Question

6. Two individuals, Harry and Ron, are both working. Harry faces a 10 percent chance of becom-
ing unemployed for three months and losing $12,000 in income. Ron’s probability of becoming

unemployed is lower, at 8 percent, but he too would be unemployed for three months and
would lose $12,000 in income.
a. Suppose the employment insurance benefit rate is 55 percent so that 55 percent of lost
earnings are replaced. Calculate the expected payout for Harry and Ron.
b. Suppose that participating in the national employment insurance program is compulsory
and that the annual premium of $594 is paid by both individuals. Does this scheme involve
redistribution? If so, who gains and who loses?
c. If an actuarially fair premium was to be charged, what annual premium would each worker
be charged?

Answer 1

Answer :

(a) :- Suppose the employment insurance benefit rate is 55 percent so that 55 percent of lost earnings are replaced. Calculate the expected payout for Harry and Ron.

For Harry,

There is a 10% difference in losing an income of 12000 and will get 55% of lost income back. So

Expected payout= 0.1*0.55*12000 = 660

For Ron,

There is a 8% possibility of losing an income. Rest stays same.

Expected payout= 0.08*0.55*12000= 528

(b) :- Suppose that participating in the national employment insurance program is compulsory
and that the annual premium of $594 is paid by both individuals. Does this scheme involve
redistribution? If so, who gains and who loses?

Yes this includes redistribution. The annual premium is 594, which is higher than the expected payout of Ron and lower than expected payout of Harry.

This implies the redistribution is from Ron to Harry, as Ron is paying higher than his expected redistribution.

(c) :- If an actuarially fair premium was to be charged, what annual premium would each worker
be charged?

First lets see what an actuarially fair insurance is. From a shopper's perspective, an insurance contract is actuarially fair if the premiums paid are equivalent to the expected estimation of the compensation got.

Given this definition, and given the expected payouts determined to a limited extent A, we can say that

- Actuarially fair premium for Harry = 660

- Actuarially fair premium for Ron = 528

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