Impact of ∆P and ∆Q on Changing Revenue and Measuring Price Elasticity

Ted Mitchell

Exam Question

• What Is the Price that maximizes Revenue If The Demand For The Product Is

»Q = a - bP

Optimal Price Max Rev

Price per Unita/2b

Quantity

Sold

a/2

Demand Equation

Q = a - bP

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Maximum Revenue

Optimal price Max Rev

Price per Unita/2b = 5000/2(500) = $5

Quantity

Sold

a/2 = 5000/2=2,500

Demand Equation

Q = 5000 – 500P

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Maximum Revenue = $5 X 2,500 = $12,500

Price per Unit$4 $5

Quantity

Sold

2,500

Demand Equation

Q = a - bP

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3,000

$4 x 3,000 =12,000

Lower Price Sells More Units

Price per Unit$4 $5

Quantity

Sold

2,500

Demand Equation

Q = a - bP

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3,000

$4 x 3,000 =12,000

Maximum Revenue = $5 X 2,500 = $12,500

Price per Unit$4 $5

Quantity

Sold

2,500

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3,000

Revenue in Period 2 $4 x 3,000 =12,000

Revenue in Period 1$5 X 2,500 = $12,500

Impact Analysis

• Impact of a Change in Price on the Change In Revenue

• Impact of a Change in Quantity on the Change in Revenue

Period 1 Period 2 Change Impact of Change on price

Quantity, Q 2,500 3,000 ∆Q= 500 I∆Q =$4(500) = $2,000

Price, P $5 $4 ∆P = -$1 I∆P =2,500(-$1) =-$2,500

Joint Impact 0

Revenue $12,500 $12,000 ∆R= -$500 ∆R = I∆Q+I∆P = -$500

Arc or Average price Elasticity = I∆Q/I∆P = $2,000/$2.500 = -0.8

Lower Price Sells More Units

Price per Unit$4 $5

Quantity

Sold

2,500

Demand Equation

Q = a - bP

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3,000

Gain =$4 x 500 =$2,000

Loss is2,500 x-$1= -$2,500

• Price Elasticity =• Customer Sensitivity to Price Change = • Sensitivity of Changes in the Quantity

purchased for a Change in Price• = %∆Q/%∆P

Price Elasticity = -1

Price per Unita/2b

Quantity

Sold

a/2

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Maximum Revenue

-0.5 -0.75 -1 -1.25 -1.5 -1.75

Revenue looks like R = aP - bP2

Revenue

Price0

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-0.5 -0.75 -1 -1.25 -1.5 -1.75Price Elasticity

a/2b

Period 1 Period 2 Change Impact of Change on price

Quantity, Q 2,500 3,000 ∆Q= 500 I∆Q =$4(500) = $2,000

Price, P $5 $4 ∆P = -$1 I∆P =2,500(-$1) =-$2,500

Joint Impact 0

Revenue $12,500 $12,000 ∆R= -$500 ∆R = I∆Q+I∆P = -$500

Arc or Average price Elasticity = I∆Q/I∆P = $2,000/$2.500 = -0.8

Price per Unit$4 $5

Quantity

Sold

2,500

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3,000

-0.5 -0.75 -1 -1.25 -1.5 -1.75Eqp = -0.8

Revenue looks like R = aP - bP2

Revenue

Price0

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-0.5 -0.75 -1 -1.25 -1.5 -1.75Arc Price Elasticity = -0.8

$4 $5

• Three Big Uses for Price Elasticity• 1) Forecasting Qty change for a

change in Price• 2) Comparing Price Sensitivity

Across Markets• 3) Indicates if a price change will

increase or decrease revenue

Exam QuestionIf your price elasticity is -1.5 then a price increase increase your revenue? True or False

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Exam QuestionIf your price elasticity is -1.5 then a price increase increase your revenue? True or False

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-0.5 -0.75 -1 -1.25 -1.5 -1.75

Exam QuestionIf your price elasticity is -1.5 then a price increase increase your revenue? True or False

Revenue

Price0TJM

-0.5 -0.75 -1 -1.25 -1.5 -1.75

Exam Question # 2If your price elasticity is -1.5 then a small price decrease will increase your revenue? True or False

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Exam Question # 2If your price elasticity is -1.5 then a small price decrease will increases your revenue? True or False

Revenue

Price0TJM

-0.5 -0.75 -1 -1.25 -1.5 -1.75

• Price Elasticity is Almost Never Used to discuss a price change increasing or decreasing Revenue!

• True

• BUT Why!!!

The Price That Maximizes Profit is always ≥ the

Price that maximizes Revenue

$

Price0TJM

Pr* Pz*

$

Price0TJM

Pr* Pz*

-0.5 -0.75 -1 -1.25 -1.5 -1.75

The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

• Most firms are maximizing profit most of the time

• Most manager expect a revenue increase if they decrease their selling price

• Price Elasticity in Most markets most of the time is between

• Eqp = -1.20 and -2.75

$

Price0TJM

Pr* Pz*

-0.5 -0.75 -1 -1.25 -1.5 -1.75

The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

Don’t Need A Max Revenue Indicator

• What we want is a NEW Elasticity That Indicates if a change in price will increase the Profits or not!