To derive optimal pricing and correct cannibalization between products, we analyze three products (A, B, and C) considering various factors such as prices, direct mail (DM), email marketing (EM), store visits, consumer confidence, and seasonal effects (dummy variables for January, December, October, and August).

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Simultaneous Equations Model

The model is represented as follows:

Results Table

The table below presents the coefficients of the simultaneous equations for products A, B, and C:

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Interpretation of the Results

Pricing Effects

• Product A:
  • The coefficient for PA is -2, indicating that a unit increase in the price of Product A decreases its sales by 2 units.
  • The positive coefficients for PB and PC (0.4 and 0.6) suggest that increasing the price of Product B and C slightly increases the sales of Product A.
• Product B:
  • The coefficient for PB is -1.8, indicating that a unit increase in the price of Product B decreases its sales by 1.8 units.
  • The positive coefficients for PA and PC​ (0.5 and 0.4) suggest that increasing the price of Product A and C slightly increases the sales of Product B.
• Product C:
  • The coefficient for PC​ is -2.1, indicating that a unit increase in the price of Product C decreases its sales by 2.1 units.
  • The positive coefficients for PA​ and PB​ (0.3 and 0.7) suggest that increasing the price of Product A and B slightly increases the sales of Product C.

Marketing Variables

• Direct Mails (DMs):
  • Direct mails positively impact the sales of all products, with the highest impact on Product B (0.15).
• Email Marketing (EMs):
  • Email marketing positively affects sales, with the highest impact on Product B (0.1).
• Store Visits:
  • Store visits positively affect sales for all products, with the highest impact on Product A (0.25).

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Consumer Confidence and Seasonal Effects

• Consumer Confidence:
  • Higher consumer confidence increases sales for all products, with the highest impact on Product A (1.8).
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• Seasonal Effects:
  • January: Sales decrease for all products in January.
  • December: Sales increase significantly in December for all products, with Product A seeing the highest increase (8).
  • October: Sales increase in October, with a smaller impact compared to December.
  • August: Sales slightly decrease in August for all products.

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Conclusion

The simultaneous equations model provides valuable insights into the interplay between different products and their demand drivers. This comprehensive analysis enables businesses to adjust pricing and marketing strategies to optimize sales and minimize cannibalization effects. By understanding these interdependencies, businesses can make more informed decisions, leading to better overall performance in dynamic market environments.