same terms— i.e. insurance contracts of the form p = βb (where b is the benefit level and p is the premium).
(c) Can you tell whether θ or δ types will demand more insurance along this choice set?
(d) True or False: Our θ types would be analogous to the car insurance consumers of type 1 in part A of the exercise while our δ types would be analogous to consumers of type 2.
(e) Suppose there are an equal number of δ and θ types and suppose that the insurance industry for some reason offered a single full set of insurance contracts p = βb and that this allowed them to earn zero profits. Would the p = βb line lie halfway between the actuarially fair contract lines for the two risk types?
(f) Suppose instead that the insurance industry offered a single insurance policy that provides full insurance — and that firms again make zero profits. Would the contract line that contains this policy lie halfway between the two actuarially fair contract lines in your graph? What is different from the previous part?
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