Question

If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p
(a) Find the price elasticity of demand by using the differentials definition of elasticity. Fully simplify your answer.
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.

Answer 1

Answer:

$\mathbf{E(p) = 1 - 3p}$

the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%

Step-by-step explanation:

Given that:

the number of units demanded $q = pe^{-3p}$

Taking differentiations ; we have,

$\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})$

$\dfrac{dq}{dp}=(1-3)e^{-3p}$

Now; the price elasticity of demand using the differentials definition of elasticity  is:

$E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}$

$E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}]$

$\mathbf{E(p) = 1 - 3p}$

(b)   Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.

The estimate of the percentage change in price is :

$=\dfrac{2.10-2.00}{2.00}*100 \%$

= 5%

From (a)

$\mathbf{E(p) = 1 - 3p}$

Now at p = $2.00

E(2) = 1 - 3 (2.00)

E(2) = 1 - 6

E(2) = -5

The percentage change in q = -5 × 5%

The percentage change in q = -25%

Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%