You would like to purchase a home and are interested to find out how much you can borrow. When your lender calculates your debt to income ratio, he determines that your maximum monthly payment can be no more than $2,231. You would like to have a 30 year fully- amortizing loan and the interest rate offered on such a loan is currently 4%. Given these constraints, what is the largest loan you can obtain? Round your answer to the nearest cent (e. g. if your answer is $600,000.0134, enter 600000.01).

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.