Noelle's diamond ring was stolen in 2017. she originally paid $16,000 for the ring, but it was worth considerably more at the time of the theft. noelle filed an insurance claim for the stolen ring, but the claim was denied. because the insurance claim was denied, noelle took a casualty loss for the stolen ring on her 2017 tax return. in 2017, noelle had agi of $80,000. after noelle threatened legal action, in early 2019, the insurance company had a "change of heart" and sent noelle a check for $9,600 for the stolen ring. the per-event floor is $100. what is the proper tax treatment of the $9,600 noelle received from the insurance company in 2019? noelle should the amount of $ .

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.