Provide a mathematical proof for the general result that, given a linear average curve, the corresponding marginal curve must have the same vertical intercept but will be twice as steep as the average curve

  • $\begingroup$ Hi, welcome to Economics SE. We tend to ask users to give some evidence that they have tried to do things that look like homework questions before just posting a question. The guidelines are readily available to you in the help section. $\endgroup$ – Kitsune Cavalry Oct 8 '15 at 0:41

That comment said, I can provide an answer here.

Take an average cost function:

$$f(x) = mx + b$$ where x is output, b is the intercept, and m is the gradient.

So total cost is:

$$C(x) = x(mx + b) = mx^2 + bx$$

And that makes marginal cost the derivative of this function:

$$C'(x) = 2mx + b$$

Best of luck with your homework.

  • $\begingroup$ If you disagree with your own comment you don't have to say it, if you agree with the comment why do you answer? $\endgroup$ – Giskard Oct 8 '15 at 6:24
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    $\begingroup$ "We tend to ask users"... Sometimes we can give new people a break I think. $\endgroup$ – Kitsune Cavalry Oct 8 '15 at 14:33

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