Which one of the following statements correctly states a relationship?
a. time and future values are inversely related, all else held constant.
b. interest rates and time are positively related, all else held constant.
c. an increase in the discount rate increases the present value, given positive rates.
d. an increase in time increases the future value given a zero rate of interest.
e. time and present value are inversely related, all else held constant.

Which of the following best explains why a large company can undersell small retailers? a. large companies can offer workers lower wages because they provide more jobs. b. large companies can pay their employees less because they do unskilled jobs. c. large companies can negotiate better prices with wholesalers. d. large companies have fewer expenses associated with overhead.

Xinhong company is considering replacing one of its manufacturing machines. the machine has a book value of $39,000 and a remaining useful life of 5 years, at which time its salvage value will be zero. it has a current market value of $49,000. variable manufacturing costs are $33,300 per year for this machine. information on two alternative replacement machines follows. alternative a alternative b cost $ 115,000 $ 117,000 variable manufacturing costs per year 22,900 10,100 1. calculate the total change in net income if alternative a and b is adopted. 2. should xinhong keep or replace its manufacturing machine

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.