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Semmy [17]
3 years ago
5

3) For a certain good we have LaTeX: q=f\left(p\right)=200e^{-0.4p}q = f ( p ) = 200 e − 0.4 p.

Mathematics
1 answer:
disa [49]3 years ago
5 0

Answer:

(a)20

(b)Elastic

(c)8

(d) Elastic

Step-by-step explanation:

Elasticity of demand(E) indicates the impact of a price change on a product's sales.

The general formula for an exponential demand curve is given as:

y=ae^{-bp}

Given the demand curve formula

q=f\left(p\right)=200e^{-0.4p}

The formula for Elasticity of demand, E

E = -\dfrac{p}{q}\dfrac{\text{d}q}{\text{d}p}

(a)When Price,  p = $50

p=50

q=200e^{-0.4*50}=200e^{-20}

\dfrac{\text{d}q}{\text{d}p}=-0.4*200e^{-0.4p}=-80e^{-0.4p}

Therefore:

E = -\dfrac{50}{200e^{-20}}*-80e^{-0.4*50}\\=\dfrac{1}{4e^{-20}}*80e^{-20}\\\\E=20

(b)At p = $50, Since elasticity is greater than 1, the demand is elastic.

An elasticity value of 20 means that a 1% increase in price causes a 20% decrease in demand.

(c)At p=$20

p=20

q=200e^{-0.4*20}=200e^{-8}

\dfrac{\text{d}q}{\text{d}p}=-0.4*200e^{-0.4p}=-80e^{-0.4p}

Therefore:

E = -\dfrac{20}{200e^{-8}}*-80e^{-0.4*20}\\=\dfrac{1}{10e^{-20}}*80e^{-20}\\\\E=8

(d)At p = $20, the demand is elastic.

An elasticity value of 8 means that a 1% increase in price causes a 8% decrease in demand.

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