### Simulation of data

To keep it simple, we will use a single product. For this, we take prices between 4.90€ and 5.90€. At higher rates, there are also fewer sales than at low prices. In this way, it is possible to estimate price elasticities. The simulated sales at the respective prices, then look like this: Likewise, an upward trend was built into the data. At the same time, the number of sales in the summer months is higher than in the other months. Thus, we can now implement a simple form of Sales Forecasting.### Calculating price elasticities and prediction of sales

The price elasticities are estimated using linear regression in which we assume a logarithmic relationship. A logarithmic relationship goes hand in hand with the assumption that demand exponentially grows as the price decreases and also that demand can not sink below zero:In this equation, is the intercept, is the price elasticity and the dummy for the summer months. In practice, such a simple model will not lead to valid results, but it should suffice for illustration:

Coefficients | Estimate | Std. Error | CI.95 (lower) | CI.95 (upper) |
---|---|---|---|---|

Intercept | 8.809 | 0.467 | 7.891 | 9.726 |

log(Price) | -0.939 | 0.277 | -1.483 | -0.384 |

0.180 | 0.010 | 0.160 | 0.199 |

### Adjusting prices according to sales targets

Now we have all the necessary results to be able to perform the last step, in which we calculate the prices required to compensate for possible differences. For this, we take as a starting point the Cobb-Douglas-function. In addition, the effect of price and elasticity on quantity was visualized:If we define the sales target as , we can transform the Cobb Douglas function as follows: With this formula, we can now use our results to calculate the price for a specific target. represents the sales target, represents the predicted sales, and is, of course, the estimated price elasticity -0.939. The formula gives us a factor around which we would have to adjust the price to reach the sales target. Also, the confidence intervals of the price elasticities can be used to calculate a range of price adjustments. In our simple example, we will now use the predicted next month with different targets. The price used for the calculation was taken from the last month, which was 5.40€.

Date | Prediction | Price | Target | Adj. Price | Adj. Price (lower CI) | Adj. Price (upper CI) |
---|---|---|---|---|---|---|

2020-01-01 | 1510 | 5.4 € | 2000 | 4.00 € | 4.47 € | 2.65 € |

2020-01-01 | 1510 | 5.4 € | 1800 | 4.48 € | 4.80 € | 3.46 € |

2020-01-01 | 1510 | 5.4 € | 1300 | 6.33 € | 5.97 € | 7.90 € |

2020-01-01 | 1510 | 5.4 € | 1000 | 8.38 € | 7.13 € | 15.37 € |