Question

There are 2 coins in a bin. When one of them is flipped, it lands on heads with probability .6, and when the other is flipped, it lands on heads with probability .3. One of these coins is to be randomly chosen and then flipped. Without knowing which coin is chosen, you can bet any amount up to 10, and you then either win that amount if the coin comes up heads or lose it if it comes up tails. Suppose, however, that an insider is willing to sell you, for an amount C, the information as to which coin was selected. What is your expected payoff if you buy this information? Note that if you buy it and then bet x, you will end up either winning x − C or −x − C (that is, losing x + C in the latter case). Also, for what values of C does it pay to purchase the information?

Short answer

In the given information the answer is

$\frac{1}{2}(0.2x-C)+\frac{1}{2}(-0.4x-C)=-0.1x-C$

we see that there do not exist $xandC$such that the expression above is equal to 0.so, there is no fair price for the information

Step-by-step solution

:Given Information

There are 2 coins in a bin. When one of them is flipped, it lands on heads with probability .6, and when the other is flipped, it lands on heads with probability .3. One of these coins is to be randomly chosen and then flipped. Without knowing which coin is chosen, you can bet any amount up to 10, and you then either win that amount if the coin comes up heads or lose it if it comes up tails .

:Explanation

Suppose that the insider tell us that the first coin has been choosen. then the expected payoff is

$0.6(x-C)+(-x-C)0.4=0.2x-C$

On the other hand, if the insider tell us that the second coin has been choosen, then the expected payoff is

$0.3(x-C)+(-x-C)0.7=-0.4x-C$

for the end ,the expected payoff in total is

$\frac{1}{2}(0.2x-C)+\frac{1}{2}(-0.4x-C)=-0.1x-C$

so we see that there do not exist x and C such that the expression above is equal to 0 . So, there is no fair price of the information.

Final Answer

The answer is$\frac{1}{2}(0.2x-C)+\frac{1}{2}(-0.4x-C)=-0.1x-C$