# How to calculate elasticity from a demand function? [closed]

PROBLEM PLEASE CLICK ---I've added a picture of the problem I am trying to solve, to make it easier to understand.

With this sort of problem, I do not understand where the numbers needed for the elasticity formula should come from with just having a demand function.

a) Calculate the elasticity of demand with respect to price at p=6

c) Calculate (with the computed elasticity value) the estimated change in demand after a rise in prices of 20% (base price p = 6 ).

also with c)is all i do to calculate multiply the result of a) with the 20%?

## closed as off-topic by Strants, Alexander Gruber♦Apr 11 at 16:39

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• Why do you think one needs more than the demand function? Are you not familiar with the definition of elasticity or how to differentiate (as in calculus)? – Lee David Chung Lin Apr 9 at 1:21

$$e= \frac{\Delta q/q}{\Delta p/p} = \frac{dq}{dp}\times \frac{p}{q},$$
where $$q=q(p)$$ is demand as a function of price.
In your case $$q(p)=10-p/2$$, and $$\frac{dq}{dp} = -1/2$$ so that $$e=\frac{-p}{2q}.$$ For $$p=6$$ and $$q=10-6/2=7$$, elasticity $$e = -6/(2\times 7) = -3/7$$. You can decide whether this is the case of elastic or non-elastic demand.
The estimated change in demand after a rise in prices of 20% (base price p = 6 ) is $$\Delta q= \frac{e q \Delta p}{p} = \frac{-3/7 \times 7 \times 0.2}{6}=-0.1$$