probability consumer will

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So I've been reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated with Field Experiments" by Fisher, Gallino, and Li. Within the paper they provide a formula that calculates the probability Prjr that a consumer will purchase a product at a retailer given a price pjr



probability formula in question, located on page 14 in paper



I'd like to create an algorithm using this formula that will return the price of a product that maximizes the probability that a consumer will purchase the product, however I'm not sure where to start with this, mostly with how to manipulate this formula to maximize price. Any advice?




optimization




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  • Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
    – Nameless
    Aug 9 at 20:41














up vote
-1
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So I've been reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated with Field Experiments" by Fisher, Gallino, and Li. Within the paper they provide a formula that calculates the probability Prjr that a consumer will purchase a product at a retailer given a price pjr



probability formula in question, located on page 14 in paper



I'd like to create an algorithm using this formula that will return the price of a product that maximizes the probability that a consumer will purchase the product, however I'm not sure where to start with this, mostly with how to manipulate this formula to maximize price. Any advice?




optimization




share|cite|improve this question




















  • Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
    – Nameless
    Aug 9 at 20:41












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











So I've been reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated with Field Experiments" by Fisher, Gallino, and Li. Within the paper they provide a formula that calculates the probability Prjr that a consumer will purchase a product at a retailer given a price pjr



probability formula in question, located on page 14 in paper



I'd like to create an algorithm using this formula that will return the price of a product that maximizes the probability that a consumer will purchase the product, however I'm not sure where to start with this, mostly with how to manipulate this formula to maximize price. Any advice?




optimization




share|cite|improve this question












So I've been reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated with Field Experiments" by Fisher, Gallino, and Li. Within the paper they provide a formula that calculates the probability Prjr that a consumer will purchase a product at a retailer given a price pjr



probability formula in question, located on page 14 in paper



I'd like to create an algorithm using this formula that will return the price of a product that maximizes the probability that a consumer will purchase the product, however I'm not sure where to start with this, mostly with how to manipulate this formula to maximize price. Any advice?





optimization





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asked Aug 8 at 20:56









amadzebra

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  • Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
    – Nameless
    Aug 9 at 20:41
















  • Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
    – Nameless
    Aug 9 at 20:41















Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
– Nameless
Aug 9 at 20:41




Your are making a contradictory statement: saying you want to maximize the probability of purchase, then "maximize price" (which is not well defined). Though, I suspect, what you really want is to find the price that maximizes your revenue or profit..
– Nameless
Aug 9 at 20:41










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Do a plot by plugging in increasing numbers for the price of said product. This way you can visually see at which price the probability is at its highest.



Alternatively you can do it in a purely theoretical way by taking the derivative of the right-hand side and set it to 0, then solve for the price.






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    Do a plot by plugging in increasing numbers for the price of said product. This way you can visually see at which price the probability is at its highest.



    Alternatively you can do it in a purely theoretical way by taking the derivative of the right-hand side and set it to 0, then solve for the price.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Do a plot by plugging in increasing numbers for the price of said product. This way you can visually see at which price the probability is at its highest.



      Alternatively you can do it in a purely theoretical way by taking the derivative of the right-hand side and set it to 0, then solve for the price.






      share|cite|improve this answer






















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        down vote










        up vote
        1
        down vote









        Do a plot by plugging in increasing numbers for the price of said product. This way you can visually see at which price the probability is at its highest.



        Alternatively you can do it in a purely theoretical way by taking the derivative of the right-hand side and set it to 0, then solve for the price.






        share|cite|improve this answer












        Do a plot by plugging in increasing numbers for the price of said product. This way you can visually see at which price the probability is at its highest.



        Alternatively you can do it in a purely theoretical way by taking the derivative of the right-hand side and set it to 0, then solve for the price.







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        answered Aug 8 at 23:22









        Sam Anderson

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