Question

The manufacture of a washing powder product used in automatic washing machines has estimated the following demand equation for its product using data from 30 appliances stores around the country.

Q= -350 - 2.0P + 1.2 Px + 5.0I + 6.0 A + 5.0U

     (3.08) (0.60) (0.55)    (0.32) (0.80) (0.021) (SEC)

The actual values for each of the independent variables are as follows. Assume the following information for the independent variables:

Q = Quantity sold per month

Price (P) of product = 3 700 cents

Price (Px) of leading competitor's product = 3 500 cents

Per capita income of the standard metropolitan area ( SMSA) in which the appliance store is located = R 25 000

Monthly  adverting expenditure = R 800 000

Number of unit of washing powder (U) sold per month in the SMSA in which the appliance store is located= 400 units

2.1 Calculate the point elasticity for advertising expenditure    (12)

2.2 Calculate the t-value ( t-statistic) for advertising expenditure   (4)

2.3 Do you think that the R 800 000 spent on advertising every month is justified? Support your answer by referring to the calculation done in 2.1 and 2.2 and referring to the " Rule of 2"

Answer 1

2.1 : Point elasticity of advertising expenditure

Now, Q= 350 - (2.0 3700) + (1.2   3500) + (5.0 25000) + (6.0 800000) + (5.0 400)

= 4924150 unit

A = 800000

dQ/dA = 6.0

Therefore, elasticity = 6.0   (800000/4924150) = 0.94

2.2: t value for advertising expenditure = estimated value of the coefficient of advertising expenditure / S.E of the coefficient.

= 6.0/0.80 = 7.5

2.3. Since the elasticity of demand is less than one therefore, the changes in demand is slower than the change in advertising expenditure. Therefore, the spending of R 800,000 on advertising is not justified.

since t value is 7.5 which is greater than the table value of t, therefore, the above justification is significant at 1% level of significance.