The make of a leading brand of low-calorie microwavable food estimated the follo
ID: 1176224 • Letter: T
Question
The make of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the contry for the month of April:
q = -5200 - 42p + 20px + 5.2l + 0.20a + 0.25m
(2002) (17.5) (6.2) (2.5) (0.09) (0.21)
r2 = 0.55 n = 26 f = 4.88
Assume the following values for the independent variables
q=quantity sold per month
p (in cents) = price of the product = 500 (in cents)
px (in cents) = price of leading competotior's product = 600
i (in dollars) = per capita income of the standard metropolitan tatistiacal arwa (SMSA) in which the supermarket is located = 5500
a ( indollars) = monthly advertising expenditure = 10000
m = number if microwaves sold in the SMSA in which the supermarket is located = 5000
Using this information answer the following.
a. Compare elasticities for each variable.
b How concerned do you think this company would be about the impact of a recession on its sales? Explain.
c. Do you think that this firm should cut its price to increase its market share.? Explain.,
d. What proportion of the variation in sales is explained by the independet variables in the equations? How confident are you about this explain.
Explanation / Answer
a-Compute the elasticity for each of the variables
for each variable %u2206Q/%u2206variable = variable coefficient
so PED = variable coefficient x variable initial value/Q
PEDP = -42X500/Q
Q= -5200-42x500+20x600+5.2x5500+0.2x10000+0.25x5000 =
= -5200-21000+12000+28600 +2000+1250=17650
PEDP = -42X500/17650 = -1.19
PEDPX = 20X600/17650 = 0.68
PEDI= 5.2X5500/17650 = 1.62
PEDA= 0.2X10000/17650 = .11
PEDM= 0.25X5000/17650 = .07
b-How concerned do you think this company would be about the impact of a recession on its sales?
As the recession has direct negative impact on per capita income and hence the income elasticity of demand shows a value above 1 (1.62) so the company should be very concerned during recession period as the demand will decrease by 1.62 units with every 1 unit decrease of per capita income
c-Do you think that this firm should cut its price to increase market share?
Yes ,cutting the price will lead to increase the company share as the price elasticity of demand is bigger than 1 (1.19)
d-what proportion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer?
55% of variation in sales is explained by the independent variables because of the value of R2=0.55 at 95% confidence level.
-because the value ofR2=0.55 is only 0.55 so we should test the F-value (5,20)to ensure that the whole equation is significant
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