## Problem

Reliable price elasticity of demand is hard to obtain from the actual market data. For assessing elasticity experimentally, conjoint methods offer by themselves but with some inherent difficulties. Elasticity coefficient is usually derived for an indirect utility model under fixed budget or other restriction to be equivalent to marginal rate of substitution. Evidently, a change in the underlying model will lead to a different estimation method and to a different coefficient value even for the same data.

The main problem lies in the data from MR being stated rather than revealed. Respondents only simulate their would-be decisions and are much more sensitive to the stimuli than in the real market. Another problem is encountered if metric-based preferences are used. Their relationship to econometric measures is usually weak. Use of a DCM - Discrete Choice Model is of a clear advantage as it leads to well defined probabilistic utilities.

## Solution

DCM model probabilistic utility is of McFadden's type. Therefore, any type of elasticity can be approximated as a function of the derivation of utility value by logarithm of price, and some method of numerical derivation can be exploited.

The inherent problem in analysis of a DCM experiment is scaling. It is influenced by many factors such as design of the experiment, ranges of attributes, number of experimental points (choice tasks) and experimental errors (noise). An advantage of hierarchical Bayes methods of estimation is a possibility to influence the final scaling using either estimates from revealed preferences (market data) or stated preferences (calibrations in the interview). Nevertheless, the scaling due to the artificial environment of an interview cannot be overcome and will be still present in the utility estimates. Elasticities computed from stated preferences are nearly always many times larger than those to be expected in the real market.

As aside
• Rank or choice preferences of an individual are, by principle, invariant to scaling of utilities. Scaled utilities can be obtained and stabilized only from data for a sufficiently large sample.

Numerical derivation of experimental data is very sensitive to random errors. To keep the errors and their propagation reasonably low the conjoint exercise and all estimation methods must be robust. Especially part-worth for the least often chosen products will have the lowest precision which means such elasticities should be always considered with utmost caution.

## General Properties

Of several possible formulations, product managers are interested in price elasticity of demand. The closest approximation that MR can provide is elasticity of choice-based share of the products covering a major portion of the market share. The method includes implicit assumption that the total number of choices on the market is constant and independent from any price changes which presumes budget constraints of individual consumers being at least partially relaxed. The latter condition adds to an experimentally estimated sensitivity to price.

An inherent problem in choice-based methods is apparently high elasticity of substitution due to completely unhindered switch between offers in the interview. It is further enhanced by a natural tendency of respondents to avoid choosing the same product again and again in an exercise in contrast to the behavior commonly observed on the real market.

A disadvantage of hierarchical Bayesian method of estimation is scaling of part-worth estimates being dependent on the setting of prior variances. However, quite stable values can be obtained from different studies using well-tried values of estimation settings. From comparisons of published data one can guess elasticities estimated from stated preferences for FMCG/CPG to be about twice of those found on the market. There are no guidelines for services and durables.

As aside
• Price elasticity of a "normal" good should be negative since demand decreases with price increase. For the sake of convenience, the formula of price elasticity is usually negated to give positive values. This convention holds in this text as well.
• The difference between share-based and demand-based elasticity is best seen for the monopolistic market with 100% share. The share-based elasticity is zero by definition as opposed to non-zero elasticity of demand. On a stabilized competitive market without a single dominant player the differences are small and can be neglected.

Individual sensitivity to price of an accepted product has in general a bell shape. It is close to zero in the region of low prices for which the product will be nearly always chosen. Above some high price the product will be nearly never chosen. A formula for an aggregated elasticity must respect this fact by weighting individual contribution to elasticity at the selected price point for which the elasticity is assessed.

Aggregate elasticity is neither a constant but the profile is different. It may be taken for a constant only in a sufficiently narrow price interval. Its actual width is problem dependent. Aggregate sensitivity to gross price of a good usually grows with price due to the fact that most consumers buy goods from some price interval and, when price of their choice is increased, instead of willing to choose a good from a higher priced category they prefer a substitute.

If a product is offered for a gross price, the most reasonable price point for assessing elasticity is the common market price. If a product is composed of several price attributes (communication tariffs, packages of goods or services, etc.) the partial elasticities should be determined for values of an existing product or products. Each product will have its own set of aggregate partial elasticities even if some prices are equal. The reason lies in the facts that individual partial elasticities of substitution are often strongly non-linear, and different products are accepted by individuals differently. An individual with an arbitrarily high sensitivity to a price does not add to the aggregated elasticity if the product is not accepted by him or her.

Marketeers are often interested in change in demand for other brands evoked by change in price of their own brand. Unfortunately, cross-elasticities are less reliable than elasticities since both accuracy and precision are strongly dependent on the scenario size and setup. A sufficient representation of the potential competition and size of the sample are the prerequisites for obtaining sensible results.

It should be remembered that price elasticity or cross-price elasticity are bidirectional measures reflecting price changes (increase or decrease) of the respective products at a demand equilibrium.

Obtaining reasonably reliable values of own and cross-elasticities requires the following.
• A brand-price conjoint exercise with simple, easily comprehensible items covering major portion of the market category.
• A sample of about 400+ respondents for durables, 600+ respondents for services or 1000+ respondents for FMCG/CPG representing the given segment of the market.
• Respect to the fact that elasticities obtained from stated data are only relative and usually bigger than those observed on the market.
As aside
• Users of a MR study often ask for modification of a preference share simulator to match the recent market shares. Some methods, e.g. use of different "external [sensitivity] coefficient" for different products, will completely distort the stated relationships between sensitivities of all kinds. Elasticities obtained from a simulator modified in this way may be misleading.

## Aggregate Own-elasticity Value

Experimentally assessed values of aggregate price elasticities fall into a broad range of values. Below we provide an approximate assignment of values determined from stated preferences obtained from MR.

 ε < 1 Inelastic Nearly never obtained for gross (total) prices in MR. Obtained (as partial elasticities) for attributes with very low importance. ε ∈ (1 .. 2) Little elastic Necessity, monopolistic or subsidized goods (e.g. utilities). Only very rarely encountered in MR for gross price of a good. Typical for least important or used payed services in a package . ε ∈ (2 .. 4) Moderately elastic Typical values for gross prices of well established consumer products. Premium or luxury consumer goods bought by a distinct segment of well-off consumers. Medium-used payed services in a package . ε ∈ (4 .. 6) Elastic Typical for average, easily substitutable consumer goods. Very well established durables. Heavily used payed services in a package . Minimal elasticity of regular payments (monthly fees, installments, etc.) ε ∈ (6 .. 8) Above-average elastic Often inferior, low-level consumer goods. Elasticity of average durables. Typical for regular payments. ε ∈ (8 .. 12) Very elastic Unnecessary, occasionally bought consumer goods. Easily substitutable durables. Regular payments considered as principally excessive. ε > 12 Extremely elastic Common durables (cars, home and personal appliances), long-term financial services, etc. If the product is from FMCG/CPG category then there must have been something wrong with the product, its price, CBC exercise or estimation method.
As aside
• The classification above is way far from being absolute or correct. It is provided just for the convenience of elasticity study users to get notion about the possible values.

## Optimal Price

A question about an optimal price is often asked but only rarely answered. Van Westendorp or Gabor-Granger methods give usually too low absolute price estimates due to projection of wishes of end-users or consumers. Interpretation is usually done as comparison of pairs of the determined and current prices for own and competing products. An additional support for a managerial move can be obtained from price elasticities.

As mentioned above, utility scaling and, therefore, absolute values of estimated elasticities are unsure. When the sample is sufficient and the selection of tested products covers a major portion of a unique segment of the market it is believed the estimated stated elasticities converge to stable values. In the category of consumer goods, namely FMCG/CPG except electronics and similar, the following guidance for moves from the current gross price of a good can be provided.

 ε < 1 Inelastic A clear spur to increase the price. However, it is hardly ever observed. ε ∈ (1 .. 2) Little elastic A hint to price increase provided loyalty to the good is above average. No change can be recommended for a common good with low sales as the low elasticity may be an estimation artefact. ε ∈ (2 .. 4) Moderately elastic A price increase is possible but with a caution. Loyalty to the product, own price elasticity and cross-elasticity of the closest competing product should be considered. ε ∈ (4 .. 6) Elastic The most common value allowing no unequivocal recommendation. In case of loyalty above average and low cross-elasticities, a moderate price increase is possible. On the other hand, if cross-elasticity is above average, a moderate decrease of price is recommendable. ε ∈ (6 .. 8) Above-average elastic A price decrease is recommendable, but with caution. A check of loyalty and cross-elasticity is indispensable. ε > 8 Very elastic In general, a price decrease is recommendable but with many exceptions. If loyalty is high the high elasticity may be caused by occasional buyers who will not support long-term increase of sales.
As aside
• The recommendations above are way far from being absolute or correct. They are provided just for the convenience of a price study users to get notion of possible interpretation. A good knowledge of the market category is indispensable.
• No similar guidance can be provided for prices of durables, services and packages. These must be decided from comparisons between own and competing products considering all aspects one by one.

## Gross margin

An important aspect of any marketing activity is profitability. At least an approximate cost structure concerning the product is known to an interpreter of an elasticity study. In a very coarse approximation, gross price P a user/consumer pays for a product unit on the market is a sum of cost and gross margin, V + Π, per unit. The first term, V, is a generalized minimized cost per unit conflating all the necessary expenditures required for production and distribution to customer. The other term, Π, is a generalized gross margin per product unit. Based on definition of price elasticity the following formulas are obtained by maximizing the gross margin over total sales.

 Π = P = V —————— —————— ε ε – 1

The formulas are valid for [positively taken] price elasticity ε > 1 and the market at a theoretical equilibrium. This is an oversimplification of a real situation as saturation, distribution, cross-elasticity, availability, and other important market factors are ignored. Only a fast and crude check of the current price against the optimal one is possible.

If the current price is set so that the current margin per unit is lower than a calculated one, the price might be increased. However, the induced decrease in share might increase the real (rather than optimized) variable cost per unit that would decrease the actual margin at a higher price. This might ask for another increase of price thus reaching a price region with higher elasticity suggesting to lower the price back.

If the current margin per unit is higher than a calculated one, a suggested price decrease might not be always reasonable. Price elasticity is often lower at lower price values which would act against the decrease.

As discussed above, stated price elasticity of a well established consumer product is usually in the range from 2 to 4. The real elasticity value can be expected to be 2 or less. This suggest the gross margin of about 50% of an end price or more. Stated price elasticity for most products purchased repeatedly lies in the the range from 4 to 6. Halving these values to estimate the market ones suggests the optimal margins should be kept between 30 and 50%. Less accepted products should be satisfied with lower margins.

Durables have generally the highest observed elasticities due to the current ways of purchase (Internet, leaflets, etc.). Relative margins are therefore very low. Sources for an increase in sales must be searched in other aspects of marketing than in end price settings.

Packages, services and other products composed of several differently priced components follow all imaginable patterns. Each component is responsible for its own partial contribution to profit. The same is true for products and services of a value-added reseller. The activities leading to products with lower (partial) price elasticities should generate higher profits.

In real situations it is advisable to make decisions based on all available behavioral and econometric properties of a given product in comparison with competing products.