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wolverine [178]
3 years ago
6

If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p

Mathematics
1 answer:
Nat2105 [25]3 years ago
7 0

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%

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