Question

Move point A to the correct position on the demand curve when price is $40. Next move point B to the correct position on the demand curve when price is $10. Now, consider a movement along this demand curve from A to B.Use the midpoint formula to calculate the percentage change in quantity demanded between A and B. (Include a negative sign if the answer is negative; round to the nearest integer.)Next, use the midpoint formula to calculate the percent change in price between A and B. (Include a negative sign if the answer is negative; round to the nearest integer.)What is the price elasticity of demand between these two points? (Include a negative sign if the answer is negative; round to two decimals.)

Answer 1

Answera and Explanation:

% change in quantity demanded = (600 - 300)/[(600 + 300)/2]

                                                      = 67%

Therefore, The % change in quantity demanded is 67%.

% change in price = (10 - 40)/[(40 + 10)/2]

                              =   -120%

Therefore, The % change in price is -120%

price elasticity of demand

= % change in quantity demanded/% change in price

= 67/-120

= -0.558

Therefore, The price elasticity of demand is -0.558.

Answer 2

The price elasticity of demand would be -0.558 when the price changes from $40 to $10 by using the formula of midpoint.

What is the price elasticity of demand?

A good's price elasticity of demand is a measurement of sensitiveness the quantity demanded is to its price. As per the law of demand, When the price rises, the quantity demanded falls for almost any good, but it falls more for some than for others.

Computation of price elasticity of demand:

Given,

Q1= 600,

Q2= 300,

P1= $40, and

P2=$10.

Percentage Change in Quantity Demanded:

$\%\triangle\text{Quantity Demanded}=\dfrac{\frac{ Q_1-Q_2}{Q_1+Q_2}}{2}\\\\\\\%\triangle\text{Quantity Demanded}=\dfrac{\frac{(600-300)}{(600+300)} }{2}\\\\\\\%\triangle\text{Quantity Demanded}= 67\%.$

Percentage Change In Price:

$\%\triangle\text{Price}=\dfrac{\frac{ P_1-P_2}{P_1+P_2}}{2}\\\\\\\%\triangle\text{Price}=\dfrac{\frac{(10-40)}{(10+40)} }{2}\\\\\\\%\triangle\text{Price}= -120\%.$

Then, The Price Elasticity Of Demand :

$\text{Price Elasticity Of Demand} =\dfrac{ \%\triangle \text{Quantity Demanded}}{ \%\triangle \text{Price}} \\\\\\ \text{Price Elasticity Of Demand} =\dfrac{67\%}{(-120\%)}\\\\\\ \text{Price Elasticity Of Demand} =-0.558.$

Therefore, the price elasticity of demand would be -0.558.

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