Calculus What Is the Original Text of Example 6(c) in Calculus by Robert A. Adams?

  • Thread starter Thread starter mcastillo356
  • Start date Start date
  • Tags Tags
    Text
AI Thread Summary
The discussion revolves around a specific example from the textbook "Calculus" by Robert A. Adams, focusing on the concept of average cost in economics. A user seeks clarification on a statement regarding production levels and average costs, particularly the phrase "because the cost is increasing at a rate lower than the average cost." The conversation highlights the distinction between average cost and marginal cost, with an explanation provided that when production increases slightly from 1000 units, the average cost per tonne decreases because the marginal cost (the cost of producing one additional unit) is lower than the current average cost. This relationship indicates that producing more units can lead to a lower average cost per tonne, as demonstrated through calculations comparing total costs at different production levels. The clarification helps the user understand the underlying economic principles.
mcastillo356
Gold Member
Messages
634
Reaction score
342
Hi, PF

I'm struggling with a sentence from the textbook "Calculus", by Robert A. Adams. At the second chapter, "Differentiation", seventh section, when it comes to talk about derivates in economics, at the example 6, the (c) question is answered in a way I don't understand. ¿Could anybody quote it the way is written originally, in English?

Greetings!
 
Physics news on Phys.org
In the 9th edition Example 6 does not have a (c) but Example 7 does

(c) If the production level x is increased slightly from x =1000, then the average cost per tonne will drop because the cost is increasing at a rate lower than the average cost. At x = 2000 the opposite is true; an increase in production will increase the average cost per tonne.
 
  • Informative
Likes mcastillo356
Thanks, caz!

caz said:
In the 9th edition Example 6 does not have a (c) but Example 7 does

(c) If the production level x is increased slightly from x =1000, then the average cost per tonne will drop because the cost is increasing at a rate lower than the average cost. At x = 2000 the opposite is true; an increase in production will increase the average cost per tonne.

I don't know if I should post a new thread. The question is: what does it mean "because the cost is increasing at a rate lower than the average cost"?
-cost means marginal cost?
-"rate"? What rate? How can I compare a rate with the average cost per tonne? Is the average cost per tonne another rate?
 
mcastillo356 said:
Thanks, caz!
I don't know if I should post a new thread. The question is: what does it mean "because the cost is increasing at a rate lower than the average cost"?
-cost means marginal cost?
-"rate"? What rate? How can I compare a rate with the average cost per tonne? Is the average cost per tonne another rate?
Let’s do the 1000 ton case

In (a) you calculated that if you bought 1000 tons it would cost you $10.60 per ton.

In (b) you calculated that the instantaneous cost was $9.40 per ton. This means if you bought a little bit more, that little bit more would cost you $9.40 per ton.

So if you bought 1000+h tons the cost would be
1000*10.6 + h*9.4 < (1000+h)*10.6 so the new average cost will be less than before
 
Last edited:
  • Like
  • Love
Likes berkeman and mcastillo356
Thank you, caz! Inmediately understood
 
  • Like
Likes Frabjous and berkeman
For the following four books, has anyone used them in a course or for self study? Compiler Construction Principles and Practice 1st Edition by Kenneth C Louden Programming Languages Principles and Practices 3rd Edition by Kenneth C Louden, and Kenneth A Lambert Programming Languages 2nd Edition by Allen B Tucker, Robert E Noonan Concepts of Programming Languages 9th Edition by Robert W Sebesta If yes to either, can you share your opinions about your personal experience using them. I...
Hi, I have notice that Ashcroft, Mermin and Wei worked at a revised edition of the original solid state physics book (here). The book, however, seems to be never available. I have also read that the reason is related to some disputes related to copyright. Do you have any further information about it? Did you have the opportunity to get your hands on this revised edition? I am really curious about it, also considering that I am planning to buy the book in the near future... Thanks!
I’ve heard that in some countries (for example, Argentina), the curriculum is structured differently from the typical American program. In the U.S., students usually take a general physics course first, then move on to a textbook like Griffiths, and only encounter Jackson at the graduate level. In contrast, in those countries students go through a general physics course (such as Resnick-Halliday) and then proceed directly to Jackson. If the slower, more gradual approach is considered...
Back
Top