The Following Is The Equation Information From Assignment 1 I Am Atta
The following is the equation information from assignment 1. I am attaching the instructions for assignment 2 at the bottom: Imagine that you work for the maker of a leading brand of low-calorie frozen, microwavable food that estimates the following demand equation for its product using data from 26 supermarkets around the country for the month of April. Estimated Demand Equation: Q
= -5200 – 42(P) + 20(P
x ) + 0.52(I) + 0.20(A) + 0.25(M). Standard Errors of Estimate are provided for each coefficient (values partially obscured in the provided data). Other Regression statistics include: n = 26, R
2
= 0.55, F = 4.88. Note: In the above regression equation, Q
D is the dependent variable, and the variables on the right-hand side are independent variables. Your supervisor has asked you to compute the elasticities for each independent variable in the above demand equation. Assume the following values for the independent variables:
= Quantity demanded of 3-pack units: 3,000 units
P (product price) = $5 per 3-pack unit
P
x (competitor’s product price) = $6 per 3-pack unit
I (per capita income) = $5,500
A (monthly advertising expenditures) = $10,000
M (number of microwave ovens sold in the SMSA) = 5,000
Paper For Above instruction
Calculating price and income elasticities of demand provides valuable insight into how consumers respond to changes in variables that influence their purchasing decisions. For a company producing low-calorie frozen, microwavable food, understanding these elasticities is crucial for devising effective pricing, advertising, and product positioning strategies.
The demand function provided in the assignment is specified as: Q
D
= -5200 – 42(P) + 20(P
x
) + 0.52(I) + 0.20(A) + 0.25(M)
Here, Q
D
is the quantity demanded, P is the firm’s product price, P
x
is the competitor’s price, I is per capita income, A is advertising expenditures, and M is the number of microwave ovens sold in the SMSA. The estimated demand equation suggests negative influence of P on demand (–42 coefficient), indicating that higher prices lead to lower demand. Conversely, the positive coefficient for P
x suggests that higher competitor prices increase demand for this product, indicative of a substitution effect.
To compute the price elasticity of demand, we utilize the formula:
= (dQ
/dP) * (P / Q
Given the estimated derivative of Q
with respect to P is –42, and using the provided values (P = $5; Q
= 3,000 units), the elasticity becomes:
P = –42 * (5 / 3,000) = –42 * 0.0016667 ≈ –0.07
This indicates that demand for the product is relatively inelastic with respect to price, as a 1% increase in price would decrease quantity demanded by approximately 0.07%.
Similarly, the income elasticity is calculated using the coefficient of I, which is 0.52. The formula is:
= (dQ D /dI) * (I / Q
) = 0.52 * (5,500 / 3,000) ≈ 0.52 * 1.833 ≈ 0.952
An income elasticity of around 0.95 suggests that demand is nearly unit elastic with respect to income, implying that a 1% increase in income would result in approximately a 0.95% increase in demand.
For the competitor’s price P
x , the coefficient is 20, and the demand elasticity can be computed as:
= 20 * (6 / 3,000) ≈ 20 * 0.002 = 0.04
This indicates a highly inelastic substitution effect; a 1% increase in P
x results in only a 0.04% increase in demand for the firm’s product, reflecting limited responsiveness to competitive pricing.
Considering advertising expenditures A, with a coefficient of 0.20, the elasticity is:
= 0.20 * (10,000 / 3,000) ≈ 0.20 * 3.333 ≈ 0.667
This demonstrates that advertising has a relatively significant impact on demand—about two-thirds elasticity—implying that increased advertising could meaningfully boost sales.
Finally, for the number of microwave ovens M, which has a coefficient of 0.25, the elasticity is:
= 0.25 * (5,000 / 3,000) ≈ 0.25 * 1.667 ≈ 0.417
This suggests moderate responsiveness of demand to the number of microwave ovens sold in the SMSA,
reflecting the role of appliance penetration in consumption.
In conclusion, the demand for this low-calorie frozen food product appears relatively inelastic with respect to price, but more elastic concerning advertising and income levels. These elasticity measures suggest that price reductions might not significantly increase demand, but strategic increases in advertising and exploiting income growth could effectively boost sales. Additionally, maintaining competitive prices remains essential, given the minimal substitution elasticity, indicating limited consumer response to competitor pricing adjustments.
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