Price is the only marketing "P" directly affecting the bottom-line.

[ W.R. Paczkowski, Data Analytics Corp. ]


Setting a reasonable and justified market price of a product is a basic but one of the most difficult problems in marketing practice.

Traditional survey-based methods rely on statements of respondents. The most often used are are Gabor-Granger "buy response" and Van Westendorp (1976) "price sensitivity meter" methods. Both the methods suffer a drawback of the estimation being done in isolation from competing products and regarded only indirectly through respondents' awareness of their prices. There is no reference frame for answering the questions and no trade-off among products as is usual at purchase decisions. The contexts of competing products is only indirect. An influence of a possible change in competition is not estimable.

Newer value-based methods are known under the common name WTP - Willingness To Pay or reservation price estimation. Reservation price is the maximum amount a person would be willing to pay, sacrifice or exchange in order to receive a good or to avoid something undesired. Most methods are based on effective "Use + Non-use + Option" values. Promising are preference-based methods where the decisions are made with respect to competing products or services. A natural way of obtaining preference values is a conjoint exercise, typically a choice-based one, as it is known to have a lower preference bias of price attributes than other methods.

Given the fact that stated price elasticities are nearly always greater than those observed on the real market it can be easily shown that maximizing a revenue using the standard logit model of choice conditional to price leads to a substantially lower price than the market one, typically by 25% or more. This unfortunate property makes use of this approach unusable. A better approach is maximization of profit, but (a) realistic costs are hardly ever known to a researcher and (b) the unrealistic sensitivities are still offending.

The main principle of a WTP estimation from conjoint data is a compensation of an increase/decrease in utility of a product (or its attribute) with increase/decrease of a price of the product (or the attribute) so that an equivalence of the two is achieved. From a practical point of view, WTP values obtained this way are often exaggerated in either of the directions. Various methodological and computational methods of dumping the stated sensitivity have been suggested but none of them has been widely adopted.

As aside

Our attempts to modify the known methods of WTP estimation were unsuccessful. We decided to develop an alternative method on a different principle.


Customers buy goods on the existing market. We assume customers optimize their choices in a conjoint exercise in a way similar to that on the market, i.e. they maximize the utilities of the chosen products given the available products, shown prices, and individual constraints and habits. The latter are both physical and/or psychological in terms of satisficing. The utilities are therefore behavioral rather than strictly econometric.

The main idea of estimation of the optimal competitive price for a product lies in standing the inspected product against predefined competing products at their market prices. The simulated choices of competing products by respondents are assumed as optimal. The steps of the estimation procedure are as follows.
  1. Define a set products composed of the inspected and competing products. This set must be a subset of products from a CBC brand-price exercise. Market prices of all the competing products must be known.
  2. For the competing products and for each respondent, create a numerical model of a hypothetical market with the following properties:
    1. If any of the competing products were added onto the model market and the stated aggregated revenues maximized for the product, the best approximation of the product current market price would be retrieved in terms of the maximal likelihood method.
    2. Each respondent contributes to the model independently with the parameters derived from the complete set of products queried in the CBC exercise and representing the product category universe.
  3. Add the inspected product in the model of a hypothetical market and maximize its stated revenue to obtain an individual optimal price and its likelihood for each respondent.
  4. Using the values from the previous step compute the statistical mean of the price. 

The final price value is not a price obtained by a maximization of aggregated revenues. It is the maximally likely price of the inspected product conditional (1) to its maximal expected revenues, (2) to the individual preferences in the sample, and (3) to the assumed current market prices of the selected competing products. In plain words, it is a mean value in currency units perceived by those who buy or would buy the product on the current market. As it is obtained from a competitive environment it has been named Optimal Competitive Price.

  • Dependence of the estimated price on the scaling of part-worth, e.g. due to number of products in a CBC exercise, number of price levels, settings in a numerical method of the experiment analysis, etc., is suppressed.
    • There is no need to refine the scaling obtained from a CBC experiment to make it closer to the revealed (market) sensitivities as is recommended by some authors.
  • The estimated optimal prices reflect the competitive context.
  • Several tens of products can be included in the estimation, i.e.much more than is feasible using the traditional methods.
  • Virtually an arbitrary number of sets of mutually competing products can be defined.
  • As the prices are derived from the common CBC exercise, their comparison is more reliable than those from unrelated questioning in the traditional methods. 
  • Expected price range of the tested products in the set of competing products should not exceed the ratio about 1 : 2. A higher ratio might lead to excessive error of the price estimate. This is due to the fact that the competing products that define the hypothetical market are treated as a single composite product. 
    • Typically, price optimization for products differing in size from competing products (single unit, multi-pack, large packaging is not feasible without additional assumptions.
  • No information on revenue values can be obtained as the method relies on the properties of a statistical mean. Of course, the optimized prices may be used as parameters in the preference share simulator built on the data from the CBC exercise. However, the problems inherent to simulation based on stated preferences, namely the sensitivity to price being usually higher than that on the real market, cannot be avoided.
As aside



The optimal competitive price of an existing product is a straightforward check if the price is set correctly or not. It may be much more useful if a new product or a product variety is to be introduced in the market. A usage, sensory or other consumer test may be completed with an optimal competitive price test to avoid the risk of setting the introductory price too low or high.

The method uses data from a brand-price CBC - Choice Based Conjoint exercise. However, certain precautions are required.


Definition of competing product sets

The method allows to compute optimal competitive price of a product for various sets of competing products. This can be useful in a targeted positioning of a product in the market. The sets must be defined prior to an estimation. The decision which products are the direct competition with the product of interest deserves an increased attention. It can be based on the current knowledge of the market or cross-elasticities obtained from the CBC exercise. It seems that product managers often wish to set the price of a product competitive to a rather narrow selection of products believed to be a threat for the product of concern.

The broader the competing set is defined the lower the estimated optimal price is as the product is forced to compete with more products. The optimal price gets always lower when low cost products and/or strong brands are added in the set. When high cost products are added (with low cost products not present) the opposite effect can be observed but it is never as pronounced. Assembly of the competition is therefor critical. Namely presence of low cost products, compared to the product of interest, should be avoided.

Of course, products of the same origin, i.e. producer or vendor, should not be used as the products competing with the inspected product(s) so that any cannibalization effects leading to lowering of the estimated prices are circumvented.

Provided timing, placement, distribution, promotion or other effects have been taken in account in the brand-price CBC exercise, these effects can be included in the estimation of optimal competitive price.



The estimated optimal competitive price is a preferential one. It is the perceived monetary value of the product in the frame of the competing products offered for their market prices. It cannot guarantee the absolutely maximal expected revenues, but is supposed to be very close.

The estimated price for a new product represents a willingness to spend this amount for the product in presence of competing products. This is clearly different from WTP - Willingness To Pay method that often tends to give higher than usable values, or from revenue maximization conditional to price that usually gives too low estimates.

The difference between the estimated and current market prices is a measure for the product market performance irrespective of the product market share.

Quite strong effects can be expected from sample variations. Availability, awareness, knowledge and preferences of some products are regionally dependent. A seasonal dependence may appear. Presence of the locally distributed products in the set may substantially influence the results.


The method has been tested on several brand-price problems with sensible results. In addition, it is believed to be useful for prices of options of products and services as well. However, there are limitations in this approach. If a product has more than one priced option, only one of the prices can be optimized at a time, and the other must be known and set fixed.

As aside


Example: Czech beers

This example is based on the same data from a brand-price CBC as used in examples of cross-elasticity and loyalty analyses. An optimal competitive price estimation requires mutual substitutability of the products, i.e. similarity in terms of usage, quantity and price. The CBC was done with 35 off-trade beer products sold in half-liter glass bottles and 1.5 liter plastic (PET) bottles. The cheapest low end beers and all beers sold in plastics were omitted. Only relatively well accepted brands sold in half-liter glass bottles entered the analysis. Market prices of all products were known.

The first competition set made of 22 brands was defined mostly in order to demonstrate the efficiency and robustness of the method. The second set contained 10 brands that made the core of sales and were priced from 7.90 K up to 10.90 K.The third set was made of 10 the most expensive beers in the test. The fourth set is a targeted solution based on external information. It might be viewed as an example of checking prices in a brand position study. 

The Czech market of beers is very competitive. One could expect the prices to copy the perceived values. Generally this has been confirmed but with some exceptions.

As aside


Optimal Competitive Prices of Czech Beers
Market Values
Estimated Values, K
Market Price Range of Competing Products
Brand Price, K 7.90 - 19.90 K 8.90 - 10.90 K 10.50 - 19.90 K 10.90 - 15.90 K
7.11 - -
7.90 9.36 - -
8.00 6.85 - -
8.50 8.78 - -
8.50 8.00 - -
8.90 7.52 - -
8.90 8.41 8.62 -
8.90 9.08 9.01 -
8.90 8.75 8.63 -
9.50 8.36 8.07 -
9.50 10.70 11.28 -
9.50 7.59 7.89 -
9.50 7.66 7.77 -
9.90 9.97 9.36 -
10.50 10.85 11.16 14.15 -
10.90 9.00 8.95 11.69 12.60
11.50 8.27 - 9.62 9.82
11.90 9.28 - 11.13 11.45
12.90 8.35 - 9.83 9.64
12.90 9.75 - 11.98 12.52
13.90 9.48 - 10.88 11.17
15.90 11.05 - 14.62 15.88
18.90 8.08 - 9.94 -
19.90 20.07 - 25.66 -
Beer type
Low End Regular Lager Premium

The pattern of the 22 competing beers gives a clear picture of perception of the beers in agreement with the common notion. Pricing of regular beers is mostly in accordance with their perceived values. On the other hand, most lagers and premiums are perceived mostly as not worth of the price except the UP and VS brands commonly recognized as the top level choices in their price ranges. 

When a competition set is narrowed, the estimated values of optimal competitive price can be expected generally higher. As can be seen, moderately priced products bought by most of consumers obey this rule only partially. However, the agreement of the computed and market prices for the both narrowed competition sets are quite good.

The differences in estimated values of the two beers (VS and OK brands) present in the first two narrowed competition sets reflect the views of consumers dominating these ranges. Evidently, consumers of lagers and premiums are willing to pay more. The lager UB is worth a special notice. While it loses when standing against all the other considered brands, it gains its position back when stood against its supposedly tantamount rivals.

There is an apparent discrepancy between the market and estimated prices of the lager and premium varieties of the brand AG. This does not mean their prices should be decreases. The regular beer AG is a work-horse of the brand and its price is clearly optimal. The lager and premium varieties, despite their lower perceived values, must be priced higher simply because of their higher classification. They are source of the brand diversity thus increasing the overall value of the brand.

The result of estimation for the premium beer OL might seem a complete failure. However, this brand was a specialty, had very low awareness and negligible penetration at the time of the study execution. Its choice frequency in the CBC exercise was exceptionally rare. It was kept in the set to demonstrate that one has to be very alert when interpreting such results. If DCM data are scarce it is often useful to discard them which is done in the last competition set setup.

One may assume the popularity of the lager VS to be temporary and its price too suggestive. In addition, it may be wise not to use price to compete with an exceptional position of the premium beer UP. The resulting optimal prices for the reduced set of 7 lagers show that the lager OK has a potential for a price increase. The market price of the beer AG is still above its perceived value. The estimated optimal price for the lager UB equal to its established market price demonstrates the utter importance of setting the targeted competition correctly