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

`\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%

Explanation:

Given that:

the number of units demanded
`q = pe^(-3p)`

Taking differentiations ; we have,

`(dq)/(dp)=e^(-3p)+p(-3e^(-3p))`

`(dq)/(dp)=(1-3)e^(-3p)`

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

`E(p) = (dq)/(dp)*(p)/(q)`

`E(p) =[(1-3)e^(-3p)]*[(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 :

`=(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%