I have a price function:
$$
\frac{8,100,000}{q^2+8,100}
$$
Where $q$ is quantity demanded.
How can I find the price elasticity when $q = 30$?
I know how to differentiate, but I'm just not sure what to differentiate… I'm used to having a demand function, not a price one.
eg:
$$
\frac{\%\text{ change in quantity}}{\%\text{ change in price}}
$$
Best Answer
The elasticity of demand is given by (dQ / dP)*(P/Q), where P is the price function and Q the demand. so you basically need the derivative of Q (at q=30) (with respect to P) multiplied by P/Q (at q=30). You have given your price as a function of quantity, but for this derivative, you will need it the other way around!
I'll leave the differentiation and algebra to you ;)!