Find Price elasticity of demand in this example [closed]

Question

ln(Q) = 10-0.7ln(P), where P is price and Q is demand.

What is the price elasticity of demand?

Answer 1

Did you know you can write price elasticity $\varepsilon$ as $\varepsilon \equiv \frac{d \log Q}{d \log P}$?

(Indeed, $\frac{d \log Q}{d \log P} =\frac{dQ}{dP} \frac{P}{Q}$. Check out wiki on elasticity of a function if you want more detail!)

Using this "log notation" for elasticity, it is easy to see without putting pen to paper that in this example, $\varepsilon = -0.7$.

Answer 2

The price elacitiy of demand is $\frac{\partial Q}{\partial P}\cdot \frac{P}{Q(P)}$. To get Q(P) you have to write both sides of the equations as an exponent of the base e.

$$ e^{ln(Q)}=e^{10-0.7ln(P)} $$

$$ Q=e^{10}\cdot e^{-0.7ln(P)}\Rightarrow Q= e^{10}\cdot \left(e^{ln(P)}\right)^{-0.7}$$

$$Q(P)=e^{10}\cdot p^{-0.7} $$

Therfore

$$ \frac{\partial Q}{\partial P}=e^{10}\cdot (-0.7)\cdot p^{-1.7}$$

I think you can take it from here. If not, feel free to ask.