Tutorial 4 Sales response models & elasticity

Question 1

What 6 sales response models were mentioned in the lectures?

Answer 1

1. Lineair model (constant marginal returns)
2. Multiplicative model
3. Semi- logarithmic model
   (decreasing marginal returns)
4. Modified exponential model
5. S-shaped models
   5a. Log-reciprocal model
   5b. Logistic model

Question 2

What are the advantages (2) and disadvantages (2) of a Lineair model?

Answer 2

Advantages
- Can be estimated easily (by regression analysis/OLS)
- Simple and easy to understand

Disadvantages
- Constant returns to scale not realistic
- Assumption that sales can be infinitely increased not realistic

Question 3

What are the advantages (3) and disadvantages (2) of multiplicative models & semi-
logarithmic models?

Answer 3

Advantages:
- Diminishing marginal returns more realistic
- Easy linearization with the help of a logarithm (applies to semi-logarithmic model).
- In the multiplicative model, the elasticity can be derived directly from the power exponent of the predictor (constant elasticity)

Disadvantages:
- No saturation level
- If X is close to 0 (and you thus take the natural logarithm of a very small number), sales would go to minus infinity, which is impossible (applies to semi-logarithmic model).

Question 4

What are the advantages (1) and disadvantages (-) of modified exponential models?

Answer 4

Advantages:
Saturation level corresponds to realistic consumer behavior

Disadvantages:
None, compared to the other models

Question 5

What are the advantages (1) and disadvantages (1) of the S-shaped models (log-reciprocal and logistic model)?

Answer 5

Advantages:
- Accounts for the phenomenon that advertising needs to be raised above a
certain level to have an impact

Disadvantages:
-Outcome variable in logistic model can only be predicted in the form of a probability (e.g., purchase probability, adoption probability)

Question 6

Describe the differences between a linear and a logistic model (5)

Answer 6

• A linear regression is used for a continuous dependent variable, whereas a logistic model is used for a discrete dependent variable.
• For a linear regression, a linear relationship between the dependent variable and independent variable(s) is required. This requirement does not hold for a logistic model.
• For a logistic regression, the predictions (output) lie in the interval 0 to 1, whereas for a linear regression predictions are not restricted to this interval and can extend far beyond.
• In a linear regression, a normal distribution of the dependent variable is assumed. In a logistic model, it is assumed that the dependent variable has a binomial distribution.
• A linear regression is modeled as a straight line, whereas the curve used to model a logistic
  regression is S-shaped

Question 7

Consider the following statements concerning a logistic model:

1. In a logistic model, the outcome variable can only be predicted in the form of a probability.
2. For a logistic model, the R square can be used to interpret the goodness of fit of the model.

What can be concluded about these statements?
A. Statement 1 is correct, statement 2 is false
B. Statement 1 is false, statement 2 is correct
C. Both statements are correct
D. Both statements are false

Answer 7

A. Statement 1 is correct, statement 2 is false

Question 8

What is the general definition of elasticity?

Answer 8

Elasticity =
% change in one variable
/
% change in another variable

So it tells you how much something changes when something else changes

Question 9

How do we calculate price elasticity?

Answer 9

ε𝑝 = 𝛅Q/𝛅P * P/Q = 𝛼𝑝 * Q/P

Question 10

How do we interpret elasticity?

Answer 10

E > 1: Elastic –> the response is strong; the variable is very sensitive
0 < E < 1: inelastic

Question 11

Q = 38 - 60 ln(P) + 80 ln(ATV) + 130 ln(AOC)+ 50 ln(ASP)
What kind of response model is this?

Answer 11

semi-logarithmic model.

Question 12

What is a Carry-over effect?

Answer 12

impulse in period t leads to lagged effect in later periods

Question 13

Which of the following statements is CORRECT:

A. The delayed response model represents a lagged effect of change in business activities on sales.
B. The hysteresis effect describes a situation in which sales will directly return to the original level after a
stimulus has been removed.
C. The hysteresis effect is an example of a semi-logarithmic sales response model.
D. In the delayed response model, sales will not decline after the stimulus has been removed

Answer 13

A. The delayed response model represents a lagged effect of change in business activities on sales.