Radha has assets worth 10,000 rupees and is facing a loss of 3,600 with a probability of 0.002. She is indifferent between paying G rupees for insurance protection and assuming the risk of loss personally. She values total assets of amount w≥0 according to the utility function u (w) = w1/2. Determine G

Radha is indifferent between paying for insurance protection and assuming the risk of loss personally when the expected utility is the same in both scenarios.

Get the full solved assignment PDF of MEC-101 of 2023-24 session now.

We can set up the equation using the utility function and the expected values of the outcomes.

The expected utility of assuming the risk is given by the utility function:
[ U_{\text{risk}} = \sqrt{10,000 – 3,600} ]

The expected utility of purchasing insurance is the weighted average of the utility in case of no loss (assets remain at 10,000) and the utility in case of a loss:
[ U_{\text{insurance}} = (1 – 0.002) \cdot \sqrt{10,000} + 0.002 \cdot \sqrt{10,000 – G} ]

Since Radha is indifferent, we can set these two expected utilities equal to each other and solve for G:
[ \sqrt{10,000 – 3,600} = (1 – 0.002) \cdot \sqrt{10,000} + 0.002 \cdot \sqrt{10,000 – G} ]

Now, solve for G to find the amount Radha is willing to pay for insurance protection. The solution to this equation gives the value of G. Keep in mind that the square root function may introduce multiple solutions, and you should check if the solution aligns with the context of the problem (i.e., G should be non-negative and reasonable in the given scenario).