Price Elasticity, Partial Derivative

levijohnson · Oct 20, 2013

Hi all,

I've got a question regarding a price elasticity problem and a partial derivative.
That's what's given for the exercise:

Printed exercise text reading: Exercise 4: Emily always spend a third of her income on clothing. a) What is the income elasticity of Emily's demand? b) What is the price elasticity of Emily's demand?

So, first of all we calculate all the demand with the given information. Which is:

Text derivation: Emily spends one third of budget B on clothes, so px = B/3, where p is price and x is quantity demanded, giving demand x = B/(3p).

And then we come to the actual problem. (4. b) )

$Worked solution text: price elasticity of demand defined as partial derivative of demand x with respect to price p times p/x; for Emily's case, the chain of fractions with B, 3p^2 and p/(B/3p) simplifies to -1/(3p^2) times 3p^2 = -1, so the elasticity is -1.$

How do they get the partial derivative here? I assume that they are using the quotient rule, right? I would be really glad for a step by step explanation.

Thank you so much!

Crake · Oct 20, 2013

Hello there,

You should write your questions (Using the template btw, which you did not use!) instead of showing us images. This is because PF can't be sure that those images will stay up, and if they don't, then this thread will be of no use.

I believe somewhere in the PF guidelines, you can read what I just said.

Price Elasticity, Partial Derivative

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