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""2. Ozark Bottled Water Products, Inc. hired a marketing consulting firm to perform atest marketing of its new brand of spring water called Liquid Ozarka. Themarketing experts selected 15 small and medium-sized towns in Arkansas andMissouri for a one-month-long sales test. For one month, Liquid Ozarka was soldat a variety of prices ranging from $3 per gallon to $4 per gallon. Specifically, inthree of the markets, price was set by the marketing experts at $3 per gallon. Inthree more markets, price was set at $3.25 per gallon, and so on. The pricescharged in each market (P) are shown in the table below. For each of the 15 marketareas, the marketing consultants collected data on average household income (M),the population of the marketing area (N), and the price of a rival brand of bottledChapter 7: Demand Estimation and Forecasting159water (PR). At the end of the month, total sales of Liquid Ozarka (Q) weretabulated to provide the following data from which the consultants estimated anempirical demand function for the new product.Market P M PR N Q1 $3.00 $45,586 $2.75 274,000 7,9522 3.00 37,521 3.50 13,450 8,2223 3.00 41,333 2.64 54,150 7,1664 3.25 47,352 2.35 6,800 6,6865 3.25 51,450 2.75 11,245 7,7156 3.25 27,655 3.15 54,500 6,6437 3.50 30,265 2.55 26,600 5,1558 3.50 39,542 3.00 158,000 7,1279 3.50 41,596 2.75 22,500 5,83410 3.75 42,657 2.45 46,150 5,09311 3.75 36,421 2.89 8,200 5,82812 3.75 47,624 2.49 38,500 6,59013 4.00 50,110 3.15 105,000 6,22814 4.00 57,421 2.80 92,000 7,21815 4.00 38,450 2.90 38,720 5,846Using the marketing data from the 15 test markets shown above, estimate theparameters of the linear empirical demand function:Q = a + bP + cM + dPR + eNIf any of the parameter estimates are not significant at the 2 percent level ofsignificance, drop the associated explanatory variable from the model and estimatethe demand function again.a. Your estimated linear demand function for Liquid Ozarka isˆQ= _______________________________________.b. What percentage of the variation in sales of Liquid Ozarka is explained byyour estimated demand function?The marketing consultants describe a “typical” market as one in which the price ofLiquid Ozarka is $3.50 per gallon, average household income is $45,000, the priceof rival bottled water is $3 per gallon, and the population is 75,000. Answer thefollowing questions for this “typical” market scenario.c. What is the estimated elasticity of demand for Liquid Ozarka? Is demandelastic or inelastic? What would be the percentage change in price requiredto increase sales of Liquid Ozarka by 10 percent?Chapter 7: Demand Estimation and Forecasting160d. What is the estimated income elasticity of demand? Is Liquid Ozarka anormal or inferior good? A 6 percent increase in average household incomewould be predicted to cause what percentage change in sales of LiquidOzarka?e. What is the estimated cross-price elasticity of demand for Liquid Ozarkawith respect to changes in price of its rival brand of bottled water? Does theestimated cross-price elasticity have the expected algebraic sign? Why orwhy not? If the price of the rival brand of water rises by 8 percent, what isthe estimated percentage change in sales of Liquid Ozarka?Using the marketing data from the preceding 15 test markets, estimate theparameters for the log-linear empirical demand function:Q = aPbMcPRdNeIf any of the parameter estimates are not significant at the 2 percent level ofsignificance, drop the associated explanatory variable from the model and estimatethe demand function again.f. Your estimated log-linear demand function for Liquid Ozarka isˆQ= _______________________________________.g. Does a log-linear specification work better than a linear specification ofdemand for Liquid Ozarka? Explain by comparing F-ratios, R2s, and t-ratios(or p-values).h. Using the estimated log-linear demand function, compute the price, income,and cross-price elasticities of demand. How do they compare to the estimatedelasticities for the linear demand specification?answer in Excel format please. thx"
