Question

Jean is a therapist and typically sees five patients per day. She charges each patient $120. So, she earns $600 a day. However, there is a 20% chance that she might fall sick and then she would have to cancel all her appointments. On such a day her income would be zero. The following represents her utility from income: U(I)=ln(I). She is considering purchasing a full and fair insurance contract. What should be the insurance premium, r and the payout, q under such a contract? r=$ and q=$

Answer 1

The insurance premium, r, would be $0 and the payout, q, would be $600.

Step-by-step explanation:

In order to determine the insurance premium, r, and the payout, q, under the insurance contract for Jean, we need to consider the probability of her falling sick.

Since there is a 20% chance of her falling sick, the insurance should cover her potential loss of income on those days.

In this case, her income would be zero.

The insurance premium, r, can be calculated by multiplying the probability of falling sick (0.2) by her average income per day ($600) and subtracting her expected income without insurance ($600).

Therefore, r = 0.2 * $600 - $600 = $0.

The payout, q, would be the amount of income that she would receive on the days she falls sick, which is $600.

So, r = $0 and q = $600.