Question

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 + 20Px + 5.2l + 0.20A + 0.25M (2.002) (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 Px (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 a) Calculate the quantity using the given values for the independent variables. b) Calculate the total revenue at this quantity. c) What proportion of the variation in sales is explained by the independent variables? d) Calculate the price elasticity of demand. Hint: Use the point elasticity method described on page 72. A numeric example is demonstrated in the second paragraph on that page. e) Based on the price elasticity of demand, do you think that this firm should cut its price to increase its market share? Why or why not? f) Compute the income elasticity. g) Based on the income elasticity of demand, do you think that this company would be extremely concerned about the impact of a recession on its sales? Why or why not?

Answer 1

A).

Consider the given problem here the demand for the good is given by.

=> Q = (-5,200) - 42*P + 20*Px + 5.2*I + 0.20*A + 0.25*M, where “P=500”, “Px=600”, “I=5,500”, “A=10,000” and “M=5,000”. So, the quantity demanded is given by.

=> Q = (-5,200) - 42*500 + 20*600 + 5.2*5,500 + 0.20*10,000 + 0.25*5,000.

=> Q = (-5,200) - 21,000 + 12,000 + 28,600 + 2,000 + 1,250 = 17,650. So, here quantity sold is given by “Q = 17,650”.

B).

Now, here the total revenue is given by, “TR = P*Q = 500*17,650 cents = $5*17,650.

=> TR = $88,250.

C).

Here the value of the coefficients of determination is given by, “R^2=0.55”, => “55%” of the variation in “total sales” can be explained by the included independent variables.

D).

The regression equation is given by.

=> Q = (-5,200) - 42*P + 20*Px + 5.2*I + 0.20*A + 0.25*M.

=> dQ/dP = (-42), => the elasticity is given by “e = (dQ/dP)*(P/Q) = (-42)*(500/17,650)”.

=> e = (-1.19)

E).

Here the price elasticity is “e = (-1.19)”, => the absolute value is more than “1”, => the demand is relatively elasticity in nature, => here to increase the market share this firm should decrease the price.