Bill casler bought a $2,000, 9-month certificate of deposit (cd) that would earn 8% annual simple interest. three months before the cd was due to mature, bill needed his cd money, so a friend agreed to lend him money and receive the value of the cd when it matured. a) what is the value of the cd when it matures? b) if their agreement allowed the friend to earn a 10% annual simple interest return on his loan to bill, how much did bill receive from his friend?

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.