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Problems

$2.$ The maker 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:

$Q=-5,200-42P+20P_x+5\mathrm{.}21+0\mathrm{.}20A+0\mathrm{.}25M$

$(2\mathrm{.}002)(17\mathrm{.}5)(6\mathrm{.}2)(2\mathrm{.}5)(0\mathrm{.}09)(0\mathrm{.}21)$

$R2=0\mathrm{.}55,n=26,F=4\mathrm{.}88$

Assume the following values for the independent variables:

$Q=$ Quantity sold per month

$P($in cents$)=$ Price of the product $=500$

$P_x($in cents$)=$ Price of leading competitor's product $=600$

I $($in dollars$)=$ Per capita income of the standard metropolitan statistical area $($SMSA$)$ in which the supermarket is located $=5,500$

A $($in dollars$)=$ Monthly advertising expenditure $=10,000$

$M=$ Number of microwave ovens sold in the SMSA in which the supermarket is located $=5,000$

Using this information, answer the following questions:

a$.$ Compute 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 independent variables in the equations? How confident are you about this answer? Explain.