Carol is obsessed about a new cryptocurrency called Cr4zYCrypto, which we will refer to as CC. Her friend David is obsessed about another one called D15cr33tD0114rz, which we will refer as DD. Both Carol and David have a starting wealth wo = $110,000. Each of the coins is priced at exactly $110,000 right now, so they're considering using all of their wealth to buy one of their preferred coins each. It is impossible to buy a fraction of either CC or DD; it is either buy one unit or nothing. They both expect that, with 50% probability, they will be able to sell their coins for $400,000 in just 6 months. But with 50% probability, the value will go to zero and they lose all their money. Their instantaneous utility is W u(W) = = 100000' where W is final wealth. Some values you may find useful: √1 = 1, √1.1 ≈ 1.05, √√2 ≈ 1.4, √√4 = 2
**Practice**
In order to alleviate their risks, they are considering a risk-sharing agreement. Carol would buy one CC and David would buy one DD. Six months from now, they would sell their coins, add up the total amount of money, and split it equally between them. Thus, if only one of the coins is successful, they would both still have some positive amount of money at the end. Assume that they can verify whether the other really made the investment. They know whether the investment is successful, since the price of the coin is public information, and they trust that the other will pay them as promised.
Which of the following statements is accurate?
A. They will not make that risk-sharing agreement.
B. Carol is willing to take the risk-sharing agreement, but David is not.
C. They may be willing to make that risk-sharing agreement, but it depends on information not given in the question.
D. They will surely make the risk-sharing agreement.
E. None of the statements above is correct.
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