Using Impact of Changes in Price
and Sales Volume on Change in
Revenue to Calculate Arc
Elasticity
Methods of Evaluating
Performance Changes
• Analysis of Sales Variance (pg.52, 90)
Differences must be explained
• Revenue in period a or Ra = Pa x Qa
•
Or Revenue in period a = Price period a (Quantity period a)
• Revenue in period b or Rb = Pb x Qb
•
Or Revenue in period b = Price period b (Quantity period b)
• Revenue in a - Revenue in b = Revenue Change
aka Variance in Revenue
• Is the difference due to changes in Price
or Quantity or both?
1
Differences must be explained
• Revenue in period a or Ra= Pa x Qa
•
Or Revenue in period a = Price period a (Quantity period a)
• Revenue in period b or Rb = Pb x Qb
•
Or Revenue in period a = Price period a (Quantity period a)
• Revenue in a - Revenue in b
Ra -Rb = Revenue Change aka Variance in
Revenue
• Is the difference due to changes in Price
or Quantity or both?
Revenue Variance Has Two Parts
• Revenue Variance =
Price Variance + Volume Variance
• 1) Price Variance =
(Price in a -Price in b)(Qty sold in a)
• 2) Quantity or Volume Variance =
(Price in b)(Qty in a - Qty in b)
Quantity
Revenue = Price x Quantity
Qa
Ra
Pa
Price
2
Quantity
Lower price gives lower
revenue
Rb
Ra
Qa
Pb
Pa
Impact on
Revenue Change
due to
Price Change
Price
Quantity
Larger Sales Volume gives
Larger Revenue
Qb
Impact due to
Price Change
Rb
Ra
Qa
Pb
Pa
Price
Quantity
Impact on
Revenue Change
due to
Quantity Change
Qb
Impact due to
Price Change
Rb
Ra
Qa
Pb
Pa
Price
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Quantity
Qb
Rb
Quantity
Impact
Ra
Qa
Price
Impact
Pb
Price
Pa
The Connection between the
Demand Curve and Impact
Analysis
Quantity
Demand Curve
Q = a-bP
Qb
Rb
Quantity
Impact
Ra
Qa
Price
Impact
Pb
Price
Pa
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Example
• Last period Sales Revenue was $10,000 but
current Revenue was $8,800.
• What amount of Revenue Change is
explained by Variance in the Volume Sold?
• What amount of Revenue Change is
explained by Variance in the Price per unit?
Last period
Current
period
Change
$10,000
$8,800
$1,200
Last period
Current
period
Change
Revenue
$10,000
$8,800
$1,200
Quantity
Sold
units
Price per
Unit
5,000
4,000
-1,000
$2.00
$2.20
+$0.20
Revenue
Quantity
Sold
units
Price per
Unit
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Last period
Current
period
Change
Revenue
$10,000
$8,800
-$1,200
Quantity
Sold
units
Price per
Unit
5,000
4,000
-1,000
Impact in
Revenue $?
$2.00
$2.20
+$0.20
Impact in
Revenue $?
Last period
Current
period
Change
Revenue
$10,000
$8,800
$1,200
Quantity
Sold
units
Price per
Unit
5,000
4,000
$2.00
$2.20
-1,000
Loss of
$2,000
$0.20
Gain of
$800
Revenue Deviation
Has Two Parts
• Change in Revenue =
$8,800 –$10,000 = –$1,200 unfavorable
1) Price Variance =
($2.00 - 2.20)(4000) = $800 favorable
2) Quantity or Volume Variance =
($2.00)(4000 - 5000) = –$2000 unfavorable
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A More General Calculation
• Ra – Rb = Pm (Qa – Qb) + Qm (Pa –Pb) + r
– where
• Ra – Rb = difference in revenue
• Pm (Qa – Qb) = impact on revenue due to deviation from
planned quantity
• Qm (Pa –Pb) = impact on revenue due to deviation from
planned price
• r = residual impact not explained by individual deviations
in price and quantity
– Subscripts a = actual, b = planned, m = minimum of planned or actual
• Calculating the Impact of Changes in Price
and Changes in Quantity on Changes in
Sales Revenue from period to period is an
Important Analysis
Closely Related to Price Sensitivity (Elasticity)
Arc Elasticity
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Elasticity
• A measure of the customer’s sensitivity to a
change in price
• If the price changes by 1% what percentage
change is to be expected in the sales volume?
Point Elasticity and
Arc Elasticity
• Point Elasticity is good if there are very
small changes in price and quantity
• Arc Elasticity is better if there are large
changes in price and quantity
Quantity
Qb
Point Elasticity =
–2.0
Rb
Point Elasticity =
-2.75
Quantity
Impact
Ra
Qa
Price
Impact
Pb
Price
Pa
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Elasticity
• Is the Domestic Market more sensitive to a
price change than the Home Market?
• With limited observations what can you do?
• Use the Impact Analysis
Elasticity
• Is the Domestic Market more sensitive to a
price change than the Home Market?
• With limited observations what can you do?
• Use the Impact Analysis
Last
period
Current
period
Change
Revenue
$10,000 $8,800
$1,200
Quantity
Sold
units
Price per
Unit
5,000
4,000
$2.00
$2.20
-1,000
$2(-1000) =
Loss of $2,000
$0.20
4000(-$0.2) =
Gain of $800
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• Arc Elasticity = Impact on Revenue due to
Change in Quantity ÷ Impact on Revenue
due to Change in Price
• Arc Elasticity = –$2,000 ÷ $800 = –2.5
Quantity
Arc Elasticity =
–2.5
Qb
Rb
Quantity
Impact
Ra
Qa
Price
Impact
Price
Pb
Pa
Quantity
Qb
Point Elasticity =
–2.0
Arc Elasticity =
–2.5
Rb
Point Elasticity =
-2.75
Quantity
Impact
Ra
Qa
Price
Impact
Pb
Price
Pa
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Hard to Compare Changes
• When you are changing several element of
the marketing mix in one period it is hard to
get accurate measures
• e.g., Change in Price and Promotion Effort
Shift in Demand due to
a change in Promotion
Quantity
Qb
Rb
Quantity
Impact
Ra
Qa
Price
Impact
Pb
Price
Pa
Any Questions?
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