Adams is selling his property to katter for $94,000, and katter is assuming an existing mortgage at 4 1/2% interest per annum, with an unpaid balance of $9,200. mortgage payments are due the first of each month and include interest up to, but not including, the day of payment. the last payment was made march 1, and settlement is to be march 26. compute the interest proration that will be credited to the buyer, using a 365-day year and holding the buyer responsible for the day of closing.

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.