The manager informs them that the room rate is $30, so each man pays $10 and they go up to bed. about an hour later the manager’s conscience makes him feel bad because the room rate is really only $25. he calls the bellboy, gives him 5 $1-dollar bills and tells him to go to the room and refund the salesmen the amount he overcharged them. on the way up the bellboy starts thinking about how hard it will be to split 5 bills three ways and decides that since they don’t know the real room rate anyway, he will refund each of them $1 and he will keep $2 for himself. but now there is a mystery. each of the salesmen paid $9 for the room for a total of $27; the bellboy has $2, making $29; who got the other dollar?

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.