Price Sensitivity Analysis using Demand Curves and Pricing Models
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Demand Curves and Pricing Models for Price Sensitivity Analysis

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 by defining the demand curve.  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 a company's prices depends also on competitor prices, it is often helpful to include in the price analysis a causal factor calculated as an index of price relative to total market or key competitor prices.

Pricing Models and Demand Curves

A pricing model is the mathematical formula that is used to descibe price sensitivity in the form of a demand curve.  A wide variety of mathematical models can be used.  If weekly or monthly historical sales and price data is available over a good period of time, usually two years or more, this can be used in the price analysis.  The historical data may only cover a relatively small range of prices and one should be careful not to extrapolate results in the form of a pricing model or demand curve much beyond the range of historical experience.  So if the historical price of a product has varied between 1.35 and 1.60 it would be dangerous to use a fitted curve to predict the demand that would result from extremely different prices of 0.50 or 3.50.

 Straight line (linear) relationships often give a good starting point in the price analysis and have the benefit that perfect mathematical solutions are available using the linear regression method that is widely available in software.  A number of other types of demand curve can be transformed to linear form using logarithmic mathematics, so are also relatively easy to use.  These include poynomials, the exponential curve and the power curve.  Other forms of curve may require the use of nonlinear regression using optimisation techniques.  These require the use of specialist statistical software and may not always come up with the same solution across different software.

Straight Line:  Sales = a + bp

a= constant. b = coefficient of price (this will be -ve), p=price

Exponential curve:  Sales = aebp

where e =  mathematical constant (approx. 2.7183)

a = constant, b = coefficient, p = price

Polynomial (2nd order):  Sales = a + bp + cp2

a = constant, b = coefficient, c = coefficient, p = price

Power curve:  Sales = apb

a = constant, b = coefficient (elasticity), p = price

The power curve is somewhat special in that it exhibits a constant price elasticity of b (see below). 

Price Elasticity

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 demand 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 at particular price may then be referred to as the 'point' price elasticity.

Cause and Effect Analysis

In cause and effect analysis, or causal analysis, the aim is to quantify the effect of factors which are suspected of causing shifts in sales volume or market share. Price sensitivity analysis in the form of pricing models and demand curves is one special example.  Other causal factors such as unseasonal weather or economic indices may also play a part.  So a full cause and effect 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 have been experienced in historical demand. That is in itself is very helpful, but to make full use of a pricing model or other causal model in forecasting it is necessary to forecast the future values of the causal factor itself before one can calculate the demand forecast.  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, the task may be easier.

Need for expert help

Specialist software is invaluable in carrying out price sensitivity analysis and other cause and effect 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, 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.