Question

3.The marker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:

Q=-5200-42p+20Px+5.2I+0.20A+0.25M

                                           (2.002) (17.5)(6.2) (2.5) (0.09)   (0.21)

R^2=0.55          n=26      F=4.88

Where the values in the parenthesis below the cofficient estimates represent the standard error of each coefficient.Aussme the following values for the independent variables:

Q=Quantity sold per month

P(in cents)=price of product=500

Px(in cents)=Price of leading competitor’s product=600

I(in dollars)=Per capita income of the standard metropolitan statistical(SMSA) in which the supermarkets is located=5500

A(in dollars)=Monthly advertising expenditure=10000

M=Number if Microwave ovens sold in the SMSA in which the supermarket is located=5000

Using the above information,answer the following questions:

a.Compute elasticities for each of the Five variables

b.How concerned do you think this company would be about the impact of recession on its sales?Explain

c.Conduct a t-test for each of the FIVE variables to determine the statistical significance of each variable(you can apply the ‘rule of 2’)

d.What proportion of the variation in sales is explained by the independent variables in the equations??

Answer 1

1. Q = -5,200 - 42P + 20Px + 5.2I + 0.20A + 0.25M

Q = -5200 – (42 X 500) + (20 X 600) + (5.2 X 5500) + (0.20 X 10,000) + (0.25 X 5000) Q = 17,650.

For each variable (?Quantity/?Variable) = the variable coefficient.

PED = Variable coefficient X variable initial value/ Q

B:- Because the income elasticity of demand is a value above 1 (at 1.62), the company’s customer base income is a major factor in quantities that will be purchased. Generally, because recession has a negative impact on income (due to job loss or pay cuts during recession), the company should be concerned with the impact of recession on their sales as for every 1 unit of decrease in per capita income; the demand will decrease by 1.62 units.

D:- 55% of the variation in sales is explained by the independent variables. This is because R² = 0.55. The confidence level for the variation in sales is 95% because R² = 0.55. It is also recommended that the F-Value be tested to ensure the equation is significant.