07 May Demand Estimation For Mrs. Smyth’s Pies
- Demand Estimation for Mrs. Smyth’s Pies 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 which can be used to estimate demand elasticities for brand-name orange juice, frozen entrees, 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 2008, 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 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 Metropolitan Statistical 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 5.3. 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 fruit pies; Y is the median dollars of disposable income per household; Pop is the population of the market area; T is the trend factor (2006-1 = 1, . . . , 2007-4 = 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 5.4.
- A. Describe the economic meaning and statistical significance of each individual independent variable included in the Mrs. Smyth’s frozen fruit pie demand equation. B. Interpret the coefficient of determination (R2) for the Mrs. Smyth’s frozen fruit pie demand equation. C. Use the regression model and 2007-4 data to estimate 2008-1 unit sales in the Washington-Arlington-Alexandria market. D. To illustrate use of the standard error of the estimate statistic, derive the 95 percent and 99 percent confidence intervals for 2008-1 unit sales in the Washington-Arlington-Alexandria market. TABLE 5.4 Estimated Demand Function for Mrs. Smyth’s Gourmet Frozen Fruit Pies Variable Coefficient Standard Error of Coefficient t statistic (1) (2) (3) (4) = (2)/(3) Intercept 529,774 271,331 1.95 Price (P) -122,607 16,422 -7.47 Advertising (A) 5.838 1.65 3.54 Competitor Price (PX) 29,867 13,449 2.22 Income (Y) 2.043 3.762 0.54 Population (Pop) 0.030 0.004 7.50 Time (T) 2,815 4,539 0.62 Coefficient of Determination = R2 = 87.1% Corrected Coefficient of Determination = R2 = 85.2% F statistic = 45.16 Standard Error of the Estimate = SEE = 67,584
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