Quantitative Demand Analysis
Managerial Economics
Kyle J. Anderson
Kelley School of Business
Indiana University
What we can learn:
• What factors affect sales of my product?
• How sensitive are my sales to these factors?
• How will a price change impact revenue?
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The demand function
• Linear demand
Qx=a + b1Px + b2Py + b3Pz + b4M
• Log linear demand
lnQx=a + b1lnPx + b2lnPy + b3lnPz + b4lnM
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Simple Regression - Daily sales quantity
300
Q = 513 – 3.68P
250
Quantity
200
150
100
50
0
60
70
80
90
Price
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100
110
120
Multiple Regression
Standard
Coefficients
Error
300.02
37.20
-3.60
0.27
Intercept
Our Price
Comp. Price
Weekend
2.08
23.19
0.26
3.28
t Stat
8.06
-13.15
P-value
0.00
0.00
8.12
7.08
0.00
0.00
Q = 300 – 3.60P + 2.08Py + 23.19W
Q = 531 – 3.60P
Simplified Demand for Weekend when Py = 100
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Elasticity
• Measurement of how one variable responds to a
change in another.
– Own price elasticity
– Cross price elasticity
– Income elasticity
– Advertising elasticity
– Other – Win Elasticity
• Percentage change in one variable due to a
percentage change in another.
Own Price Elasticity
EQ X , PX
•
•
•
•
Own price elasticity is always negative.
Elastic demand – absolute value greater than 1.
Inelastic demand – abs. value less than 1.
Unitary elasticity – E= -1.
Inelastic
0
% Q X

% PX
d
Elastic
-1
Unitary
-∞
Own Price Elasticity Spectrum
Perfectly Elastic Demand
Price
D
Quantity
Perfectly Elastic ( EQX ,PX  )
Exists for some sellers
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The demand facing a seller
may be perfectly elastic.
Perfectly Inelastic Demand
Price
D
Quantity
Perfectly Inelastic ( EQX , PX  0)
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Nothing has
perfectly
inelastic
demand.
Factors Affecting Own Price Elasticity
– Available Substitutes
• The more close substitutes available for the good, the more
elastic the demand.
Similar products 
More elastic demand
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Brand loyal  less elastic
Factors Affecting Own Price Elasticity
– Available Substitutes
• The more close substitutes available for the good, the more
elastic the demand.
Miller Lite
Beer:
Many
substitutes:
Elastic
demand
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No substitute – inelastic demand
Factors Affecting Own Price Elasticity
– Time
• Demand tends to be more inelastic in the short term than in
the long term.
• Time allows consumers to seek out available substitutes.
Short-term e = -.53
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Long-term e = -.81
Factors Affecting Own Price Elasticity
– Expenditure Share
• Larger share  more elastic demand
Small purchase – less elastic
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Large purchase – more elastic
Own Price Elasticity and Linear Demand
Price
Elastic
Unitary Elastic
Inelastic
D
Quantity
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• Elasticity is different at
different prices.
• Higher prices –
demand is more
elastic.
Calculating elasticity
Linear demand: Q= b0 – b1P
% Q
E
% P
Q
Q
E
P
P
Q P
E
P Q
Loglinear demand: lnQ = b0 + b1lnP
E = b1
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P
E  b1
Q
Conclusion
•
•
•
•
Defined Elasticity
Determinants of Elasticity
Calculate Elasticity
Next: Elasticity and Revenue
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