9781118041581

Summary 61

Suggested References

The following references provide advanced treatments of marginal analysis using differential calculus.

Baldani, J., J. Bradford, and R. Turner. Mathematical Economics.Fort Worth, TX: Cengage Learning,

2004.

Besanko, D., and W. R. Braeutigam. Microeconomics. New York: John Wiley & Sons, 2010.

Valuable references on optimization methods include:

Fourer, R., and J.-P. Goux. “Optimization as an Internet Resource.”Interfaces(March–April 2001):

130–150.

Fylstra, D., et al. “Design and Use of the Microsoft Excel Solver.” Interfaces(September–October

1998): 29–55.

Can a disastrous decision result from mistaking a minimum for a maximum? For a dramatic example, see:

Biddle, W. “Skeleton Alleged in the Stealth Bomber’s Closet.” Science,May 12, 1989, 650–651.

A guide to optimization software and resources on the World Wide Web is provided by H. D. Mit-

telmann, “Decision Tree for Optimization Software.” http://plato.asu.edu/guide.html, 2007.

1. The revenue function is R 340Q  .8Q^2.


2. The profit function is R C  120 240Q  .8Q^2.


3. At Q 100,  120 (240)(100)  .8(100)^2 15,880.
   At Q 99,  120 (240)(99)  .8(99)^2 15,799.2.
   Thus, M(15,880 15,799.2)/(100 99) 80.8.


4. Marginal profit is Md/dQ  240 1.6Q. Setting this equal to zero
   implies that 240 1.6Q 0, or Q 150.


5. Setting MR MC implies that 340 1.6Q 100. Therefore, Q 150.
   Substituting Q 150 into the price equation implies that P  340 
   .8(150) 220.


6. a. Plugging each quantity value into the inverse demand equation
   generates the corresponding market-clearing price.
   b. From the price equation P $294 35Q, it follows that MR 
   $294 70Q. Setting MR MC $126 implies Q 2.4 million
   units and P $210.
   c. Adding $100 in e-book net revenue means that Amazon’s MR equation is
   now: MR $394 70Q. Setting MR MC implies Q 3.829 million
   units. In order to sell this volume, Amazon must lower its price to:
   P  294 (35)(3.829) $160. (Note:To find this price, we have used
   the unchangeddemand curve P $294 35Q.) By lowering its price
   margin, Amazon is deliberately sacrificing profit at the point of sale. But
   it is more than making up for it by way of additional e-book profit.

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