As the price of gummy bears rises from $2.65 to $3.05, what is the price elasticity of demand of (i) sugar-free gummy bears and of (ii) ordinary gummy bears? use the midpoint method and specify answers to one decimal place.

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18-03-2020
Business

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As the price of gummy bears rises from $2.65 to $3.05, what is the price elasticity of demand of (i) sugar-free gummy bears and of (ii) ordinary gummy bears? use the midpoint method and specify answers to one decimal place.

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thaovtp1407 thaovtp1407 · Answer 1 · 2020-03-22T04:03:07+01:00

Answer:

Explanation:

Please have a look at the attached photo below

We know the formula of the price elasticity of demand:

percentage change of quantity demanded/percentage change of price

Given:

P1: $2.65 => D1 (quantity sugar-free gummy bears) = 181 and O1 (quantity ordinary gummy bears) =485

P2: $3.05=>D2 (quantity sugar-free gummy bears) = 157 and O2 (quantity ordinary gummy bears) =273

So:

[tex]E_{1}[/tex] = %ΔD / %ΔP

= (ΔD/ [tex]\frac{1}{2}[/tex](D1+D2) ) / (ΔP/ [tex]\frac{1}{2}[/tex](P1+P2))

= (181-175) / [tex]\frac{1}{2}[/tex] ( 157+181 ) : (3.05 -2.65)/ [tex]\frac{1}{2}[/tex] ( 3.05 +2.65 )

= [tex]\frac{3}{89}[/tex] : [tex]\frac{8}{57}[/tex] = 0.24

[tex]E_{2}[/tex] = %ΔO / %ΔP

= (ΔO/ [tex]\frac{1}{2}[/tex](O1+O2) ) / (ΔP/ [tex]\frac{1}{2}[/tex](P1+P2))

= (273-485) / [tex]\frac{1}{2}[/tex] ( 273+485) : (3.05 -2.65)/ [tex]\frac{1}{2}[/tex] ( 3.05 +2.65 )

= [tex]\frac{-212}{739}[/tex] : [tex]\frac{8}{57}[/tex] =- 3.9

TonieCee TonieCee · Answer 2 · 2020-03-22T04:08:07+01:00

Answer: In order to answer this question, a table showing different prices and quantities demanded of sugar-free gummy bears and of ordinary gummy bears will be added in the explanation section.

Explanation: from the table we can see that the quantities that correspond to $2.65 and $3.05 are 175 and 157 respectively for sugar-free gummy bears, and 379 and 273 respectively for ordinary gummy bears.

Using the midpoint formula, we will calculate thus:

Price Elasticity of demand for sugar-free gummy bears.

P2 - P1/(P2 + P1/2)

= 3.05 - 2.65/(3.05 + 2.64/2)

= 0.4/2.85

= 0.14

For sugar-free gummy bears:

Q2 - Q1/(Q2 + Q1/2)

= 157 - 175/(157 + 175/2)

= -18/166

= -0.11

Price elasticity = change in quantity demanded/change in price

= -0.11/0.14

= -0.8

For ordinary gummy bears:

Q2 - Q1/(Q2 + Q1/2)

= 273 - 379/(273 + 379/2)

= -106/326

= -0.33

Price elasticity = -0.33/0.14

= -2.4

From the calculations above, we can see that their price elasticities are negative i.e. -0.8 and -2.4, this means that quantity demanded reduced when price increased, and that the demand for both types of gummy bears was elastic.