Demand Estimation for Branded Consumer Products
Demand estimation for brand-name consumer products is made difficult by the fact that managers must rely on proprietary data. There simply is not any publicly available data that can be used to estimate demand elasticities for brand-name orange juice, frozen entrés, pies, and the like—and with good reason. Competitors would be delighted to know profit margins across a broad array of competing products so that advertising, pricing policy, and product development strategy could all be targeted for maximum benefit. Product demand information is valuable, and jealously guarded.
To see the process that might be undertaken to develop a better understanding of product demand conditions, consider the hypothetical example of Mrs. Smyth's Inc., a Chicago-based food company. In early 2002, Mrs. Smyth's initiated an empirical estimation of demand for its gourmet frozen fruit pies. The firm is formulating pricing and promotional plans for the coming year, and management is interested in learning how pricing and promotional decisions might affect sales. Mrs. Smyth's has been marketing frozen fruit pies for several years, and its
CASE STUDY (continued)
market research department has collected quarterly data over two years for six important marketing areas, including sales quantity, the retail price charged for the pies, local advertising and promotional expenditures, and the price charged by a major competing brand of frozen pies. Statistical data published by the U.S. Census Bureau (http://www.census.gov) on population and disposable income in each of the six market areas were also available for analysis. It was therefore possible to include a wide range of hypothesized demand determinants in an empirical estimation of fruit pie demand. These data appear in Table 5.6.
The following regression equation was fit to these data:
Qit = b0 + b1Pit + b2Ait + b3PXit + b4Yit + b5PoPit + b6Tit + Uit
Q is the quantity of pies sold during the tth quarter; P is the retail price in dollars of Mrs. Smyth's frozen pies; A represents the dollars spent for advertising; PX is the price, measured in dollars, charged for competing premium-quality frozen fuit pies; Y is dollars of disposable income per capita; Pop is the population of the market area; T is the trend factor (2000-1 = 1, . . . , 2001-4 = 8); and uit is a residual (or disturbance) term. The subscript i indicates the regional market from which the observation was taken, whereas the subscript t represents the quarter during which the observation occurred. Least squares estimation of the regression equation on the basis of the 48 data observations (eight quarters of data for each of six areas) resulted in the estimated regression coefficients and other statistics given in Table 5.7.
The individual coefficients for the Mrs. Smyth's pie demand regression equation can be interpreted as follows. The intercept term, 646,958, has no economic meaning in this instance; it lies far outside the range of observed data and obviously cannot be interpreted as the demand for Mrs. Smyth's frozen fruit pies when all the independent variables take on zero values. The coefficient for each independent variable indicates the marginal relation between that variable and sales of pies, holding constant the effect of all the other variables in the demand function. For example, the -127,443 coefficient for P, the price charged for Mrs. Smyth's pies, indicates that when the effects of all other demand variables are held constant, each $1 increase in price causes quarterly sales to decline by roughly 127,443 pies. Similarly, the 5.353 coefficient for A, the advertising variable, indicates that for each $1 increase in advertising during the quarter, roughly 5.353 additional pies are sold. The 29,337 coefficient for the competitor-price variable indicates that demand for Mrs. Smyth's pies rises by roughly 29,337 pies with every $1 increase in competitor prices. The 0.344 coefficient for the Y variable indicates that, on average, a $1 increase in the average disposable income per capita for a given market leads to roughly a 0.344-unit increase in quarterly pie demand. Similarly, a one person increase in the population of a given market area leads to a small 0.024-unit increase in quarterly pie demand. Finally, the -4,406 coefficient for the trend variable indicates that pie demand is falling in a typical market by roughly 4,406 units per quarter. This means that Mrs. Smyth's is enjoying secular growth in pie demand, perhaps as a result of the growing popularity of Mrs. Smyth's products or of frozen foods in general.
Individual coefficients provide useful estimates of the expected marginal influence on demand following a one-unit change in each respective variable. However, they are only estimates. For example, it would be very unusual for a increase in price to cause exactly a -127,443-unit change in the quantity demanded. The actual effect could be more or less. For decision-making purposes, it would be helpful to know if the marginal influences suggested by the regression model are stable or instead tend to vary widely over the sample analyzed.
In general, if it is known with certainty that Y = a + bX, then a one-unit change in X will always lead to a b-unit change in Y.If b > 0, X and Y will be directly related; if b < 0, X and Y will be inversely related. If no relation at all holds between X and Y, then b = 0. Although the true parameter b is unobservable, its value is estimated by the regression coefficient b. If b = 10, a one-unit change in X will increase Y by 10 units. This effect may appear to be
CASE STUDY (continued)
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