Question

Peter is risk-neutral.

He can invest an amount of $x into a project.

The project is successful with probability \sqrt{x/1600}, where x is the number of dollars Peter has invested.

If successful, the project pays Peter $3200, otherwise nothing.

The project takes place in a country on the verge of civil war. Peter thinks there is a 10% chance that a civil war will break out so that Peter will be unable to claim any payments of a successful project, leaving Peter with nothing.

What is the optimal investment into the project if Peter is maximizing expected payoff?

Possible answers: (0, 36, 49, 81, 108, 252, 288, 324, 432, 594, 729, 810, 1296, 1336, 1801, 2025, 2525, 2732, 2916, 3281, 4900, 5625, 8100, 9000)

Answer 1

There are 4 conditions :-

- war with successful project

- war with unsuccessful project

- no war with successful project

- no war with unsuccessful project

Out of these unsuccessful project are of no worth.

Out of remaining 2, war will give nothing so we have only one condition for expected payoff, No war with successful project so that our expected payoff shall be:-

= .9*3200*X^.5/40

Hence after putting the values provided, we can calculate expected payoff.

Here I believe that probability is given wrong as it cannot be more than one, hence please check ones the probability for successful project and let me know for any further clarifications.

Thank you!!