Using impact analysis to calculate arc elasticity of price
Download
1 / 30

Using Impact Analysis to Calculate Arc Elasticity of Price - PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on

Using Impact Analysis to Calculate Arc Elasticity of Price. Ted Mitchell. Review Major Use of Impact Analysis. To measure the individual impacts that the changes in two variables have on a third variable. ∆Price and ∆Quantity each have an impact on the change in Revenue, ∆R

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Using Impact Analysis to Calculate Arc Elasticity of Price' - renate


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Review major use of impact analysis
Review Major Use of Impact Analysis

  • To measure the individual impacts that the changes in two variables have on a third variable.

    • ∆Price and ∆Quantity each have an impact on the change in Revenue, ∆R

    • ∆Market Share and ∆Market Size each have an impact on the change in Quantity sold, ∆Q

    • ∆Advertising productivity and ∆Advertising Expense each have an impact on the change in Quantity sold, ∆Q


Impact analysis helps us explain
Impact Analysis helps us explain

  • 1) why revenue is at a maximum, when the price elasticity is equal to -1.0

  • 2) why profit is at a maximum, when the elasticity of markup is equal to -1.0

  • 3) why profit from promotional efforts, such as advertising, are at a maximum, when the elasticity of the Return on Advertising is equal to -1.0


Impact analysis is related to
Impact Analysis is Related to

  • 1) Price and Sales Variance Analysis for measuring Differences between Budgeted and Actual revenues in Managerial Accounting

  • 2) Impact of Price and Quantity Changes on the Change in Revenue in Marketing Management

  • 3) Ratio of Quantity Impact to the Price Impact is Arc Elasticity in Marketing, Economics


We remember that
We remember that

  • There is a Two-Factor model of the marketing machine

  • Output = (conversion rate, r) x Input

  • Conversion rate, r = Output/Input

  • Revenue, R =(conversion rate, r) x Price Tag, P

  • Conversion rate, r = (Revenue, R)/(Price Tag, P)

  • Mind bending observation: Quantity sold, Q= R/P

  • Conversion rate, r = Quantity sold, Q


Two factor marketing machine
Two-Factor Marketing Machine

  • Revenue, R =(conversion rate, r) x Price Tag, P

  • Conversion rate, r = (Revenue)/(Price Tag)

  • Conversion rate, r = Quantity sold, Q

  • Revenue, R = Quantity sold, Q x Price Tag, P

  • R = Q(P)

  • Review An Impact analysis of the Price and Quantity differences on a change in Revenue



Quantity

Sold

The starting point (Q1=3,000, P1 = $4) The revenue, R, is P x Q = $12,000

Q1 = 3,000

X

X

P1 = $4

Price per Unit

TJM


Quantity

Sold

The end point (Q2= 2,500, P1 = $5) The revenue is P x Q = $12,500

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the change in price on the change in revenue

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the change in price on the change in Revenue is I∆P = 2,500 x ($5-$4)

I∆P = $2,500

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the decrease in quantity on the change in Revenue

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the decrease in quantity on the change in Revenue

I∆Q = $4 x (2,500 -3,000)

I∆Q = -$2,000

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM



Impact analysis
Impact Analysis

  • The $500 change in Revenue has to be equal to the impact of the change in price and the impact of the change in quantity

  • ∆R = R2 – R1 = $12,500 – $12,000 = $500

  • ∆R = I∆Q + I∆P + Joint

  • $500 = I∆Q + I∆P + J

    $500 = Pmin(Q2-Q1) + Qmin(P2-P1) + J


R i q i p j
∆R = I∆Q + I∆P + J

  • The net of two impacts equals the change in Revenue = $500

  • Since ∆P is positive and ∆Q is negative the Joint Impact, J = 0

  • The impact on the change in Revenue by the increase in the price is calculated as

  • I∆P = Qmin(∆P) = 2,500 x ($5-$4) = $2,500

  • The impact on the change in Revenue by the decrease in Quantity is calculated as

  • I∆Q = Pmin (∆Q) = $4 x (2,500-3,000) = -$2,000


Quantity

Sold

The impact of the decrease in quantity on the change in Revenue =

I∆Q = -$2,000

The impact of the change in price on the change in Revenue =I∆P = 2,500

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the decrease in quantity on the change in Revenue =

I∆Q = -$2,000

The impact of the change in price on the change in Revenue =I∆P = 2,500

Q1 = 3,000

X

Q2 = 2,500

X

Joint Impact, J = 0

P1 = $4

Price per Unit

P2 = $5

TJM


Quantity

Sold

The impact of the decrease in quantity on the change in Revenue =

I∆Q = -$2,000

The impact of the change in price on the change in Revenue =I∆P = 2,500

Q1 = 3,000

X

Q2 = 2,500

X

Net Impact is a

I∆Q + I∆P + J = $500 increase in Revenue

P1 = $4

Price per Unit

P2 = $5

TJM


We have reviewed
We have reviewed

  • To Price Elasticity


Price elasticity 1
Price Elasticity = -1

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

Quantity

Sold

Maximum Revenue

a/2

Price per Unit

a/2b

TJM


Revenue looks like r ap bp 2
Revenue looks like R = aP - bP2

Revenue

Price Elasticity

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

0

Price

Optimal price, Pr = a/2b

TJM


Start with a low price
Start with a low price

  • As it grows larger, then the sizes of the two impacts become more equal to each other


Quantity

Sold

Q1 = 3,000

X

Q2 = 2,500

X

P1 = $4

Price per Unit

P2 = $5

TJM


Larger impact due to ∆Q

Quantity

Sold

Q1 = 3,000

Smaller Impact due to ∆P

X

Q2 = 2,500

X

Q3 = 2,000

P1 = $4

Price per Unit

P3 =$6

P2 = $5

TJM


The concept you have to know
The Concept You have to Know

  • When the impacts of the two changes are equal the revenue is at a maximum and ratio of the two impacts is equal to -1

  • Arc Price Elasticity = I∆Q/I∆P = -1

  • Arc Eqp = Impact of the difference in Quantity divided by the Impact of the difference in Price Tag


Linkage
Linkage

  • The ratio of the impact due to the changing quantity and the impact due to the changing price is the Arc Elasticity of Price.

  • Arc Elasticity of Price = I∆Q/I∆P

  • Arc Elasticity of Price = Pmin(∆Q)/Qmin(∆P)

  • Remember the definition of elasticity!

  • Arc Elasticity of Price = (∆Q/Qmin)/(∆P/Pmin)

  • (∆Q/Qmin)/(∆P/Pmin) = (∆Q/Qmin) x (Pmin/∆P) = Pmin(∆Q)/Qmin(∆P)


Calculating price elasticity from impact analysis
Calculating Price Elasticity from Impact Analysis


What did we learn
What did we learn?

  • Arc Elasticity of Price, Eqp, is equal to the ratio of the impact of the change in quantity, I∆Q,on the change in revenue, to the ratio of the impact of the change in price, I∆P, on the change in revenue and the %∆Qmin / %∆Pmin

  • Arc Eqp=I∆Q / I∆P = %∆Qmin/ %∆Pmin



ad