The kingdom of Arendelle has equal numbers of two types of workers, domestic ser

Question

The kingdom of Arendelle has equal numbers of two types of workers, domestic servants and ice sellers, which both earn $1,000 per week. All workers face a risk of being laid off next year due to bad market conditions, in which case they will have an income of only $250/week from an alternative part-time job. Domestic servants have a 10% probability of being laid off, and ice sellers have a 30% probability. All have the same utility function: U = ln(C).

a. Suppose that workers would like to insure against being laid off. If insurers can offer different insurance contracts to each type of worker, what will be the actuarially fair premiums for full insurance for each group? (Assume that full insurance pays a benefit of $1000 per week, so that part time work is not necessary.)

b. Explain why a private market for unemployment insurance is unlikely to exist.

Explanation / Answer

a) Payment is $1000

domestic servants laying off probability = 10%

So fair premium = domestic servants laying off probability x payment = .1*1000 = $100

ice-sellers laying off probability = 30%

So fair premium = ice-sellers laying off probability x payment = .3*1000 = $300

b. Now from insurance, employees are getting same their full earning whithout working a bit. So this will lead to moral hazard i.e. they will intentionally leave jobs and still get paid from insurance. So private insurers will not enter a market where there is a definite chance of moral hazard.

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