Graph demand data & use midpoint formula

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Price Elasticity Demonstration

Elasticity Lecture © 2008 James Geffert
Enter successively lower prices in the green cell. See what happens.
Price = 8 Elasticity = 5.67 ELASTIC X=-Y+12 Lines 8
Price Quantity Rev Elasticity Quantity Line Price9 Price8 Price7 Price6 Price5 Price4 Price3 Price2 Price1
0 10 0 -0.05 0 9 8
1 9 9 -0.18 1 0.1 9.9 9 8
2 8 16 -0.33 2 0.2 9 8
3 7 -0.54 3 0.3 9 8
4 6 -0.82 4 0.4 9 8
5 5 -1.22 5 0.5 9 8
6 4 -1.86 6 0.6 9 8
7 3 -3.00 7 0.7 9 8
8 2 -5.67 8 0.8 9 8
9 1 -19.00 9 0.9 9 8
10 0 UNDF 10 1 8
1.1 8
1.2 8
1.3 8
1.4 8
1.5 8
1.6 8
1.7 8
1.8 8
1.9 8
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9 0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10 0

DEMAND

Price = $9 0.1 0.2 0.30000000000000004 0.4 0.5 0.6 0.7 0.79999999999999993 0.89999999999999991 0.99999999999999989 1.0999999999999999 1.2 1.3 1.40000 00000000001 1.5000000000000002 1.6000000000000003 1.7000000000000004 1.8000000000000005 1.9000000000000006 2.0000000000000004 2.1000000000000005 2.2000000000000006 2.3000000000000007 2.4000000000000008 2.5000000000000009 2.600000000000001 2.7000000000000011 2.8000000000000012 2.9000000000000012 3.0000000000000013 3.1000000000000014 3.2000000000000015 3.3000000000000016 3.4000000000000017 3.5000000000000018 3.6000000000000019 3.700000000000002 3.800000000000002 3.9000000000000021 4.0000000000000018 4.1000000000000014 4.2000000000000011 4.3000000000000007 4.4000000000000004 4.5 4.5999999999999996 4.6999999999999993 4.7999999999999989 4.8999999999999986 4.9999999999999982 5.0999999999999979 5.1999999999999975 5.2999999999999972 5.3999999999999968 5.4999999999999964 5.5999999999999961 5.6999999999999957 5.7999999999999954 5.899999999999995 5.9999999999999947 6.0999999999999943 6.199999999999994 6.2999999999999936 6.3999999999999932 6.4999999999999929 6.5999999999999925 6.6999999999999922 6.7999999999999918 6.8999999999999915 6.9999999999999911 7.0999999999999908 7.1999999999999904 7.2999999999999901 7.3999999999999897 7.4999999999999893 7.599999999999989 7.6999999999999886 7.7999999999999883 7.8999999999999879 7.9999999999999876 8.0999999999999872 8.1999999999999869 8.2999999999999865 8.3999999999999861 8.4999999999999858 8.5999999999999854 8.6999999999999851 8.7999999999999847 8.8999999999999844 8.999999999999984 9.0999999999999837 9.1999999999999833 9.2999999999999829 9.3999999999999826 9.4999999999999822 9.5999999999999819 9.6999999999999815 9.7999999999999812 9.8999999999999808 9.9999999999999805 9 9 9 9 9 9 9 9 9 9 0 Demand 9.9 0 Price = $7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price = $6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price=$5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price= $4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price= $3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price= $2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price= $1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Price = $8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

Quantity

Price

Total Revenue

0 1 2 3 4 5 6 7 8 9 10 0 9 16 0 0 0 0 0 0 0 0

Quantity

Revenue

Price Elasticity Formula

Evaluating the Elasticity of Demand Formula
© 2008 James A. Geffert
Remember, each point on a line is an ordered pair of numbers, (q,p).
Quantity Price
6 4
7 3
The formula for calculating demand elasticity between two points on the demand curve is
shown above for two points P1 and P2. Let's evaluate (find the value of) the expression.
We substitute the values for price and quantity at each of the points and turn the algebraic crank.
Since the number you reach will always be negative, it is customary to use its absolute (positive) value.
Thus E = .5384
Compare this value to the previous page for a price of 3.
Let's make a little machine to evaluate this formula for any two points on a demand curve.
Notice that we need only enter the price and quantity pairs to let EXCEL evaluate
the elasticity formula for any combination of variables.
For ease of analysis I've split the calculation into numerator and denominator before calculating
the Elasticity coefficient.
P1 10
Q1 100
P2 9
Q2 120
Numerator 0.1818181818
Denominator -0.1052631579
E 1.7272727273 ELASTIC
END

Demand

6 7 4 3

Quantity

Price per Unit

Income Elasticity

Income Elasticity of Demand
Income 1 30 Use midpoint assumptions
Quantity 1 20
Income 2 50
Quantity 2 30
Numerator -0.400
Denominator -0.500
Coefficient 0.800 Normal and a Necessity

Cross Price Elasticity

Cross-price Elasticity of Demand
Price 1 30 Use midpoint assumptions
Quantity 1 40
Price 2 50
Quantity 2 30
Numerator -0.286
Denominator 0.500
Coefficient -0.571 Complements

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