Sky Masterson warned Nathan Detroit to avoid sucker bets lest he get cider

1: Sky Masterson warned Nathan Detroit to avoid sucker bets lest he get cider in his ear. One obvious truth about betting, which underscores Sky's advice, is that one person's gain must be someone else's loss. Since Nathan won't play ball, Sky recruits Sister Sarah Brown. Suppose Sky and Sister Sarah are presented with two envelopes full of money. Each envelope contains $5, $10, $20, $40, $80, or $160, and both know this. They also know that one envelope contains exactly twice the amount of money in the other envelope. One envelope is given to Sky and the other to Sister Sarah. Each opens the envelope to see the amount of money but does not share that information with anyone. Subsequently, each person is given the opportunity to switch envelopes; if both want to switch, we let them.

Assume the risk is negligible for monetary amounts this small. Keeping in mind that one of this week's topics is expected value, should either or both people offer to switch? Write up your thoughts and final answer in no more than half a page.

2:

Consider health care in the United States. For simplicity, suppose we divide the entire population into two categories: sick people and healthy people. With this as the starting point, think about the two ends of the health-care spectrum: the government mandates coverage for everyone versus the market determines who is covered and to what degree.

• Universal health insurance (i.e., every person is insured, no questions asked) would solve the adverse selection problem immediately. Explain how. Keep it simple. Do not get sidetracked into a discussion of logistics, enforceability, etc. Just assume every person will be insured. Keep this part of your answer to less than half a page.
• Allowing a free market of health insurance companies to provide health insurance would attack the moral hazard problem. Explain how. Keep it simple. Keep this part of your answer to less than half a page.
• Discuss a mix of the two alternatives. Is your "mix" superior to either of the two provided alternatives? Keep in mind that the answer here could go on forever. Keep it to less than half a page.