You play a game where if the flip of a fair coin results in heads, you get $1,00

Question

You play a game where if the flip of a fair coin results in heads, you get $1,000; and nothing if it comes up tails. Answer each of the following questions:

a) What is the expected value of the game?

b) You’re offered $400 to not play the game. If you’re risk neutral (A=0) do you take the $400 or do you play the game? Why?

c) If you’re risk averse, what is the amount (specify amount using either <, >, =) you would need to be paid to NOT play the game?

d) If you’re risk seeking, what is the amount (specify $ amount using either <, >, =) you would need to be paid to NOT play the game?

e) If you’re risk neutral, what is the amount (specify $ amount using either <, >, =) you would need to be paid to NOT play the game?

Explanation / Answer

As event is a coin flip so chance of success is 0.5 i.e. 50%

So Probability of Success, Ps= 0.5; Probability of Failure, Pf= 0.5;

Amount received on Success, S= $1000; Amount received on Failure, F= $0;

a) Expected Value of game= S*Ps+ F*Pf= $500

b) If we are risk neutral i.e. we are neutral toward risk taking, we will not take $400 to not play the game as it is lower than the value of the game i.e. $500

c) If we are risk averse i.e. we avoid taking risk, we will prefer to take any amount =>$0(greater or equal to $0) as it is better than 50% of the game's outcome i.e. $0.

d) If we are risk seeking i.e. we love taking risk, we will need amount to take any amount >$1000(greater than $1000) in order to stop playing the game as it is better than 50% of the game's outcome i.e. $1000.

e) If we are risk neutral i.e. we are neutral toward risk taking, we will need amount to take any amount =>$500(greater than or equal to $500) as it is equal to the value of the game.

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