Micro question..

[Jackass]

Don't know where to begin with this one...could somebody be so kind as to help show me how to do this please?

Suppose a firms average cost curve is described by the equation AC = 2q^2 - 16q + 90, at what output level does the marginal cost curve cross the average cost curve?

does the marginal cost curve always cut the average cost curve at the minimum of average cost or can it be anywhere?

Any help very much appreciated.

noodler

Okay, I will tell you this much:

You have Average Cost now.



You need Marginal Cost.
Marginal Cost is Total Cost Differentiated.


So you need to get Total Cost first.......Given that AC = TC/Q....................

[Jackass]

Ok, so AC = TC / Q

therefore TC = 2q^3 - 16q^2 + 90q

TC differentiated to find MC = 6q^2 - 32q + 90

And to find intercept, put MC = AC

6q^2 - 32q + 90 = 2q^2 - 16q + 90

4q^2 = 16q

q = 4

So, is that the solution? Thanks for pointing me in right direction.

Is that the minimum of average cost or can AC intercept MC at any point?

noodler

MC will intersect the lowest point of the AC Curve as long as marginal costs are increasing IIRC.

I can't remember if there is a theoretical scenario where this would nto be the case. I think you'd have to consult the textbook to be sure.

[Jackass]

That's excellent, thank you, it seems you're correct re MC always intersecting AC at minimum point also. Would it be cheeky if I asked another question? Just to point me in the right direction again?

Production function is q = L^2

Find Marginal Cost..

I'm just confusing myself with the format and what formula to use...

So marginal cost is the derrivative of variable cost with respect to q.

The derrivative of variable cost with respect to q = dVC / dL . dL / dQ

dL / dQ = 2L? and I have to introduce the wage rate here...sorry, getting completely lost.

I'm not looking for someone to do my revision for me, just honestly attempting these question and confusing myself along the way, any help very much appreciated.

noodler

Yah there is only a marginal cost to the variable costs so 2L looks right to me.

Not too sure about introducing the wage rate bit. Was there more detail in the question?

[Jackass]

The question just reads:

A firm has a production function given by q = L2
Find an expression for the firm's marginal cost

and it gives 5 possible answers:

a. MC = wq-1/2
b. MC = 0.5w
c. MC = 0.5wq-1/2
d. None of these
e. MC = 0.5wq-2

I've been trying to use this guide, but I'm not able to decifer all of the values I need...

http://www.mcgrawhill.ca/college/olcsupport/mcconnell9/domath/marginalcostandmarginalproduct.html

noodler

I get (b). Although I am slightly rusty.

It seems to be pretty much done for you in the firts paragraph of your link.