Trying to Find Optimal Price Point in a Data Set
Question:
I have a data set that looks like this.
Year Quarter Quantity Price
2000 1 23 142
2000 2 23 144
2000 3 23 147
2000 4 23 151
2001 1 22 160
2001 2 22 183
2001 3 22 186
2001 4 22 186
2002 1 21 212
2002 2 19 232
2002 3 19 223
2002 4 19 224
2003 1 19 231
2003 2 19 228
2003 3 19 238
2003 4 19 238
2004 1 19 234
2004 2 19 231
2004 3 20 239
2004 4 19 235
2005 1 19 233
2005 2 19 243
2005 3 20 244
2005 4 19 233
2006 1 19 234
2006 2 19 241
I am trying to figure out a pricing strategy to maximize revenue (optimal price) using Python. I found a few example online, but didn’t know how to adapt them to my specific scenario.
This one looks good, but I’m not sure how to modify it to fit my data set.
https://www.datascience.com/resources/notebooks/python-dynamic-pricing
This one looks goo too, but again, I’m not sure how to make it work for me.
https://cscherrer.github.io/post/max-profit/
If someone here knows how to modify the sample code at one of those sites to fit the data I’m working with, I’d really like to see it. Or, if you have a link to another site that answers my question, please do share it. Thanks!
Answers:
Fundamentally I don’t think there’s a enough data here to be able to implement a pricing strategy based on pure statistics. The differences in quantity are barely outside of the standard deviation (std 1.6, mean 20.2). However theoretically what you want to do is:
- convert the data to a more easily importable formate such as csv
Year,Quarter,Quantity,Price
2000,1,23,142
2000,2,23,144
2000,3,23,147
2000,4,23,151
2001,1,22,160
2001,2,22,183
2001,3,22,186
2001,4,22,186
2002,1,21,212
2002,2,19,232
2002,3,19,223
2002,4,19,224
2003,1,19,231
2003,2,19,228
2003,3,19,238
2003,4,19,238
2004,1,19,234
2004,2,19,231
2004,3,20,239
2004,4,19,235
2005,1,19,233
2005,2,19,243
2005,3,20,244
2005,4,19,233
2006,1,19,234
2006,2,19,241
- load in the data
prices = pd.read_csv("price_data.csv")
- make a graph to visually show change in price with respect to quantity
sns.scatterplot(x=prices["Price"], y=prices["Quantity"])
- add columns for change in quantity and change in price
prices["% Change in Quantity"] = prices["Quantity"].pct_change()
prices["% Change in Price"] = prices["Price"].pct_change()
- calculate the price elasticity
prices["Price Elasticity"] = prices["% Change in Quantity"] / prices["% Change in Price"]
- Graph price elasticity vs the price
from this data you could then fit a model (depending on the complexity some order of polynomial makes sense), and use this to figure out at what point the price elasticity becomes too high and you wouldn’t be making enough sales. But that’s highly subjective and based more on business needs than anything else.
You can fit a linear regression model to the data, with quantity as the dependent variable and price as the independent variable.
The regression model will provide you with an equation that describes the relationship between price and quantity, and you can use this equation to find the optimal price that maximizes the quantity sold:
import pandas as pd
from sklearn.linear_model import LinearRegression
# Load the data into a pandas dataframe
data = pd.read_csv("data.csv")
# Fit a linear regression model to the data
reg = LinearRegression().fit(data[["Price"]], data["Quantity"])
# Find the optimal price that maximizes the quantity sold
optimal_price = -reg.intercept_/reg.coef_[0]
Note: This is a simple linear regression example for your data, and more complex models and data may be necessary to better capture the relationship between price and quantity. Also, keep in mind that this model is based on past data and may not always predict future behavior in a given market and its conditions accurately.
I have a data set that looks like this.
Year Quarter Quantity Price
2000 1 23 142
2000 2 23 144
2000 3 23 147
2000 4 23 151
2001 1 22 160
2001 2 22 183
2001 3 22 186
2001 4 22 186
2002 1 21 212
2002 2 19 232
2002 3 19 223
2002 4 19 224
2003 1 19 231
2003 2 19 228
2003 3 19 238
2003 4 19 238
2004 1 19 234
2004 2 19 231
2004 3 20 239
2004 4 19 235
2005 1 19 233
2005 2 19 243
2005 3 20 244
2005 4 19 233
2006 1 19 234
2006 2 19 241
I am trying to figure out a pricing strategy to maximize revenue (optimal price) using Python. I found a few example online, but didn’t know how to adapt them to my specific scenario.
This one looks good, but I’m not sure how to modify it to fit my data set.
https://www.datascience.com/resources/notebooks/python-dynamic-pricing
This one looks goo too, but again, I’m not sure how to make it work for me.
https://cscherrer.github.io/post/max-profit/
If someone here knows how to modify the sample code at one of those sites to fit the data I’m working with, I’d really like to see it. Or, if you have a link to another site that answers my question, please do share it. Thanks!
Fundamentally I don’t think there’s a enough data here to be able to implement a pricing strategy based on pure statistics. The differences in quantity are barely outside of the standard deviation (std 1.6, mean 20.2). However theoretically what you want to do is:
- convert the data to a more easily importable formate such as csv
Year,Quarter,Quantity,Price
2000,1,23,142
2000,2,23,144
2000,3,23,147
2000,4,23,151
2001,1,22,160
2001,2,22,183
2001,3,22,186
2001,4,22,186
2002,1,21,212
2002,2,19,232
2002,3,19,223
2002,4,19,224
2003,1,19,231
2003,2,19,228
2003,3,19,238
2003,4,19,238
2004,1,19,234
2004,2,19,231
2004,3,20,239
2004,4,19,235
2005,1,19,233
2005,2,19,243
2005,3,20,244
2005,4,19,233
2006,1,19,234
2006,2,19,241
- load in the data
prices = pd.read_csv("price_data.csv") - make a graph to visually show change in price with respect to quantity
sns.scatterplot(x=prices["Price"], y=prices["Quantity"])
- add columns for change in quantity and change in price
prices["% Change in Quantity"] = prices["Quantity"].pct_change()
prices["% Change in Price"] = prices["Price"].pct_change()
- calculate the price elasticity
prices["Price Elasticity"] = prices["% Change in Quantity"] / prices["% Change in Price"] - Graph price elasticity vs the price
from this data you could then fit a model (depending on the complexity some order of polynomial makes sense), and use this to figure out at what point the price elasticity becomes too high and you wouldn’t be making enough sales. But that’s highly subjective and based more on business needs than anything else.
You can fit a linear regression model to the data, with quantity as the dependent variable and price as the independent variable.
The regression model will provide you with an equation that describes the relationship between price and quantity, and you can use this equation to find the optimal price that maximizes the quantity sold:
import pandas as pd
from sklearn.linear_model import LinearRegression
# Load the data into a pandas dataframe
data = pd.read_csv("data.csv")
# Fit a linear regression model to the data
reg = LinearRegression().fit(data[["Price"]], data["Quantity"])
# Find the optimal price that maximizes the quantity sold
optimal_price = -reg.intercept_/reg.coef_[0]
Note: This is a simple linear regression example for your data, and more complex models and data may be necessary to better capture the relationship between price and quantity. Also, keep in mind that this model is based on past data and may not always predict future behavior in a given market and its conditions accurately.