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
(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.
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.
To compute the elasticities for each variable, we will use the formula:
Elasticity = (% change in quantity / % change in variable)
1. Price Elasticity (Px):
Elasticity = -2.1 * (Px / Q)
= -2.1 * (600 / Q)
2. Cross-Price Elasticity (Py):
Elasticity = 2.5 * (Py / Q)
= 2.5 * (400 / Q)
3. Cross-Price Elasticity (Pz):
Elasticity = -2.25 * (Pz / Q)
= -2.25 * (350 / Q)
4. Income Elasticity (Inc):
Elasticity = 0.52 * (Inc / Q)
= 0.52 * (12,000 / Q)
5. Advertising Elasticity (A):
Elasticity = 0.30 * (A / Q)
= 0.30 * (2,000 / Q)
Now, let's interpret each elasticity:
1. Price Elasticity (Px):
The price elasticity (Px) measures the responsiveness of the quantity demanded to a change in the price of Kellogg's Blueberry Waffles. A negative value implies that the waffles are a normal good. In this case, the elasticity of -2.1 indicates that a 1% increase in the price of Kellogg's Blueberry Waffles will result in a 2.1% decrease in the quantity demanded.
2. Cross-Price Elasticity (Py):
The cross-price elasticity (Py) measures the responsiveness of the quantity demanded to a change in the price of Vans Gluten-Free Blueberry Waffles. A positive value indicates that the two products are substitutes. In this case, the elasticity of 2.5 suggests that a 1% increase in the price of Vans Gluten-Free Blueberry Waffles will result in a 2.5% increase in the quantity demanded of Kellogg's Blueberry Waffles.
3. Cross-Price Elasticity (Pz):
The cross-price elasticity (Pz) measures the responsiveness of the quantity demanded to a change in the price of Land of Lakes Butter. A negative value implies that the two products are complements. In this case, the elasticity of -2.25 suggests that a 1% increase in the price of Land of Lakes Butter will result in a 2.25% decrease in the quantity demanded of Kellogg's Blueberry Waffles.
4. Income Elasticity (Inc):
The income elasticity (Inc) measures the responsiveness of the quantity demanded to a change in per-capita monthly income. A positive value indicates that the product is a normal good. In this case, the elasticity of 0.52 suggests that a 1% increase in per-capita monthly income will result in a 0.52% increase in the quantity demanded of Kellogg's Blueberry Waffles.
5. Advertising Elasticity (A):
The advertising elasticity (A) measures the responsiveness of the quantity demanded to a change in advertising expenditures. A positive value indicates that advertising has a positive impact on demand. In this case, the elasticity of 0.30 suggests that a 1% increase in advertising expenditures will result in a 0.30% increase in the quantity demanded of Kellogg's Blueberry Waffles.
Remember that the magnitude of the elasticities determines the extent of the responsiveness. The larger the absolute value, the more responsive the quantity demanded is to changes in the respective variable.