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