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Understanding Market Share Dynamics: How Price Influences Sales of Peanut Butter

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This course provides an insightful exploration into the relationship between price and market share using the example of selling peanut butter. It covers how market share is influenced by price per item, the mathematical dependencies involved, and various approaches to modeling these concepts. By examining both glass box (known mechanisms) and black box (data-driven) models, learners will gain a comprehensive understanding of how pricing strategies affect sales, profit calculations, and overall business success in the peanut butter market.

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Understanding Market Share Dynamics: How Price Influences Sales of Peanut Butter

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.19

  2. Example 3: • “How can we get rich • sellingpeanutbutter?” http://commons.wikimedia.org/wiki/File:PeanutButter.jpg

  3. relations dimensions todo assumptions profit income expenses pricePerItem nrSoldItems nrSoldTotal marketShare profit = income - expenses [Euro / year] = [Euro/year] no taxes, no inflation no discount with larger quantities per purchase income = pricePerItem * nrSoldItems [Euro / year] = [Euro/myPB] * [myPB/year] my PB will not increase the total market nrSoldItems = nrSoldTotal * marketShare [myPB / year] = [allPB / year] * [myPB/allPB] http://www.watnouweg.nl/nieuws/nieuwsitem.php?id=348&back=1&page=29 nrSoldTotal = 2x107[allPB/year] pricePerItem = … marketShare = …

  4. Dependency: • how does marketShare • depend on pricePerItem? http://www.sxc.hu/browse.phtml?f=download&id=366244

  5. marketShare 1 0 • pricePerItem Approach 1: Glass Box ?

  6. QUIZ How does market share depend on price per item? How canthisrelationbeexpressed in a mathematicalformula?

  7. marketShare 1 0 • pricePerItem Approach 1: Glass Box ? • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  8. 1st guess: straight lines • advantage: simple • disadvantage: not smooth • uncertainifthisfollowsthe actualbehavior • cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 1: Glass Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  9. 2nd, 3rd guess: arctan, logistic, …? • advantage: smooth • disadvantage: more parameters? • whatvaluesfor the parameters? • uncertainifthisfollows the actualbehaviour • cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 1: Glass Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  10. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  11. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box ask a panel iftheywouldpay € ... for your PB • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  12. cheapest • competitor • most expensive • competitor • marketShare 1 0 • pricePerItem Approach 2: Black Box ask a panel iftheywouldpay € ... for your PB • WhatmechanismdeterminesmarketShare(pricePerItem)? • monotonicallydecreasing • between 0 and 1 • asymptote: marketShare0 ifpricePerItem  • asymptote: marketShare1 ifpricePerItem -  • whatsort of mathematicaldependency ???

  13. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like

  14. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like • known or assumedmechanism: glass box http://www.sxc.hu/browse.phtml?f=download&id=596438

  15. Summary: • while making a model: • encouter a new quantity • ask: what does itdepend on • ask: how does the dependency look like • known or assumedmechanism: glass box • measure or guessed data: black box • data mayneed a smooth interpolation http://www.sxc.hu/browse.phtml?f=download&id=36217

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