an agent must choose between 1 and 100 boxes to open. One of the boxes contains

Question

an agent must choose between 1 and 100 boxes to open. One of the boxes contains 1 a bomb, and the bomb is equally likely to be in each of the 100 boxes. If the agent opens a box with a bomb in it then they earn $0. Otherwise, the agent earns $1 for every box opened. For example, if an agent opens 18 boxes they are effectively selecting the lottery (18, 0.82; 0, 0.18). Prove that a risk neutral agent should open 50 boxes. [Hint: Recall that for a risk neutral agent, their certainty equivalent of a lottery is equal to the expected value of the lottery. Furthermore, an agent should select the lottery for which they subjectively ascribe the highest certainty equivalent.]

Explanation / Answer

Based on the theory of neautrality an individual:-

a) is not for or against taking risks hence termed as risk neutral.

c) wishes to maximise returns for 50 percent chances taken.

d) takes risks in proportion to the higher expected/guaranteed return.

Therefore, he must open 50 boxes to maximize returns & reduce instances of errors.

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