Katie buys a new pair of sunglass for spring break. within an hour of arriving home, her dog chews her new purchase and ruins them. she heads back to the store and asks if there is any way to have them repaired. the clerk promptly takes the glasses and hands her a new pair. she is shocked at how the store went above and beyond her expectations and plans to shop there from now on. this is an example of the level of a product.

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.