Suppose Kellogg company estimates the demand equation for its Blueberry Waffles, using data from grocery stores in the Dallas Metroplex for November, 2022: Q = - 4000 – 2.1 (Px) + 2. 5 (Py) + 0.52 (Inc) + 0.30 (A) - 2.25 (Pz); R2 =0. 51

Question

(2.002) (1.75) (0.62) (2.4) (0.59) (0. 75)
Assume the following values for the independent variables: Q = Quantity of Kellogg’s Eggo Blueberry Waffles sold per month Px (in cents) = Price of Kellogg’s Blueberry Waffles = 600 Py (in cents) = Price of Vans Gluten-Free Blueberry Waffles = 400 Inc (in dollars) = Per-Capita monthly Income of the trade area in which the stores are located = 12,000 A (in dollars) = Advertising expenditures = 2000 units Pz = Price of Land of Lakes Butter (cents) = 350
A. Compute elasticities for each variable – price, cross-price (there are two), income, advertising and make interpretation of each of them as spelled out in the textbook.

Answer 1

To compute the elasticities for each variable, we will use the formula:

Elasticity = (∂Q/∂X) * (X/Q)

where X refers to the respective independent variable. Let's calculate the elasticities for each variable:

1. Price Elasticity (Px):
Elasticity = (∂Q/∂Px) * (Px/Q)
Elasticity = (-2.1) * (600/Q)
Elasticity = -1260/Q

The price elasticity of demand for Blueberry Waffles is -1260/Q. This means that a 1% increase in the price of Blueberry Waffles would lead to a 1260/Q% decrease in the quantity sold.

2. Cross-Price Elasticity (Py):
Elasticity = (∂Q/∂Py) * (Py/Q)
Elasticity = (2.5) * (400/Q)
Elasticity = 1000/Q

The cross-price elasticity of demand with respect to the price of Vans Gluten-Free Blueberry Waffles is 1000/Q. This means that a 1% increase in the price of Vans Gluten-Free Blueberry Waffles would lead to a 1000/Q% increase in the quantity of Kellogg's Blueberry Waffles sold.

3. Cross-Price Elasticity (Pz):
Elasticity = (∂Q/∂Pz) * (Pz/Q)
Elasticity = (-2.25) * (350/Q)
Elasticity = -787.5/Q

The cross-price elasticity of demand with respect to the price of Land of Lakes Butter is -787.5/Q. This means that a 1% increase in the price of Land of Lakes Butter would lead to a 787.5/Q% decrease in the quantity of Kellogg's Blueberry Waffles sold.

4. Income Elasticity (Inc):
Elasticity = (∂Q/∂Inc) * (Inc/Q)
Elasticity = (0.52) * (12000/Q)
Elasticity = 6240/Q

The income elasticity of demand is 6240/Q. This means that a 1% increase in per-capita monthly income would lead to a 6240/Q% increase in the quantity of Kellogg's Blueberry Waffles sold.

5. Advertising Elasticity (A):
Elasticity = (∂Q/∂A) * (A/Q)
Elasticity = (0.30) * (2000/Q)
Elasticity = 600/Q

The advertising elasticity of demand is 600/Q. This means that a 1% increase in advertising expenditures would lead to a 600/Q% increase in the quantity of Kellogg's Blueberry Waffles sold.

Interpretation:

- Price Elasticity: The demand for Blueberry Waffles is price elastic, as the price elasticity (-1260/Q) is negative. This indicates that consumers are sensitive to changes in price, and a higher price will lead to a larger decrease in the quantity sold.

- Cross-Price Elasticities: The cross-price elasticity with respect to the price of Vans Gluten-Free Blueberry Waffles (1000/Q) indicates that the two products are substitutes. An increase in the price of Vans Gluten-Free Blueberry Waffles will lead to an increase in the quantity of Kellogg's Blueberry Waffles sold.

The cross-price elasticity with respect to the price of Land of Lakes Butter (-787.5/Q) indicates that the two products are complements. An increase in the price of Land of Lakes Butter will lead to a decrease in the quantity of Kellogg's Blueberry Waffles sold.

- Income Elasticity: The income elasticity (6240/Q) indicates that Blueberry Waffles are a normal good. An increase in per-capita monthly income will lead to an increase in the quantity of Blueberry Waffles sold.

- Advertising Elasticity: The advertising elasticity (600/Q) indicates that advertising has a positive impact on the demand for Blueberry Waffles. An increase in advertising expenditures will lead to an increase in the quantity of Blueberry Waffles sold.