retail-stats 0.0.2.post1

A simple library to calculate price elasticity, cross elasticity

Retail Stats

This repository contains code to calculate various values used in retail for products whose sales and prices are provided.

Metrics currently available:

1. Price Elasticity (In Progress)
2. Cross Elasticity (Complete)

These simple, almost naive, implementations are taken from the Wikipedia definitions of the metrics. All performance benefits are from the work of Numpy. The purpose of this repository is to provide some convenience functions.

Installation

Install from PyPi.

pip install retail-stats

If installing outside of a [virtualenv]() then use --user to avoid permission issues:

pip install --user retail-stats

Dependencies

1. numpy~=1.19

Calculations

Cross Elasticity

From Wikipedia,

measures the responsiveness of the quantity demanded for a good to a change in the price of another good, ceteris paribus.

This can be seen written using the formula:

Percentage Change in Quantity Sold of Product B
-------------------------------------------------
Percentage Change in Price Charged for Product A

The implementation is a direct copy of the formula.

from retail_stats.elasticity import calculate_cross_elasticity

Calculate Cross Elasticity for a single pair of products

from math import isclose
from retail_stats import elasticity

original_quantity = 200
new_quantity = 400

original_price = 1000
new_price = 1050
# (200 / 300) / (50 / 1025)
expected_ced = 13.66666666666666
ced = elasticity.calculate_cross_elasticity(original_quantity, 
                                            new_quantity, 
                                            original_price, 
                                            new_price)

assert isclose(expected_ced, ced)

Calculate All Cross Elasticities

from math import isclose

import numpy as np

from retail_stats.elasticity import get_all_cross_elasticities

skus = np.array(list("ABCD"))
# [original, new]
qty_a = [200, 0]
qty_b = [200, 400]
prc_a = [1000, 1050]
prc_b = [1000, 1000]

qty_c = [1000, 1050]
qty_d = [1000, 1100]
prc_c = [100, 80]
prc_d = [80, 80]

original_quantities = [qty_a[0], qty_b[0], qty_c[0], qty_d[0]]
new_quantities = [qty_a[1], qty_b[1], qty_c[1], qty_d[1]]
original_prices = [prc_a[0], prc_b[0], prc_c[0], prc_d[0]]
new_prices = [prc_a[1], prc_b[1], prc_c[1], prc_d[1]]

"""
Cross Elasticities between pairs A,B and C,D

  | A | B | C | D 
A |   |   |   |
B |   |   |   | 
C |   |   |   | 
D |   |   |   |
"""

ceds = get_all_cross_elasticities(original_quantities=original_quantities,
                                  new_quantities=new_quantities,
                                  original_prices=original_prices,
                                  new_prices=new_prices)

assert ceds.shape == (len(skus), len(skus))
assert isclose(ceds[np.argwhere(skus == "A"), np.argwhere(skus == "A")], -41)
assert isclose(ceds[np.argwhere(skus == "B"), np.argwhere(skus == "A")], 13.66666666666666)
assert isclose(ceds[np.argwhere(skus == "D"), np.argwhere(skus == "C")], -0.4285714286)
assert isclose(ceds[np.argwhere(skus == "C"), np.argwhere(skus == "A")], 1)
assert isclose(ceds[np.argwhere(skus == "A"), np.argwhere(skus == "C")], 9)

Performance

Core elasticity function

Number of Products	Time in Seconds
1,000	0.065512
10,000	0.200022
100,000	1.727269
1,000,000	26.730988