Harold owns several gas stations. he realizes that among the several risks associated with this type of business is the risk of minor damage to cars from dirty or contaminated fuel. he also knows that there is a small chance of a major loss if a fire occurred at one of his gas stations. harold wants to control his insurance costs while still maintaining a reasonable risk management program. he is considering self-insurance. if he decides to use this approach, he will probably:

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.