Problem involving Marginal cost and Average cost

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thatguy47

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The answer I got for this problem is two off of what it is in the back of the book. I probably just did something wrong. Let me know what answer you get for this:

The average cost of producing x units of a commodity is c(x) = 21.4 - 0.002x. Find the marginal cost at a production level of 1000 units.

All I did was solve the equation >>> c(1000) = 21.4 - 0.002(1000) and got 19.4 but the answer in the back is $17.40 per unit so I must of done something wrong.
 
thatguy47 said:
The average cost of producing x units of a commodity is c(x) = 21.4 - 0.002x. Find the marginal cost at a production level of 1000 units.
Click to expand...
Is "marginal cost" really defined in your book to be the same as "average cost"...?

Eliz.
 


I learned that the rate of change of production cost with respect to number of units produced is the marginal cost.

Too bad c(x) is the average cost (whatever that means), instead of the production cost. If c(x) were the production cost, then the original poster could take its derivative to get the marginal cost function.

~ Mark :|

 
Re:

stapel said:
thatguy47 said:
The average cost of producing x units of a commodity is c(x) = 21.4 - 0.002x. Find the marginal cost at a production level of 1000 units.
Click to expand...
Is "marginal cost" really defined in your book to be the same as "average cost"...?

Eliz.
Click to expand...

According to our book "If the average cost is a minimum then marginal cost = average cost".

Also, c(x) = C(x)/x = C'(x) C(x) = the cost function

.....working on problem......solved!

I figured out how to do it. If c(x) = 21.4 - 0.002x is the average cost then C(x) must be 21.4x - 0.002x^2 . This is because to find average cost you divide C(x) by x. To find C(x) you just multiply c(x) by x. To find marginal cost I take C'(x) = 21.4 - 0.004x so C'(x) = 17.4
 
Re: Re:

thatguy47 said:
According to our book "If the average cost is a minimum then marginal cost = average cost".
Click to expand...


"If the average cost is a minimum of what?", I wonder.

c(x) is linear.

c(10000) is much smaller than c(1000).

Anyways, good job Guy on reading your book and figuring out the exercise.

 
All it says is:

This principle is plausible because if our marginal cost is smaller than our average cost, then we should produce more, thereby lowering our average cost. Similarly, if our marginal cost is larger than our average cost, then we should produce less in order to lower our average cost.
 
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