# I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)with equal probability while the other coin is weighted so that it always lands H. Bothcoins are magical: if either is flipped and lands H then a \$1 bill appears in your wallet,but when it lands T nothing happens. You may only flip a coin once per period. Theinterest rate is i per period. You are risk-neutral and thus only concern yourself withexpected values (and not variance). For simplicity, in the questions below assumeyou will live forever.1. How much are you willing to pay for such a coin that you know is fair?2. How much are you willing to pay for such a coin that you know is weighted?3. I currently own the coins and know which is fair and which is weighted, but youcannot tell which is which. You may make an offer to purchase a coin of yourchoosing, which I am free to accept or reject. What is the most you are willingto offer? Explain how you arrived at this answer.

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I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)
with equal probability while the other coin is weighted so that it always lands H. Both
coins are magical: if either is flipped and lands H then a \$1 bill appears in your wallet,
but when it lands T nothing happens. You may only flip a coin once per period. The
interest rate is i per period. You are risk-neutral and thus only concern yourself with
expected values (and not variance). For simplicity, in the questions below assume
you will live forever.
1. How much are you willing to pay for such a coin that you know is fair?

2. How much are you willing to pay for such a coin that you know is weighted?

3. I currently own the coins and know which is fair and which is weighted, but you
cannot tell which is which. You may make an offer to purchase a coin of your
choosing, which I am free to accept or reject. What is the most you are willing
to offer? Explain how you arrived at this answer.

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Step 1

1:
For a fair coin, the chance for getting a Head H as well as chance for getting a tail T is the same. The probability of getting the desired value from flipping the fair coin is thus equal to half. Thus, when the coin flips to give a H, it would generate \$1 and when it lands on T, nothing will be received by the individual. Thus, the value that is expected to receive from getting a H multiplied with the probability of winning determines the willing to pay price by the individual. This means that the individual will be willing to pay \$0.50 for the fair coin.

Step 2

2.

The weighted coin always lands on the H and that means the chance of winning the amount of \$1 is hundred percent. The individual can receive the price amount at all the tria...

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