Transcript Profit Models

Marketing Engineering Model
Marketing Actions
Inputs
Observed Market
Outputs
Competitive Actions
(2)
Product design
Price
Advertising
Selling effort
etc.
(1)
Market
Response
Model
Awareness level
Preference level
Sales Level
(4)
(3)
Environmental
Conditions
Control / Adaptation
(6)
Objectives
e.g., Profits
Evaluation
(5)
Steps in Creating a Marketing
Response Model
1. Develop a relationship between sales and
marketing variables
•
Sales = f(marketing variables)
2. Calibrate the model
•
Statistically or judgmentally
3. Create a profit model
•
Profits = unit volume x contribution margin – fixed costs
4. Optimize
•
What if or optimum
Linear Response Model:
• Y = a + b1X1 + b2 X2
• Examples:
–
–
–
–
Medical advertising
Conjoint analysis
Bookbinders Book Club
Price, cart, and coupon exercise
• Easy to estimate, robust, good within certain ranges
• Optimum is either zero or infinity
• Judgmental – sales at current level of effort and
change in sales for a one unit change in effort.
Weight Loss Response and Profit Model
• Response Model
Cˆ  aˆ  bˆ  Ads  12.6  36.1 Ads
• Profit Model
  Cˆ  Mar  Cost / Ad   Ads
 12.6  36.1 Ads  $59  $1300 Ads
Linear Models - Statistical Concepts
Least Squares
2
(
y

y
)
i 1 i
n
Variance of y 
(n  1)
T otalSum of Squares (T SS)  i 1 ( y i  y )
n
Regression Equat ion:
y i  aˆ  bˆxi  ei  yˆ i  ei or ei  y i  yˆ i
Solve by minimizing:
2
2
ˆ
e

(
y

y
)
i  i i
2
Linear Models - Statistical Concepts
R2
2
ˆ
 ( yi  y )  e  ( yi  y )
2
TSS
2
i
 RSS 
2
ˆ
( yi  y )
ESS

2
R 

2
 ( yi  y ) TSS
ESS
2
e
TSS  RSS

i

 1
2
TSS
(
y

y
)
 i
Nonlinear Response Models: ADBUDG
 X 
 X  0
Y  b  (a  b) c
 X d 
c
b – minimum Y
a – maximum Y
c – shape, 0 < c < 1 concave; c > 1 s-shaped
d – works with c to determine specific shape
c
Response function:
r ( X i )  b  (a  b )
R(X  )
R(X
1.5
Expected
Sales
Relative
to
Base
R(X
1.0
)
)
R(X )
0
0
Base 1.5  Base
Effort Relative to Base
Xi
d  Xi
c
ADBUDG Model
• Examples:
– Response Modeler: units of marketing effort and sales
– Conglomerate: four cities responding to sales
promotion
– Spreadsheet Exercise: (Blue Mountain Coffee) sales
response to advertising
– Syntex: 7 products or 9 specialties responding to
number of sales calls
– John French: 4 accounts responding to call frequency
Using Solver to Estimate Response
Functions
• Locate parameters and choose starting values
• Create columns for independent and dependent variables.
Calculate mean of dependent variable.
• Create column of predicted dependent variables based on
parameters and independent variables.
• Create column of squared errors between actual and
predicted dependent variable. Sum this column.
• Use solver to search over parameters to minimize sum
squared errors.
Judgmental Calibration of ADBUDG
• Data: R(Xminimum), R(Xsaturation), R(X1.0), and
R(X1.5)
• Parameters:
• a = R(Xsaturation)
• b = R(Xminimum)
• d = (a-R(X1.0))/(R(X1.0)-b)
• c = ln((d*(R(X1.5)-b)/(a-R(X1.5))/ln(1.5)
Judgmental Calibration of ADBUDG
• Data: R(Xminimum), R(Xsaturation), R(X0.5), R(X1.0), and
R(X1.5)
• Parameters:
• a = R(Xsaturation), b = R(Xminimum)
• d = (a-R(X1.0))/(R(X1.0)-b)
• Solve for c using least squares over R(X0.5) and R(X1.5)
cˆ


X
.
5
e.5  R( X .5 )  Rˆ ( X .5 )  R( X .5 )   b  (a  b)( cˆ
) 
X .5  d 

cˆ

X 1.5 
ˆ
e1.5  R( X 1.5 )  R( X 1.5 )  R( X 1.5 )   b  (a  b)( cˆ
) 
X 1.5  d 

Profit Models
• Unit Sales = f(marketing variables) Response Function
• Profits = Unit Sales(margin) – fixed costs
• Example: Example on page 38
Xc
U ( X )  b  ( a  b)  ( c
)
X d
P rofit U( X )(margin)  X
X 2.2
U( X )  4.7  (36.8  4.7)  ( 2.2
)
X  53.9
P rofit U( X )($1  $.25)  X
Different Shapes of Multiplicative
Model : Y= aXb
b>1
0<b<1
Y=a
b<0
X=1
Linearizable Response Models:
Multiplicative Model
Y  aX X 2
b1
1
X i  0 i  1,2
b2
T akelogarithmsof originalequation:
Ln(Y )  Ln(aX X 2 )  Ln(a)  Ln( X )  Ln( X 2 )
b1
1
b2
b1
1
b2
 Ln(a)  b1 Ln( X 1 )  b2 Ln( X 2 )
Estimateequation:
Ln(Y )    1 Ln( X 1 )   2 Ln( X 2 )

T ransformback : a  e and bi   i

1
Y  e X1 X 2
2
 aX X 2
b1
1
b2
where   Ln(a)
i  1,2
Multiplicative Models Cont’d
• Estimate judgmentally
– Sales at current level of marketing variable(s)
– Percent change in sales for a percent change in
marketing variable i = exponent bi
– Yc=a Xcb
– Solve for a
Multiplicative Models Cont’d
• Examples:
– Allegro: Sales = a price-b . Advc
– Nonlinear Advertising Sales Exercise
– Forte Hotel Yield Management: Sales = a price-b
• Constant elasticity – exponents are elasticities
• Models both increasing (adv) and decreasing
(price) functions as well as both increasing
(positive feedback) and decreasing (adv and price)
returns
Other Linearizable Models
• Exponential Model: Y = aebx; x > 0
– Ln Y = Ln a + bX
– Models increasing (b>1) or decreasing (b<1) returns .
• Semi-Log Model: Y = a + b Ln X
• Reciprocal Model: Y = a + b/X = a + b (1/X)
– Models saturation
• Quadratic Model: Y = a + bX + c X2
– Supersaturation
– Ideal points in MDS
– Bass Model
Choose model based on:
•
•
•
•
Theory
Fit
Pattern of error terms
Signs and T-statistics of coefficients
Response Function
Max
Sales
Response
Response
Function
Current
Sales
Min
Current
Effort
Effort Level
Elasticity - Percent change in the
dependent variable divided by the percent
change in the independent variable
•  = (Y/Y)/(X/X) = (Y/X) (X/Y) = (dy/dx)(X/Y)
• If Y = bX then  = 1 For example, if we double X
(from x to 2x), Y also doubles (from bx to 2bx), so the
percent change in X is always the same as the percent
change in Y.
• If Y = a + bX, then Y/X = b(x)/ x = b and X/Y = X
/ (a + bX) and  = (Y/X) (X/Y) = bX/(a+bX) <1 if
a>0
Elasticities with a Multiplicative Model
Y = aXb
•  = (dy/dx)(X/Y)
• dy/dx = a bXb-1
•  = (a bXb-1) (X/aXb) = (a bXb-1 X)/aXb = b
Elasticity – A way to compare various
marketing instruments
•  = (Y/Y)/(X/X) = (Y/X) (X/Y) =
(dy/dx)(X/Y)
•
•
•
•
•
(Adv Existing Product) = .05 - .15
(Adv New Product) = .20 - .40
Advertising Long Term = 2X Short Term
(Price) = -2.5
 (Coupons) = .07
Source:Bucklin and Gupta, 1999
Elasticity in Product Classes where
P&G Competes
•
•
•
•
(Adv) = .039
(Price) = -.541
 (Deals) = .092
 (Coupons) = .125
Source: Ailawadi, Lehmann, and Neslin 2001
Effect of Increasing Advertising
• Assume 100 units sold at $1.00/unit, 50% contribution
margin, advertising elasticity of .22, and 10% A/S
ratio
• No change in advertising:
– Profit = (100 * $.50) - $10 = $40
• A 50% increase in advertising – sales increase by 11%
– New Profit = (111 * $.50) - $15 = $40.50
Conglomerate Market Share
Calculations – New York
Promotion
Level
E4
Response
Multiplier
P56
Non-Deal
Prone Share
Deal Prone
Share
Total Share
E10
0
.4
69% x .05 =
3.45
31% x .05x
.4 = .62
4.07
100%
1
3.45
31% x.05 x 1 5.0
= 1.55
150%
1.64
3.45
31% x .05 x
1.7 = 2.635
6.0
Saturation
2.7
3.45
31% x .05 x
2.7 =4.185
7.635
Aggregate Response Models:
Dynamics
• Dynamic response model
•
Yt = a0 + a1 Xt + l Yt–1
current
effect
carry-over
effect
Easy to estimate.
Difficult to interpret correctly