You have $16,000 to invest in a mutual fund with a nav = $45. you choose a fund with a 4 percent front load, a 1 percent management fee, and a 0.25 percent 12b-1 fee. assume that the management and 12b-1 fees are charged on year-end assets. the gross annual return on the fund's shares was 9 percent. what was your net annual rate of return to the nearest basis point?

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.