Hale's tv production is considering producing a pilot for a comedy series in the hope of selling it to a major television network. the network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. at this point in time, hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $100,000. hale's decision alternatives and profits (in thousands of dollars) are as follows:

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.