This paper applies a multiple regression demand function to a frozen microwavable food product sold across 26 supermarkets. Using the estimated equation QD = −2,000 − 100P + 15A + 25Px + 10Y, the paper computes elasticities for price, cross-price, income, and advertising, then interprets their implications for short-term and long-term pricing strategy. It evaluates whether the firm should cut its price to gain market share, plots demand and supply curves across a range of prices, solves for equilibrium price and quantity, and identifies market conditions that could shift either curve.
The demand function estimated for a frozen microwavable food product sold across 26 supermarkets is:
QD = −2,000 − 100P + 15A + 25Px + 10Y (R² = 0.85)
The variables are defined as follows:
QD = Quantity demanded (dependent variable)
P = Price per unit = 200 cents
Px = Price of the leading competitor's product = 300 cents
Y = Per capita income in the Standard Metropolitan Statistical Area (SMSA) = $5,000
A = Monthly advertising expenditures = $640
Using these values, quantity demanded is computed as:
Q = −2,000 − 100(2) + 15(640) + 25(3) + 10(5,000)
Q = 57,475 units
The R² value of 0.85 indicates that approximately 85% of the variation in quantity demanded is explained by the independent variables in the model, suggesting a strong overall fit.
Elasticity is a measure used to describe the relationship between two variables — specifically, the percentage change in a dependent variable resulting from a one-percent change in an independent variable (Mudida, 2003):
Elasticity = % change in dependent variable / % change in independent variable
Own-Price Elasticity
The own-price elasticity is −0.003479. This implies that a 1% increase in the price of the frozen microwavable food product will cause quantity demanded to decline by approximately 0.0035%. Although the sign is negative — consistent with the law of demand — the magnitude is very small, indicating that demand is relatively inelastic with respect to its own price at this point. Nevertheless, any increase in price may still discourage some consumers over time.
Cross-Price Elasticity
The cross-price elasticity is 0.167. This implies that a 1% increase in the price of a competing product will cause the quantity demanded of this product to increase by approximately 0.17%. Because this value is positive but small, the frozen microwavable food product is a substitute for the competitor's product, though the relationship is fairly weak. This suggests there is limited need for concern about rivals' pricing strategies, as their price changes will not have a strongly adverse impact on this firm's sales (Keat et al., 2013).
Income Elasticity
The income elasticity is 0.001305. A 1% increase in average per capita income will induce an increase in quantity demanded of approximately 0.0013%. Because the elasticity is positive, the product behaves as a normal good. The small magnitude suggests demand is very inelastic with respect to income, though the firm may consider modest price increases when consumer incomes rise.
Advertising Elasticity
The advertising elasticity is 0.87. A 1% increase in advertising expenditures will increase quantity demanded by approximately 0.87%. Demand is therefore somewhat inelastic to advertising, meaning that increased advertising has a meaningful positive effect on demand but does not on its own justify a price increase, since higher prices could still deter consumers regardless of advertising levels (Keat et al., 2013).
"Recommends price cut to grow market share"
"Plots curves and solves for equilibrium price and quantity"
"Identifies short- and long-run demand and supply shifters"
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