But at practical use of tools of pricing retailers face a set of problems, it leads to errors at determination of the price and, as a result, to losses in profit.

For example, when the retailer reduces the price, the consumer demand grows, but there is no profit. Increases the goods price — demand falls.

As we see, there is a strong dependence between the price, demand and profit.

Elasticity allows to find the optimum ratio of cost and the number of sales allowing to increase profit. In other words, the price acts as the balancing factor between the expected demand and the income.

Many existing models of price elasticity apply for "world supremacy", but a problem in what it is impossible to consider all factors influencing the price and demand when modeling.

The model developed by us offers correction of goods price on each shop separately, using historical data for half a year and considering factors of frequency, quantity and stability of sales which increase analysis accuracy. The model does not assume the maximum scope of all possible factors and cases of the change in price, but works for price adjustment of separate goods in shops of our clients.

Our approach differs from classical, and below we will explain than.

Classical model of price elasticity — determination of coefficient of point price elasticity.

This approach is good in the theory, but insufficiently reliable in practice because:

- Sales of goods are influenced by a set of factors except the price — the competition, advertizing, loyalty of buyers to a brand, availability of goods, etc.
- The model does not include time factor, so excludes seasonal influences on consumer demand, important for a retail.
- It is not enough two indicators of the price for the exact analysis.

Shortcomings of model of price elasticity can be seen having visualized a ratio of the changes in price and sales for specific goods.

Let's construct the diagram:

in horizontal direction — the changes in price;

in vertical direction — changes of sales of goods.

What did we receive? The majority of points with concentration about 0, both on at, and on x. As we see, the changes in price practically do not influence demand in any way and demand varies at the stable price. It is not possible to trace specific dependences.

Let's look for other approach for determination of the optimal price on goods.

**1. It is necessary will decide on the period for the analysis of price relation and demand.**

The period selected by us for the analysis of price elasticity — half a year. It allows to minimize risks of inflation, other external fluctuations of the market of a retail when calculating.

**2. Calculations are carried out for each shop separately.**

The optimal price for goods of each shop is calculated separately as each shop has the size, the range, the contingent of buyers, consumer demand.

**3. For the analysis we take only goods with rather stable demand which are on sale at least two times a week.**

**4. We monitor fluctuations of demand depending on the price.**

Let's construct the diagram, having placed sales of goods on a vertical axis, the goods price — on horizontal.

As we see, sales outlets on the diagram were grouped concerning axis X in the changes in price.

In a product retail where the prices do not change cardinally, logically will be to group sales in the changes in price with a step of 0,5 UAH. We define the average number of sales in each group further and we exclude all single sales from the analysis as doubtful.

**5. Let's locate the received points of average sales of goods for each price group on the diagram.**

On the diagram it is accurately visible that there is a dependence of data retrieveds and we can define a linear regression (trend).

Experimentally we defined that it is possible to use model if the price of goods changed at least 4 times, otherwise the result will be inaccurate.

**6. We received a formula for determination of dependence of number of sales on the price.**

As doubtful we will also consider options when b indicator> = 0. In this case for any reasons, demand for goods grows, though the price grows. So such indicators need to be studied separately. The option is possible that demand for these goods is not elastic at all, so it does not get to our model.

Visually the diagram when b indicator> = 0, looks so:

**7. Let's construct model of dependence of profit on the goods price.**

For this purpose we need to define dependence of a margin on the price.

The profit is equal to the dependence of sales increased by a margin from the price.

Let's substitute in a formula dependence of sales and a margin on the price.

**8. Let's construct the diagram of dependence of profit on the goods price.**

In vertical direction — day profit.

In horizontal direction — the goods price.

The diagram begins is under construction of a price point without margin, the got profit is equal in it to 0.

We find a point on graphics in which the got profit will be maximum and we define value of the optimal price.

The model shows recommendations about reduction in price from flowing to optimum that will make additional profit due to increase in number of sales in day.

To consider the possibility of an advance in price to optimum (as on the diagram below) we will not be. At pricing it is necessary to consider a set of external factors: price of competitors, price policy of a network, state recommendations and restrictions.

Let's sort several cases of use of functionality of BI Datawiz.io for the choice of the optimal price on goods. Service carries out the analysis of the change in price and demand for each goods of shop, and on the basis of the described model creates recommendations about the optimum change in price for goods where it will cause increase in profit.

In

**Shop 1**one recommendation for goods Champagne Soviet from a brand our Kiev is created.

In the table it is specified:

- description of goods;
- the price without margin;
- the current price with a margin;
- recommended price;
- the average number of sales in day;
- the predicted number of sales at the change in price;
- the predicted increase in profit on specific goods and on shop in general.

I.e. all necessary information for decision-making.

For deeper analysis and reasonable decision-making, the retailer can look at diagrams of dependence of number of sales on the price and will make sure of correctness of calculations and recommendations.

As we see, at short-term reduction of price (most likely during this period actions on goods took place), sales of goods considerably increased. Increase in the price of all alcohol, and champagne including, since September 1 caused drop in sales.

On the second diagram we see how average sales in day depending on the price and the created trend line changed.

On the 3rd diagram the current and recommended price for Champagne our Kiev is determined.

So, at the moment champagne is on sale at the price 51, 83 UAH for unit, the profit in day makes 14,71 UAH. At reduction of price will grow to 45,99 UAH of sale and the got day profit will make 40,04 UAH.

It is 25,33 UAH more, than the current daily profit.

In

**Shop 2**we see recommendations about the change in price for 5 goods. The general daily profit of shop will make 127,13 UAH.

Let's consider diagrams of forming of the optimal price on the example of beer Lviv in PET bottles of 1,2 l.

As we see, for the current half a year, the price of these goods changed 6 times. And consumer demand rather strongly fluctuated even at the identical price.

Here linear relation is visible.

It is recommended to reduce the price from 16,91 UAH to 15,57 UAH at the same time the day profit will increase by 2,65 UAH and will make 30,22 UAH, apparently on a curve below.

In

**Shop 3**service constructed recommendations for 4 goods.

Let's analyze price elasticity of goods the Chocolate biscuit from a brand Roshen.

On the diagram we see 5 changes in price, but at the last advance in price to 33,5 UAH everyday sales of goods do not exceed 1, so we do not use such data. It is visible on diagram 2 where 4 indicators of sales are considered.

On the following diagram the current price of a biscuit which makes 32,66 UAH with the everyday income in 16,42 UAH is displayed. The recommended price makes 29,62 UAH that will increase profit by 7,05 UAH.

Let's notice that the approach to determination of the optimal price offered by us is approximate to practice and a real situation in a retail, excludes risks of classical approach to price elasticity which uses only two indicators, does not consider seasonality and other factors.

The model developed by us considers a time factor, frequency, quantity and stability of sales. Gives the chance for the independent analysis by means of visualization of historical data of the change in price and demand.

The BI Datawiz.io service by means of the developed model processes all data volume on sales and shows results in the form of the list of goods, reduction of price of which will make profit for the retailer.

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