Pricing Optimization Analysis

Analysis for price optimization

One of the dramatic lessons that is learned by most companies is the importance of the marketplace as the final judge of pricing decisions. In the expanded economy, pricing decisions will become even more important. Understanding the sensitivity of the market to different pricing policies is essential to successful participation in the high stakes game of marketing.

To the manufacturer with multiple products in a complex market, setting the prices of all the products in the portfolio can be an imposing task, particularly if the products compete with one another. Moreover, any adjustments in the price of the product portfolio will undoubtedly cause changes to the competitor's prices. In the face of such complexity, it is not surprising that many companies choose to use ad-hoc methods and to set each product as a separate decision.

ValueScope can help with these complex decisions.

Finding the demand function

Let's imagine a situation in which our client has one or more products competing for sales with competitors' products in the market. Suppose further that we have conducted a conjoint analysis survey over a sample of customers in this market. This will produce for each respondent in the survey the following:

• The utility for price, U_i(P), where the index i refers to the ith respondent.
• The utility of all the other attributes for each product in the market; let's call this utility for the ith respondent and the jth product U_ij
• The number of customers represented by each respondent; W_i will denote this "weight" for the ith respondent.

Notice that the first two quantities are measurements resulting from the conjoint analysis survey, while the third is determined by the sampling plan used to recruit respondents.

With these three quantities it is possible to estimate a demand function over the products in the market. To do so we need an additional model to describe how respondents' ultimate choice of products depends on the measured utilities.

Estimating sensitivities to price

The availability of an analytic demand function is a powerful tool for pricing analysis. For example, with the demand function it is now possible to calculate each product's elasticity with respect to price. Since the elasticity of demand to price is just the percentage change in demand per percentage change in price, the elasticity is just the quantity of the demand for the product with respect to its price.

Price elasticities are an important source of information about how a market is likely to react to changes in price. They can be used to determine which products will have large changes in demand and which will have relatively small changes for a fixed percentage change in price.

This idea can be taken one step further. Suppose that our client has several products in the market and wants to estimate how changing the price of one will affect the demand of another. This cross-pricing effect can be represented as a cross-elasticity, defined as the percentage change in the demand of one product per percentage change in the price of another. The cross-elasticity of the demand of the product to the price of the other product is the derivative of the demand of the first product with respect to the price of the second product. These cross-elasticities can be calculated analytically from a demand function and so can be reported as a direct output of the conjoint analysis study.

Finding the optimal price

The availability of a multi-product demand function along with elasticities and cross-elasticities raises the possibility of calculating an optimal price.

Finding the optimal price is just a question of finding the price that causes the above equations 3 to equal zero. There are many sophisticated techniques in the arsenal of operations research for solving this type of problem.

The best approach is to build a simple model of how the competition will respond. This competitive response model can then be incorporated into the optimization of prices. If there is uncertainty about the competitive response, then this can be included in the model so that a probabilistic competition model results. Once the competitive response model has been constructed, sensitivity analyses can be conducted over the uncertain elements of the model. In most cases, there will be a few key factors about competitive responses that Significantly affect the optimal price settings. Once identified, attention can be focused on resolving the uncertainty about these key factors.

Limitations of the approach

The optimization scheme proposed above is based on several simplifying assumptions, each of which can be relaxed at the expense of increased complexity. Some of these assumptions are discussed below:

Logit choice model

The logit model has the obvious advantage of analytical simplicity. Other choice models such as the mUltivariate probit could be used instead, although the probit model in particular requires considerably more complex numerical computations.

Preference model

Regardless of the form used, the demand function only describes customer preferences for products rather than actual sales. It is quite feasible to add a separate module to the above structure that describes those aspects of the market not contained in simple preferences. Examples of issues that might be included are the distribution network, manufacturing capacity constraints, sales force coverage and effectiveness, and customer reluctance to change.

Linear cost model

The formulation of the optimal pricing problem assumes that the incremental cost of each additional product sold is constant. If there are significant economies of scale over the range of demand considered in the demand function, then the cost model can be modified to include these effects.

Homogeneous market

The formulation of the demand function assumes implicitly that the size of the market to be distributed among the products is constant. As the prices of products change it is reasonable to expect that customers will enter or leave the market in response to the overall price level. To include this effect requires a separate model of the total market size and its dependence on overall price levels.

Designing the survey

If the utilities from a conjoint analysis survey are to be used to estimate optimal prices, care must be taken that the utilities adequately represent customer attitudes toward product prices. There are four issues that require particular attention:

• Form of the price utility
• Choosing price differentials
• Adapting the price range to the individual
• Adapting pricing units to the individual