1. No, unhealthy employees do not have an incentive to become healthy.
2. The new actuarially fair cost of insurance would be $5000 at the original firm.
3. The actuarial fair cost of insurance for all the workers would be $3000
No, unhealthy employees do not have an incentive to become healthy. This is due to the fact that the only employer in the city is giving jobs to everyone regardless of their health status. Besides, their health care cost is covered and managed by the employer by the insurance. Therefore, unhealthy employees do not have an incentive to become healthy.
The new actuarially fair cost of insurance can be determined by taking the probability of healthy employees and unhealthy employees with their health costs.
However, provided that all healthy people worked for the new employee, it implies that the original firm comprise of only the unhealthy workers and the new actuarially fair cost of insurance can be computed as follows:
∴
Actuarial Fair cost of insurance = Probability ( Healthy employee × cost of health) + Probability (unhealthy employee × cost of health)
Actuarial Fair cost of insurance = (0 × $1000) + (1 × $5000)
Actuarial Fair cost of insurance = $5000
Therefore, the new actuarially fair cost of insurance would be $5000 at the original firm.
The actuarial fair cost of insurance for all the workers refers to the total sum of required payoffs for both the healthy employees and unhealthy employees
Actuarial Fair cost of insurance = Probability ( Healthy employee × cost of health) + Probability (unhealthy employee × cost of health)
Actuarial Fair cost of insurance = [tex]\mathbf{(\dfrac{1}{2} \times \$1000) + (\dfrac{1}{2} \times \$5000)}[/tex]
Actuarial Fair cost of insurance = $500 + $2500
Actuarial Fair cost of insurance = $3000
Therefore, the actuarial fair cost of insurance for all the workers would be $3000
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