Price Sensitivity Modelling: Analysing the effects of Pricing
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Pricing Models

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Pricing Models in support of Pricing Strategy

A good understanding of the effect that pricing has on market share is fundamental to the setting of pricing strategy.  Price sensitivity can always be explored by live experimentation, but that course of action is often fraught with the dangers of lost sales and/or lost profits.  If a satisfactory pricing model can be constructed by carrying out a statistical analysis of historical data, then a pricing strategy can often be defined with far less accompanying risk. 

The purpose of price modelling or price sensitivity analysis is to identify and quantify those price effects.

Forecast Solutions makes use of specialist statistical software to construct pricing models using linear and non-linear regression techniques.  Of course a company's prices interact with competitors prices, so it is often be helpful to create a causal factor calculated as the ratio of company price to the total market price or to the price of a key competitor product.

Price Elasticity

Price elasticity is one way of describing price sensitivity.  Price elasticity is measured as the % change in sales likely to take place as a result of a 1% change in price.  The price elasticity of demand is always expected to be a -ve figure, as an increase in price will in most circumstances result in a decrease in demand.  Unit price elasticity refers to the unusual situation where a 1% change in price causes a change of exactly -1% in sales. 

In most price models the price elasticity will change depending on the particular point of reference on the sales to price response curve.  So the elasticity from a point where the price is 8.00 may vary from the elasticity when the price is 9.00.  The elasticity is sometimes then referred to as the point price elasticity.

Pricing Models to describe Price Sensitivity

A wide variety of mathematical pricing models can be used to describe price sensitivity.  The price sensitivity analysis often starts by exploring linear (straight line) relationships and this may well be helpful provided one is only exploring the effect of small price changes from a point close to the historical norm.

As it is unlikely that that price effects will truly occur in the fashion of a straight line, it is often useful to investigate alternatives in the form of non-linear relationships.  The exponential curve and power curve are especially popular as, by applying logarithmic transforms, they can be fitted exactly using linear regression techniques.  Other forms of curve are likely to require non-linear regression using optimisation techniques.

Exponential curve:  Sales = aebp

where e =  mathematical constant (approx. 2.7183)

a = constant, b = constant, p = price

Power curve:  Sales = apb

a = constant, b = constant (elasticity)

So the power curve exhibits a constant price elasticity of b. 

Regression Analysis and Causal Modelling

In causal analysis of any sort the aim is to quantify the effect of factors which are suspected of causing shifts in sales volume or market share. Price effects are one good example.  Other causal factors such as the unseasonal weather or economic indices may play a part.  So a full analysis incorporating the effects of other factors as well as pricing may lead to a fuller understanding and a better platform for the formulation of pricing strategy and other business strategy

When a causal relationship has been identified and quantified it can immediately help to explain variations that has been experienced in historical demand. That is in itself very helpful, but to make full use of a pricing model or more complete causal model in future forecasting it is necessary to forecast the causal factor itself.  If the causal factor is a leading indicator and/or some well known index for which other organisations publish forecasts, this can ease the task.

Need for expert help

Specialist software is invaluable in carrying out price sensitivity analysis and other causal analysis. Care is needed to avoid confusion of the results with natural seasonality or inherent trends in market size or share. Forecast Solutions can expertly carry out the work using specialist statistical software, examining the price effects and the influence of economic indices, sales force calling or other potential causal factors. The results can then be taken into account in defining pricing strategy, other business strategy and the demand forecasting process.

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