Question

A general exponential demand function has the form q = Ae−bp (A and b nonzero constants). (a) Obtain a formula for the price elasticity E of demand at a unit price of p.

Answer 1

E = (p/q)(dq/dp) 

dq/dp = -bAe^(−bp) 
(p/q)(dq/dp) = [p/Ae^(−bp)] (-bAe^(−bp)) 
                    = -pb

Answer 2

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, $E = -pb$