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Marketing Engineering Model
Marketing Actions Inputs Observed Market Outputs Competitive Actions (2) Product design Price Advertising Selling effort etc. Market Response Model Awareness level Preference level Sales Level (1) (4) (3) Environmental Conditions Control / Adaptation (6) Evaluation (5) Objectives e.g., Profits 4
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Steps in Creating a Marketing Response Model
Develop a relationship between sales and marketing variables Sales = f(marketing variables) Calibrate the model Statistically or judgmentally Create a profit model Profits = unit volume x contribution margin – fixed costs Optimize What if or optimum
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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. 8 9
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Weight Loss Response and Profit Model
Response Model Profit Model
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Linear Models - Statistical Concepts Least Squares
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Linear Models - Statistical Concepts R2
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Nonlinear Response Models: ADBUDG
b – minimum Y a – maximum Y c – shape, 0 < c < 1 concave; c > 1 s-shaped d – works with c to determine specific shape 12 13
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Response function: Expected Sales Relative to Base
R(X ) R(X ) 1.5 Expected Sales Relative to Base R(X ) 1.0 R(X ) Base 1.5 ´ Base Effort Relative to Base 12
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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
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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.
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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)
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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)
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Profit Models Unit Sales = f(marketing variables) Response Function
Profits = Unit Sales(margin) – fixed costs Example: Example on page 38
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Different Shapes of Multiplicative Model : Y= aXb
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Linearizable Response Models: Multiplicative Model
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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
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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
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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
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Choose model based on: Theory Fit Pattern of error terms
Signs and T-statistics of coefficients
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Response Function Sales Response Effort Level Max Response Function
Current Sales Min Current Effort Effort Level 5
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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
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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 14 15
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Elasticity – A way to compare various marketing instruments
= (Y/Y)/(X/X) = (Y/X) (X/Y) = (dy/dx)(X/Y) (Adv Existing Product) = (Adv New Product) = Advertising Long Term = 2X Short Term (Price) = -2.5 (Coupons) = .07 Source:Bucklin and Gupta, 1999
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Elasticity in Product Classes where P&G Competes
(Adv) = .039 (Price) = -.541 (Deals) = .092 (Coupons) = .125 Source: Ailawadi, Lehmann, and Neslin 2001
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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
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Conglomerate Market Share Calculations – New York
Promotion Level E4 Response Multiplier P56 Non-Deal Prone Share Deal Prone Share Total Share E10 .4 69% x .05 = 3.45 31% x .05x .4 = .62 4.07 100% 1 3.45 31% x.05 x 1 = 1.55 5.0 150% 1.64 31% x .05 x 1.7 = 2.635 6.0 Saturation 2.7 31% x .05 x 2.7 =4.185 7.635
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Aggregate Response Models: Dynamics
Dynamic response model Yt = a0 + a1 Xt + l Yt–1 Easy to estimate. Difficult to interpret correctly carry-over effect current effect 15 21
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