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I am stuck at a very simple problem:

Suppose, I am running out of insurance, and as a result, I am incurring a the cost of A with event 1 + the cost of B with event 2. Now, I go ahead and buy an insurance that will protect me from event 1, but will incur me a total cost of C. I will remain vulnerable to Event 2.

What is the total profit I am receiving from making the investment.

Logical calculation is, Prior total cost: A+B New total cost: B+C Total profit: (A+B)-(B+C) = A-C

But my mind is constantly pesking me with the total profit to be: A-B-C.

I am essentially doing cost-benefit analysis. Can someone please tell me where I am wrong?

I know my benefit function to be A, and not A-B. Please indicate what is wrong.

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This feels like trying to read your mind, so I’m probably wrong. I will venture an answer regardless :D . I think that what is happening is that the benefit from buying the insurance is certainly the reduction in exposure: A-C. However maybe you are thinking about the remaining exposure after buying the insurance, in that case it is (A-C) + B. So I think you are thinking about the total costs after buying insurance while the question was asking about the change in costs. I prefer the term exposure, but I thought that using your terms will make the exposition clear.

P.S. I hope it is understood that we are not literally adding costs, since they occur in different states of the world, but rather using it as a short hand notation to focus on the relevant issues.

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  • $\begingroup$ Excellent answer. $\endgroup$ – Eval May 17 '19 at 15:22

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