2 Advantageous Selection Consider the market for life insurance with consumers w

Question

2 Advantageous Selection Consider the market for life insurance with consumers who purchase life insurance. Suppose this insurance is basic, a consumer pays for life insurance and then if they die before say 65, their family gets paid a large sum of money. Thus, from the insurance companies point of view, the consumers that are the least likely to die are the ones that cost the least. Suppose there is no moral hazard (no hidden action), but consumers do vary in their type and their type is unobserved by the insurance company. Suppose consumers have different levels of risk aversion. So the amount of risk aversion a consumer has is their hidden type and the insurance company cannot observe this Recall, in the market for health insurance the least healthiest consumers, which are the most costly for the insurance company, are the ones who have a high demand for health insurance. In the market for life insurance, the consumers who are the most risk averse, which are the ones least likely to die, are the least costly. This leads to increasing MC and AC curves and this is known as advantageous selection. Suppose demand, marginal cost, and average cost are given by: P = 100-Q. MC-10-2Q, and AC 104 Q

Explanation / Answer

Socially optimal quantiy is at intersection of Demand and MC curves.

100 - Q = 10 + 2Q

3Q = 90

Q = 30

Equilibrium quantity is at intersection of Marginal revenue (MR) and MC curves.

P = 100 - Q

Total revenue (TR) = P x Q = 100Q - Q2

MR = dTR / dQ = 100 - 2Q

Equating with MC,

100 - 2Q = 10 + 2Q

4Q = 90

Q = 22.5

Therefore, socially optimal quantity is higher than private market equilibrium quantity.

Note: Since previous models are not specified, comparison with them is not possible.

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