Christopher likes cupcakes (C) and muffins (M). His preferences can be represented by the utility function U(C, M) = C0.5M0.5. He received a gift basket with 16 cupcakes and 4 muffins, but when he was about to eat them, he found out his younger brother Dan had eaten 14 cupcakes and 2 muffins. Christopher made Dan buy what he'd eaten back. However, the bakery was out of muffins and Dan only bought cupcakes. How many cupcakes did Dan buy if, in addition to what he had not eaten from the basket, the new cupcakes provide Christopher with the same level of utility as the original gift basket?

What happens when a bank is required to hold more money in reserve?

Helen tells her nephew, bernard, that she will pay him $100 if he will stop smoking for six months. helen was hopeful that if bernard stopped smoking for six months, he would stop altogether. bernard stops smoking for six months but then resumes his smoking. helen will not pay him. she says that the type of promise she made cannot constitute a binding contract and that, furthermore, it was at least implied that he would stop smoking for good. can bernard legally collect $100 from helen

Rate of return douglas keel, a financial analyst for orange industries, wishes to estimate the rate of return for two similar-risk investments, x and y. douglas's research indicates that the immediate past returns will serve as reasonable estimates of future returns. a year earlier, investment x had a market value of $27 comma 000; and investment y had a market value of $46 comma 000. during the year, investment x generated cash flow of $2 comma 025 and investment y generated cash flow of $ 6 comma 770. the current market values of investments x and y are $28 comma 582 and $46 comma 000, respectively. a. calculate the expected rate of return on investments x and y using the most recent year's data. b. assuming that the two investments are equally risky, which one should douglas recommend? why?