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

[mcastillo356]

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!

 

[Frabjous]

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.

 

[mcastillo356]

Thanks, caz!

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?

 

[Frabjous]

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

 

[mcastillo356]

Thank you, caz! Inmediately understood