Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built the machine wi1l last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. a. If the interest rate is 9.5% per year, what should your buddy do? b. How would your answer change if the machine takes one year to build?

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.