Elasticity

• Oct 19th 2012, 09:41 PM
arcticreaver
Elasticity
I need help with a problem.

the question is q^2+2p^2=35

I know that the E(q) is -p/q dp/dq

however in this case i do not know how to solve for q

can someone help me with this?
• Oct 20th 2012, 12:35 AM
tom@ballooncalculus
Re: Elasticity
'E(q)' suggests elasticity of demand, which suggests your derivative quotient is upside down:

Quote:

Originally Posted by the above wiki page under 'point-price elasticity'
In other words, it is equal to the absolute value of the first derivative of quantity with respect to price (dQ/dP) multiplied by the point's price (P) divided by its quantity

So you do want to solve for dq/dp after differentiating implicitly. Have you done that?

Spoiler:
Just in case a picture helps...

http://www.ballooncalculus.org/draw/implicit/five.png

... where (key in spoiler) ...

Spoiler:
http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case p), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

The general drift is...

http://www.ballooncalculus.org/asy/maps/diffChain.png

Then you have E(q) in terms of p and q, i.e. for any particular point on the demand/price curve.

So, not sure why you want to solve for q. But if I've mis-read, please explain / supply more detail.

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• Oct 20th 2012, 08:25 AM
arcticreaver
Re: Elasticity
that's just the thing, the book give the E(q) = 2p^2/2p^2-35 and i'm not sure how it came to this....