Present Value of Multiple Annuities A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,000 per month for the next three years and then $2,000 per month for two years after that. If the bank is charging customers 7.5% APR, how much would it be willing to lend the business owner?

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.