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

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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.
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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!
 
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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.
 
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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
 
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Thank you, caz! Inmediately understood
 
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