Design of Price and Advertising Elasticity Models


The biggest problem that many marketing managers face is the pricing of the products. As a marketing manager, you need to know how to:

  1) Maximize Sales
  2) Increase Share Price
  3) Lower Inventory Cost
  4) Maximize Profit Margin

Price is constantly changing with the economy, and its overall environment. We also are already familiar with the price elasticity, if you have taken microeconomics course in high school. (Note: This article gets bit more technical in the marketing statistic, so it would require you to have some understanding in the Ln log and regression analysis knowledge)

Historical data of your product sales is often the best answer to how the price change occurs. To identify the pricing of a product, we use two important concepts:

  • Price Elasticity of Demand
  • Advertising Elasticity of Demand

Before jumping into the elasticity of the pricing and advertising, let’s review the degree of pricing, so we can understand how price change over time. 

  • Highly Inelastic Pricing
  • Unitary Elastic Pricing
  • Relatively Inelastic Pricing

The following image shows the three elasticity pricing graphs.
Pricing Elasticity
Highly Elastic Demand  – LUXURY

  • Proportionate change in the quantity demanded is more than a given change in price.
  • Ep > 1 (in absolute term)

Unitary Elastic Demand

  • Proportionate change in the price brings about an equal proportionate change in the quantity demanded.
  • Ep = 1 (in absolute term)
  • Demand curve will shape like a rectangular hyperbola.

Relatively Inelastic Demand  – NECESSITIES

  • Proportionate change in quantity demanded is less than a proportionate change in price
  • Ep < 1 (Absolute term)

Pricing Elasticity of Demand

PED, known as the Pricing Elasticity of Demand, can be calculated below equation.

How to Calculate PED
PED = [Change in Sales ÷ Change in Price] x [Price ÷ Sales]
         = (∆Q ÷ P) x (P ÷ Q)
where ∆Q is change in quantity, ∆ P is change in advertising cost.

For LN-LN model, PED is the coefficient of Price when Ln (Sales) Is Regressed on
Ln (Price):  Ln(sales) = α1+ 1 x Ln(price) + ɛ1, where ᵦ1 represents the price elasticity in the preceding case and ɛ1 is the random error term drawn from a normal distribution

Advertising Elasticity of Demand

Advertising Elasticity of Demand (AED) is the measure of the responsiveness in the demand of a product to changes in the level of advertising.

AED = [Change in Sales ÷ Change in Advertising] x [Price ÷ Advertising]
= (
∆Q ÷ A) x (A ÷ Q)  

Similar to price elasticity procedure, the advertising elasticity runs a regression log of sales on log of advertising.  Ln(Sales) = α2+ 1 x Ln(advertising) + ɛ1, where α2 is the advertising elasticity of demand and ɛ1 is the random error term drawn from a normal distribution.

Building a Comprehensive Model

If both PED & AED are significant, the regression model would include both the price and advertising  variables, as shown below:
Ln(Sales)=α0+ ᵦ1 x Ln(price) + ᵦ2 x Ln(advertising) + ɛ1

Within this model, there is bias, describing the effect of omitted variables.
If advertising elasticity > true value = positive bias.
If advertising elasticity < true value = negative bias.

If the True model is:
Ln(Y) = αo+ α1 x Ln(price) + α2 x Z + ɛ1

But you can estimate the model as: Ln(Y) = + 0 x Ln(price) + ɛ1

The true value of coefficient 1 will be the sum of the estimated coefficient 1 and the bias: 1 true = 1 + Bias

If r = co-variance between the independent variables Ln(Price) and Z, then bias can be shown with the product between co-variance of independent variables [f(r)] and coefficient of omitted variable (α2):  Bias = α2 x f(r).

Factors that influence marketing mix model for price & advertising elasticity

Product Quality
If Better quality = higher price, then correlation coefficient for a regression model on price & quality positive.

Firms with higher-priced brands have usually exclusive or better distribution, then the correlation coefficient for a regression model between distribution and price would be positive.

Brand Life Cycle
Early adopters are less price-sensitive, thus price elasticity increases over time with life cycle of the brand. Price elasticity for brand have two components: (1) a within Brand component, and (2) a between-brand component. If within-brand component is weak, then the data aggregation over time will be positive bias. To better understand the relationship between price, brand and sales direction, weekly sampling would be recommended.

Contextual Factors
Contextual Factors can be socioeconomic and demographic information that influences the advertising elasticity. For example, higher income leads to lower price elasticity (less negative), while bigger family size can also lead to positive bias in advertising elasticity.
Two forms can be taken: (1) Increasing product awareness through digital ads, or (2) Incentive customers on using coupons, rebate and others. Increasing brand awareness often relates to lower price of the product, while the higher price is associated with coupon or rebate program, so the bias relationship is positive within price and promotion for rebates.

Price elasticity is affected by competitive products and their prices. Depending on the competition activity, bias effect changes. For example, the increased competition product price is positive, while decreased competition price is negative. The relative product price matters when considering the effect on the customer, not the price of the absolute product.

Share vs Volume
If sales volume is dependent, while the advertising is independent, the sales can be gained on market expansion or from competition’s market. If market share is used as dependent, then the market expansion is eliminated for positive increase effect.