Price Sensitivity Analysis : Analysing the Effects of Pricing
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Causal Analysis to Measure the Effect of Price on Demand

Measurement of the effect of price changes on product demand is fundamental to the formulation of a pricing strategy.  Price sensitivity analysis fulfills that need by measuring the effect of price on demand through a causal analysis of historical price and demand data.  If a pricing model can be formulated by analysis of historical demand, then a marketing strategy can be defined with much lower risk than would be the case with live experimentation.  Because the effect of price changes depends also on competitor prices, it is often helpful to include in the analysis a causal factor that is calculated as an index of the company's price relative to total market or key competitor prices.

Price Analysis

Price elasticity is one way of describing price sensitivity and the effect of price change.  Price elasticity is defined as the % change in sales likely to take place as a result of a 1% change in price.  As increased price results in a reduction in demand the price elasticity of demand will always be a negative figure.  Unit price elasticity refers to the specific situation where a 1% change in price causes exactly a 1% decrease in sales. 

In most price models, including simple linear relationships, the price elasticity will vary depending on the particular point of reference on the 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 for Price Sensitivity

A wide variety of mathematical models can be used in price analysis to describe price sensitivity.  The investigation usually starts by looking for linear (straight line) relationships and this may well be useful provided one is only exploring the effect of small price changes from a point close to the historical norm.  Historical data usually covers a relatively small range of prices and we should not extrapolate any pricing model much beyond the range of historical experience, therefore straight line formulae are often adequate.

Over a broad range of prices a straight line relationship of price to demand is unlikely to apply.  If a sufficiently wide range of prices has been displayed across the product sales history it may be worthwhile to investigate alternative price models using nonlinear formulae.  The exponential curve and power curve are popular options that can be calibrated exactly in a wide range of software.  Other forms of curve may require the use of nonlinear regression using various optimisation techniques and this will require specialist statistical sofware.

Exponential curve:  Sales = aebp

where e =  mathematical constant (approx. 2.7183)

a = constant, b = coefficient, p = price

Power curve:  Sales = apb

a = constant, b = coefficient (elasticity)

The power curve exhibits a constant price elasticity of b. 

Econometric Modelling and Causal Analysis

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 unseasonal weather or economic indices may also 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 or other 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 such as GDP or RPI 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 econometric modelling.  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, analysing the effect of price change and the influence of unseasonal weather, 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.