Question

A. when going from a price of $160 per unit to a price of $140 per unit, what is the price elasticity of demand of gps units? -4

b. when going from a price of $140 per unit to a price of $160 per unit, what is the price elasticity of demand of gps units? -2.33
c. using the midpoint formula, what is the midpoint price elasticity of demand of gps units between a price of $140 per unit and a price of $160 per unit? -3
d. when going from a price of $40 per unit to a price of $20 per unit, what is the price elasticity of demand of gps units? -.13
e. when going from a price of $20 per unit to a price of $40 per unit, what is the price elasticity of demand of gps units? f. using the midpoint formula, what is the midpoint price elasticity of demand of gps units between a price of $20 per unit and a price of $40 per unit?

Answer 1

A. -4

b. -2.33

c. -3

d. -0.125

e. -0.11

f. -0.176

Step-by-step explanation:

Price elasticity of demand defies the degree of responsiveness of the quantity demanded for a good or service to changes in price when other factors remained unchanged. The price elasticity of demand is calculated as the ratio of the percentage change in the quantity demanded of a good or service to the percentage change in the price.

An elastic demand: elasticity ≥ 1 , indicating a high degree of responsiveness to changes in price.

Inelastic demand : Elasticities ≤ 1, correspond to a low degree of responsiveness to price changes.

Unitary elasticities equals one, indicating a proportional responsiveness of demand to changes in price.

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)`

A.

`A. Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (80-120)/(80) * (160)/(160-140)\\\\Elasticity = (-40)/(80) * (160)/(20) = -4`

b.

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (80-120)/(120) * (140)/(160-140)\\\\Elasticity = (-40)/(120) * (140)/(20) = -(7)/(3) = -2.33`

c. using the midpoint formula

`Percentage\ change\ in \ quantity = \frac {Q2-Q1}{(Q2+Q1)/2 } \\\\`

`Percentage\ change\ in \ Price = \frac {Q2-Q1}{(Q2+Q1)/2 }`

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (80-120)/((120 + 80)/2) * ((140+160)/2)/(160-140)\\\\Elasticity = (-40)/(100) * (150)/(20) = -3`

d.

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (360-320)/(320) * (40)/(20-40)\\\\Elasticity = (40)/(320) * (20)/(-20) = -(1)/(8) = -0.125`

e.

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (320-360)/(360) * (20)/(40-20)\\\\Elasticity = (-40)/(360) * (20)/(20) = -(1)/(9) = -0.11`

f.

`Elasticity = (percentage\ change\ in\ quantity)/(percentage\ change\ in\ price)\\\\Elasticity = (360-320)/((360 + 320)/2) * ((40+20)/2)/(40-20)\\\\Elasticity = (40)/(340) * (30)/(20) = -(3)/(17) = -0.176`

Answer 2

Answer: Elasticity of demand mesures the responsivness of quantit demanded to a change in the price of the product. It is calculated as,

`e=(Change in Q)/(Original Quantity) * (Original Price)/(Change in Price)`

a. P1 = $160 , P2= $140, Q1=80, Q2= 120

e=
`image`

b. P1 = $140 , P2= $160, Q1=120, Q2= 80

e=
`image`

c. Mid-point method is given by

`e=(Q2-Q1)/(Q1+Q2/2) * (P1+P2/2)/(P2-P1)`

So, we have

`image`

d. P1=$40, P2= $20, Q1= 320, Q2= 360

`image`

e. P1=$20, P2= $40, Q1= 360, Q2= 320

`image`

f. [tex] e= \frac{360 - 320}{360+320/2} * \frac{40+20/2}{20-40}

=\frac{40}{340} * \frac{30}{-20}

= - 0.17