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Logic Puzzle in Microeconomics

So today in microeconomics we were given a logic puzzle to solve and if you got the right answer you got a cash reward, and I got it right.

The question went like two people are each given an envelope and inside there is either $5, $10, $20, $40, $80, or $160, and they are told one person had double the other so for example if one person has $20 the other person has $10 or $40. After given the envelopes they are given the option to either trade or leave but they can not tell the other person their amount of money until a trade has taken place. Why is it better to just leave with the money you are first given.

The way I decided to answer it was that you should just leave because if you try and trade you will just end up with less than you started with because the other person will only want to trade if they have the lower number out of the two. So for example, if you are given the $80 one and the other person leaves you can assume they have the $160 but if they stay and want to trade the probably only have $40. And if you end up with the $5 you should probably just leave because no one will trade will you unless they are feeling very risky. And I didn’t have the idea fully planned out to explain every number but it was enough that I won and got $5 out of it so that was pretty exciting.

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