You are a coin trader. You have $1,000,000, and today one coin costs $2000. Tomorrow the coin will either cost $1000 or $4000, each with equal probability. Assume the prices are constant all day and change instantly at midnight. For each of the following, give a strategy and why it’s correct: (a) If you want to maximize the expected amount of money you have tomorrow, what should you do? (b) If you want to maximize the expected number of coins you have tomorrow, what should you do?

Any risk-averse individual would always (Select all that applies) a) take a 30% chance at $100 rather than a sure $20. b) take a sure $20 rather than a 30% chance at $100. c) take a sure $2 rather than a 50% chance at $5 and a 50% chance at losing $1. d) take a 50% chance at $5 and a 50% chance at losing $1 rather than a sure $1.

**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.

Suppose that there is a 45 percent change that George's coffee shop will make $10000 in profits in January and a 45 percent chance it will make 0 profits and a 10 percent chance that it will make -$1000 in profits (i.e., it will lose $1000). Calculate the coffee shop's expected profits