Question

The manufacturers of the X brand increase the price of their product from $ 3 to $ 5 dollars per unity. As a result, sales go down from 2,000 to 1,000 units per month for a year. Calculate the average elasticity of demand for the X mark among the price demand combinations. Is the demand for the X brand elastic or inelastic between the two brands? Present your graph.

I put this question two times and i keep getting different results. Help!!!! :)

Answer 1

Answer
First wee go towards making of the demand function
We have two points on a line, and a demand function is a form of
P=a+bQ

b=slope of the line
the slope of a line =(change in Y-axis variable )/change in X-axis variable
Generally Price of on the Y-axis and quantity on the X-axis

The provided two points are (2000,3) and (1000,5)

b=(5-3)/(1000-2000)=-(2/1000)=-0.002
now the equation is
P=a-0.002Q
using one point to find a
(2000,3)
3=a-0.002*2000
3=a-4
a=7
Now the demand function is
P=7-0.002Q
Using the second point to check the demand equation
If Q=1000 then P should be $5
P=7-0.002*1000=5
and it is, so the demand curve is
P=7-0.002Q

We can draw the curve by joining these two points and extending towards each axis.

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there are two fromulas used to find elastcity

Mid point method:
Elasticity of demand=(change in quantity/average quantity)/(change in price/average price)
Change in quantity=1000-2000=-1000
average quantity=(1000+2000)/2=1500
change in price=5-3=2
average price=(5+3)/2=4
Elasticity of demand=(-1000/1500)/(2/4)=-1.33333333=-1.33
The elastcity of demand is -1.33 and it is elastic as the elastcity is below -1.
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Percentage change/point slope formula:
elastcity=%change in quantity/%change in price

%change in quantity=((new Q-old Q)/old Q)*100=((1000-2000)/2000)*100
=-50%

%change in price =((new P-old P)/old P)*100
=((5-3)/3)*100
=66.6666667

Elasticity =-50/66.6666667
=-0.75

The elasticity is inelastic as the elasticity is above -1.

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The question asks for average elasticity and it means it is mid-point elasticity so the demand is elastic.