Constructing A Meta-Marketing Machine For Pricing

Ted Mitchell

We need a better method

• Of forecasting than using a slope-origin model based on a single performance

• A single performance might be the typical, the average, or the last observed

• 1) it is too inaccurate• 2) Implies a positive relationships between

Input and Output which are invalid with inverse relationships such as price tags

We have created a Meta-Conversion Rate, m

• To identify direct and inverse relationships between Input and Output

• We will construct a • Meta-Marketing Machine • to provide more accurate forecasts and be

valid for direct and inverse relationships

A Two-Factor Meta-Marketing Machine

• Uses the difference in two inputs, ∆I = I2-I1 as its Input, π

• Uses the difference in two outputs, ∆O = O2-O1

as its Output, ø• Uses the meta-conversion rate,

m = ∆O/∆I = ø/πAs the rate of the process that converts the size of the change in Input to the size of the change in Output

• Yes! It Does Sound a little Abstract

A Meta-Marketing Machine

Meta- Marketing Conversion

Rate, m

Inputs to The Meta-Marketing Machine are the

size of change, ∆I

∆ Price Tags∆ Product Quality

∆Promotion

∆Place

Outputs from The Meta-Marketing

Machine are the size of the change in output, ∆O

∆Revenues∆Quantity of Goods Sold

∆Profits∆Demand

The Slope-Origin Equation for a Meta-Marketing Machine is

• Output, ø = (meta-conversion rate, m) x (Input, π)

• where

• The Output, ø, is the Difference between two outputs: O2-O1 = ∆O

• The Input, π, is the Difference between two inputs: I2 – I1 = ∆I

• The Meta-Conversion rate, m, is the ratio of the difference in Outputs, ∆O, to the difference in Inputs, ∆I,

• m = ∆O/∆I = (O2-O1)/I2-I1)

The Meta-Marketing Machine

• In the Slope-Origin Form presented on a Cartesian Mapping the same as a single performance Two-Factor Model

• O = r x I• But is now a richer input and output• Ø = m x π• It looks like a similar format but it is far more

accurate for making predictions

Meta-Marketing Machine

Input Factor, ∆I

Output, ∆O

0, 0∆I

∆O X

Calibration point

(∆I, ∆O)

Meta-Conversion rate or Slope

m = rise/run

m = ∆O/∆I

Slope-Origin Equation for Two-Factor Meta-machine

∆ø = m x ∆I

Rise

Run

In tabular form the Meta-Marketing Machine

Performance 1 Performance 2 Meta-Marketing Machine

Input: I1 I2 Input, π = ∆I = I2 – I1

Conversion rate, r = O1/I1Not Used

r = O2/I2Not Used

Meta-conversion rate, m = ø/π = ∆O/∆I

Output: O1 O2 Output, ø = ∆O ø = O2 – O1

Example: Meta-Marketing Machine that converts change in servers hired into a change in coffee sales

Example: Meta-Marketing Machine that converts change in servers hired into a change in coffee sales

Performance 1 Performance 2 Meta-Service Machine

Input: Servers, S S1 = 16 S2 = 20 π = ∆S = 4 servers

Conversion rate, R = Q1/S1Not Used

R = Q2/S2Not Used

Meta-conversion rate, m = ∆Q/∆S m = 128/4 = 32 cups per server is positive

Output: Cups Sold, Q

Q1 = 2,000 Q2 = 2,128 Ø = ∆Q = 128 cups

Example: Meta-Marketing Machine that converts change in servers hired into a change in coffee sales

Meta-Service Machine

Input: Servers, S π = ∆S = 4 servers

Conversion rate, Meta-conversion rate, m = ∆Q/∆S m = 128/4 = 32 cups per server is positive

Output: Cups Sold, Q

Ø = ∆Q = 128 cups

The meta-conversion rate is positive

• m = 32 cup increase for every extra server hired

• Therefore there is a positive relationship• Between the number of servers and the

number of cups sold in the Meta-Service Machine

• because

Basic Marketing Machine Allows for only Positive Amounts of Input & Output

0, 0 Positive Input

Positive Output

Negative Amounts of Input?

Negative Amounts of output?

Conversion rate has a Positive Slope when both Input and output are positive amounts

r = O/I

Non-Applicable Quadrant

Non-Applicable Quadrant

Non-Applicable Quadrant

Meta-Marketing Machine Allows for Positive and Negative Changes

0, 0 Positive Change in Input, +∆I

Positive Change in Output +∆O

Negative Change in Input -∆I

Negative Change in Output, -∆O

Meta-Conversion rate has a Positive Slope

when both changes are positive or negative

m = ∆O/∆I

Consider a Meta-Marketing Machine

• In which there is an inverse relationship between Input and Output

• The Meta-Pricing Machine• Converts the size of the change in the Price

Tag, ∆P, into the size of the change in quantity sold, ∆Q

You could Not do Price and Quantity as a Direct Relationship

0, 0 Positive Input

Positive Output

Negative Amounts of Input?

Negative Amounts of output?

Non-Applicable Quadrant

Non-Applicable Quadrant

Non-Applicable Quadrant

A positive increase in Price Tag creating a negative sales Quantity makes no sense

Meta-Marketing Machine Allows for Positive and Negative Changes

0, 0 Positive Change in Price, +∆P

Positive Change in Quantity, +∆Q

Negative Change in Price -∆I

Negative Change in Quantity, -∆Q

Meta-Conversion rate has a Negative Slope when one changes is

positive and the other is negative

–m = –∆Q/∆P

In Tabular Form Meta-Pricing Machine

Performance 1 Performance 2 Meta-Pricing Machine

Input: price tag P1 = $3.50 P2 =$4.50 ∆P = $4.50 - $3.50 ∆P = $1 (positive)

Conversion rate, Not Used Not Used Meta-conversion rate,m = ∆Q/∆P m = -400 cups/$1(negative sloping conversion rate)

Output Number of Cups Sold, Q

Q1 = 2,000 Q2 = 1,600 ∆Q = 1,600 – 2,000 ∆Q = -400 cups(negative)

In Tabular Form Meta-Pricing Machine

Meta-Pricing Machine

Input: price tag ∆P = $4.50 - $3.50 ∆P = $1

Conversion rate, Meta-conversion rate,m = ∆Q/∆P m = -400 cups/$1

Output Number of Cups Sold, Q

∆Q = 1,600 – 2,000 ∆Q = -400 cups

The meta-conversion rate is negative

• m = -400 cups per dollar increase in price tag• Every dollar increase in price reduces quantity

sold by 400 cups• Therefore the relationship between Price and

Quantity sold is behaves like an Inverse relationship

• But it is NOT an Inverse relationship

Input Change in Price, ∆P

0, 0

∆P =$1

In a Direct Relationship the

ratio has a constant negative slope

Meta-Conversion rate m = rise/run

m = –∆Q/∆Im = -400/$1

Rise

Run

Output Change in Quantity, ∆Q

∆Q -400 cups X

Meta-Marketing Machine can present an Inverse relations

In a Inverse relationship the product of the two variables has a constant value

Quantity Sold, Q

Price Tag, P

The product of the two variables is a constant

valueP x Q = k

P0 P1

Q0

Q1

The area at two different points must be equal by definitionP1 x P1 = Q0 x P0 = kQ1/Q0 = P0/P1

Constant Area k = P x Q

Inverse Relationships do not pass through the origin

Any Questions?

• Calculating Meta-conversion rate, m = ∆O/∆I Using the changes in the inputs, ∆I, as the input, π

• And the changes in the output, ∆O, as the output, ø

• The sign of the slope Provides the Direction of the Relationship between input and output– A positive slope is a positive change relationship– A negative slope is a negative change relationship