# Market Intersection (MIX) Charts

Market Simulations use Artificial Intelligence (AI) to predict the behavior of thousands of Customers in a Market.

You may have thought that predicting such Customer Behavior would first require a massive amount of historic data. In fact, the opposite is true – very little data is required to model a Market with AI.

This Market Simulation workflow illustrates how only two simple observations of a Market is enough to mathematical map a duopoly: that is, a Market with two Products and thousands of Customers. Each Market Observation typically comprises of both:

• the Price of each Product
• the Quantity sold (or Market Share) of each Product at those Prices

Customers make purchase decisions based upon the differentiation between Products. There are two main types of Product differentiation:

Simply put, Vertical Differentiation are those qualities that make a Product better, while Horizontal Differentiation are those qualities that make a Product unique. Follow the links above for a more detailed description of both.

There are two Products in this Market Simulation.The Vertical and Horizontal Differentiation between both can be plotted on a two-dimensional chart: Vertical Differentiation along one axis, and Horizontal Differentiation along the other axis. A line on the chart connects all combinations of [Vertical + Horizontal] Differentiation that can explain the first [Price x Quantity] Market Observation.

When Prices vary, a second [Price x Quantity] Market Observation can be made. This can be used to plot a second line on the [Vertical + Horizontal] chart.

The intersection of those two lines represents the actual degree of Vertical Differentiation and Horizontal Differentiation that distinguish the two Products.

X marks the spot!

This Case Study provides a high-level overview of the workflow without detailed explanation. It assumes you are already somewhat familiar with KNIME and Market Simulation. If not, start by reviewing the Building Blocks and Community Nodes.

# #1 Market Observations

Each Market Observation comprises of both:

• the Price of Product_A and Product_B
• the Quantity sold of Product_A and Product_B at those Prices

Observation #0: When the Price of Product_A is \$50 and the Price of Product_B is \$60, the relative Market Share of both is 65% : 35%.

Observation #1: When Price_A is \$50 but Price_B is raised to \$70, the relative Market Shares become 80% : 20%.

A reference Mean and Standard Deviation (SD) of Product_A is fixed in this Market Observations table. The Mean of a Customer Distribution is a measure of Vertical Differentiation. A goal of this workflow is to calculate the relative Vertical Differentiation of Product _B: that is, the Mean of Product_B’s Customer Distribution relative to Product _A. It could be higher or lower than Product_A’s Mean.

Observation #0: This Market Simulation will first generate a [Vertical + Horizontal] line representing all possible combinations that could explain the 65% : 35% Market Share given the initial Prices [Price x Quantity].

Observation #1: Next, this Market Simulation will generate a second [Vertical + Horizontal] line explaining the 80% : 20% Market Share after Prices change.

# #2 Test Correlations

The workflow iterates over a range of Mean values and a range of Correlation values. Each [Mean x Correlation] combination is tested to see if the Market Simulation matches the observed [Price x Quantity].

The Correlation between the Customer Distributions for Product_A and Product_B is a measure of the Horizontal Differentiation between both. The tests start with a Correlation of +1.0 (perfect correlation), sweep past 0.0 (no correlation), and finish at -1.0 (negative correlation).

21 Correlation values are tested, and 41 Mean values are tested for each of the 2 Market Observations. All together, the Market Simulation loop is run:

2 Observations x 21 Correlations x 41 Means = 1,722 Simulations

# #3 Test Mean / SD

Product_A was set a reference Mean of \$100. The Market Simulation will run a series of tests using different Means for Product_B. The tests will range from Mean_B = \$50 to Mean_B = \$150. The Standard Deviation (SD) is fixed to be proportional to the Mean.

# #4 Simulate Test Market

There are three outer and inner loops. The workflow loops over each Market Observation [2] x each Test Correlation [21] x each Test Mean / SD [41]. Altogether 1,722 Market Simulations are run to cover each combination.

At the end of the Correlation loop, only the best fitting Mean that results in the lowest ‘Quantity Error’ is preserved for each test Correlation value.

# #5 Chart Results

The final results are further scrubbed before being charted. While the Correlation Loop eliminated poorly fitting Mean values, there remains Mean values with several possible Correlations. The further scrubbing ensures that only the best fitting Correlation value is preserved for each Mean.

The results for Observation_0 are separated from the results for Observation_1. Both sets of results are then plotted in scatter charts. The results are also saved to an Excel spreadsheet for further analysis.

# Economic Theory

#### MIX Charts

A “MIX” Chart is an abbreviation of “Market Intersection X-Chart”. This type of chart is appropriate when there are 2 Market Observations and 2 unknown values, such as the Mean and Correlation for Vertical and Horizontal Differentiation. The two lines intersect to form an X-shape. Two Products competing in a duopoly Market is a good example of when to use this type of chart to generate and tune a Market Simulation.

An Excel scatter plot of the two Market Observations is helpful in identifying the exact combination of Vertical and Horizontal Differentiation in the Market. In this case, the Willingness To Pay (WTP) Customer Distributions for Product_A and Product_B would have the following attributes:

• Product_A Mean = \$100
• Product_B Mean = \$102.50
• Correlation_AB = 0.5

For greater accuracy, or when there is Strange Differentiation in a Market and the relative Standard Deviation (SD) becomes important, there may be 3 or more unknown values. In this case, three intersecting planes might be used. These three planes would intersect to form a Y-shape. Hence these charts would be called “MIY” Charts.

The category of these charts are collectively known as “MIY MIX” Charts (pronounced “My Mix Charts”).

#### Normal Distributions

There is an important underlying assumption that these MIX Charts depend upon: namely the Willingness To Pay (WTP) that Customers have for each Product falls within a Normal Distribution.

This assumption is reasonable because of the Central Limit Theorem. The Central Limit Theorem states that:

When independent random variables are added, their normalized sum tends toward a normal distribution (a “bell curve”) even if the original variables themselves are not normally distributed.

In other words, the more variables that are added to a distribution, the more normal it will appear.

Most Products are made up many Features, and the value Customers place upon each make up all of the Feature Distributions. The ‘Brand’ Feature, in itself, is immensely rich and complicated, with many CMO’s shaping their Brand as if it were a person or character.

Products that sum together the value of these many Features will very likely result in a Willingness To Pay (WTP) Customer Distribution that is normally shaped.