Sales Response Models

Question 1

Linear model (constant marginal returns)

Answer 1

Ads: can be estimated easily (by regression analysis / OLS)
Simple and easy to understand

Dis: constant returns to scale not realistic
Assumption that sales can be indefinitely increased not realistic

Question 2

Multiplicative model and semi logarithmic model (decreasing marginal returns)

Answer 2

Ads: diminishing marginal returns more realistic
Easy linerarization with the help of a logarithm (semi log model)
In the multiplicative model, the elasticity can be derived directly from the power exponent of the predictor (constant elasticity)

Dis: no sat level
I x is close to 0 ( and you thus take the natural log of a very small number) sales would go to minus infinity, which is impossible (semi log model)

Question 3

Modified exponential model

Answer 3

Ads: saturation level corresponds to realistic consumer behaviour

Question 4

S shaped model (log reciprocal and logistic mode)

Answer 4

Ads: accounts for the phenomenon that advertising needs to be raised above a certain level to have an impact

Dis: outcome variable in logistic model can only be predicted in the form of a probability (eg purchase probability, adoption probability