Answer:
\(E = -pb\)
Step-by-step explanation:
The Elasticity(E) of demand at a unit price of p is given by:
\(E= (\frac{p}{q}) \cdot (\frac{dq}{dp})\)
As per the statement:
A general exponential demand function has the form :
\(q = Ae^{-bp}\)
where, A and b is non zero constants.
Using derivative formula:
\(\frac{d}{dx}(e^{-x})= -e^{-x}\)
First find the derivative of q with respect to p.
\(\frac{dq}{dp} = -Ab \cdot e^{-bp}\)
⇒\(\frac{dq}{dp} = -b \cdot Ae^{-bp}\)
Using \(q = Ae^{-bp}\)
⇒\(\frac{dq}{dp} = -bq\)
then;
\(E = \frac{p}{q} \cdot (-bq) = -pb\)
⇒\(E = -pb\)
Therefore, a formula for the price elasticity E of demand at a unit price of p is, \(E = -pb\)
