Adams Corporation owns and operates two manufacturing facilities, one in State X and the other in State Y. Due to a temporary decline in the corporation’s sales, Adams has rented 20% of its Y facility to an unaffiliated corporation. Adams generated $1,000,000 net rental income and $5,000,000 income from manufacturing. Adams is incorporated in Y. For X and Y purposes, rental income is classified as allocable nonbusiness income. By applying the statutes of each state, Adams determined that its apportionment factors are .65 for X and .35 for Y. Adams’s income attributed to X is:

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.