Problem Set #4-Key. Retail Channel Price Differentials

Transcription

1 Problem Set #4-Key Sonoma State University Economics 494- Seminar in Quantitative Marketing Dr. Cuellar Retail Channel Differentials The following questions relate to the data set Econ494_Channel which contains US retail scanner data on US wine sales by retail channel. 1. Summary Statistics: Note, for uniformity, examine only standard 750 ML bottles of wine. a. Construct a table showing the average, minimum, maximum, standard deviation and the number of observations of price across channels. market Mean Median Minimum Maximum Observations DRUG $8.11 $7.25 $0.57 $ ,949 FOOD $11.77 $9.96 $0.15 $ ,067 LIQUOR $13.22 $10.78 $0.48 $ ,454 b. Construct a graph showing the average price across channels DRUG FOOD LIQUOR

2 c. Are the mean price differentials statistically significant? Explain fully. Yes, the coefficients on Drug and Liquor are statistically significant. DRUG LIQUOR Constant Observations Adjusted R-squared 0.02 Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level d. Construct a histogram showing the distribution of prices across channels. Describe your graph. DRUG FOOD Percent LIQUOR Per Bottle

3 e. Construct a box and whiskers graph to show the distribution of prices across channels. Describe your graph. f. Based on the above, what can you say about the retail channel price differentials? There are clearly price differentials across retail channels and they are statistically significant, but based on the difference in the number of observations across channels, there appears to be sample selection bias driving much of the price differentials.

4 2. Summary Statistics. a. Construct a table showing the mean, median, minimum, maximum, and the number of observations of price across channels. market mean median minimum maximum Observations DRUG $8.41 $7.63 $1.18 $ ,479 FOOD $9.07 $8.27 $1.98 $ ,664 LIQUOR $9.34 $8.66 $2.69 $ ,692 b. Construct a graph showing the mean price across channels DRUG FOOD LIQUOR c. Are the mean price differentials statistically significant? Explain fully. OLS LAD OLS Median lnprice DRUG LIQUOR Constant Observations Adjusted R-squared Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level Yes, the Drug and Liquor coefficients which measure the mean price differentials are statistically significant.

5 d. Construct a 99% confidence interval on the mean price differentials. Explain your answer. 99% Confidence Interval Mean Median Log Drug-Food -$0.76 -$0.57 -$0.74 -$ % -7.29% Liquor Food $0.18 $0.36 $0.29 $ % 5.06% Food $9.01 $9.14 $8.21 $ e. Construct a histogram showing the distribution of prices across channels. Describe your graph. DRUG FOOD Percent LIQUOR Per Bottle f. Construct a box and whiskers graph to show the distribution of prices across channels. Describe your graph. 0 Per Bottle DRUG FOOD LIQUOR

6 g. Construct a graph showing the median price across channels. Per Bottle DRUG FOOD LIQUOR h. Are the median price differentials statistically significant? Explain fully. Yes, from the table above, the Drug and Liquor coefficients which measure the median price differentials are statistically significant. i. Construct a 99% confidence interval on the median price differentials. Explain your answer. See table above. j. Construct a graph showing the log price across channels..5 Per Bottle DRUG FOOD LIQUOR

7 k. Are the log price differentials statistically significant? Explain fully. Yes, from the table above, the Drug and Liquor coefficients which measure the log price differentials are statistically significant. l. Construct a 99% confidence interval on the log price differentials. Explain your answer. See table above. m. Construct a histogram showing the distribution of log prices across channels. Describe your graph. DRUG FOOD Percent LIQUOR Per Bottle n. Construct a box and whiskers graph to show the distribution of log prices across channels. Describe your graph. Per Bottle DRUG FOOD LIQUOR

8 o. Based on the above, what can you say about the retail channel price differentials? differentials are consistent across the mean, median and log prices. 3. Estimating the Elasticity of Demand. a. Construct a model to estimate the price elasticity of demand across all three retail channels. Show your model. Casesi = β0+ β1i + β2drug + β3liquor + β4drug*i + β5liquor* + θmonth +ui b. Estimate your model. Are the price elasticities of demand different across the three channels? Are they statistically significant? Are they statistically different from each other? Explain fully. lncases lnprice FOOD LIQUOR FOOD*lnprice LIQUOR*lnprice February March April May June July August September October November December [0.05] Constant Observations Adjusted R-squared 0.47 Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

9 Elasticity Drug Food Liquor c. Are the estimated price elasticities consistent with the price differentials? Explain. Drug < Food < Liquor εdrug > ε Food > ε Liquor d. Are the estimated price elasticities consistent with the demographic profile hypothesized about each market channel? Explain fully. Yes, the demographic profile is that: Drug store shoppers are poorer and older shoppers and are expected to be more price elastic. Grocery store shoppers are there to buy alcohol as well as other goods and may be time constrained and are expected to have a relatively lower price elasticity of demand Liquor store shoppers are there to purchase alcohol and are expected to be the least price elastic. 4. Demand Estimation. For these questions examine the data for Chateau St. Michelle Cabernet Sauvignon, which is sold across all three retail channels. a. Construct a scatter diagram showing the relationship between price and quantity for Chateau St. Michelle Cabernet Sauvignon by retail channel. Describe your graph. Does the law of demand appear to hold? Cases Sold Per Month DRUG FOOD LIQUOR Per Bottle

10 b. Set up a model estimating the demand for Chateau St. Michelle Cabernet Sauvignon across all three retail channels. Be sure to account for differential effects that may occur across channels and across months. Casesi = β0+ β1i + δchannel + ΩMonth + ΠChannel*i + ΦMonth* + θchannel*month* + ui Where: Channel is a vector of dummy variables for the Liquor and Drug channels. Month is a vector of dummies for months Channel* is a vector of interactions of channel and price. Month* is a vector of interactions of month and price Channel*Month* is a vector of interactions of channel, month and price. c. Show your regression results in a table. Use the outreg command. Explain your results. How well does your model fit the data? Decomposing the full regression for each channel results in the following: Drug Food Liquor Cases Cases Cases , , [0.02]* February , , [0.18] [0.03]* March -1, , , [0.37] [0.17] April -1, , , [0.12] [0.51] May , , [0.24] [0.44] June -1, , , [0.03]* [0.53] July -1, , , [0.32] [0.39] August -1, , , [0.03]* [0.24] September , , [0.40] [0.04]* October , , [0.87] [0.21] [0.10] November , , [0.62] [0.60] December , , [0.92] [0.73] February* , , [0.21] [0.03]* March* , , [0.38] [0.16] April* , , [0.14] [0.55] May* , [0.28] [0.52] June* , [0.04]* [0.65] July* , [0.36] [0.49] August* , ,807.92

11 [0.04]* [0.32] September* , , [0.47] [0.05] October* , , [0.82] [0.23] [0.10] November* , [0.72] [0.66] December* , [0.85] [0.77] Constant 2, , , [0.01]** Observations Adjusted R-squared Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level d. Are the price elasticities across channel different? Are they statistically significant? Using the table above you can compare the regression coefficients for each month. For example, note that the price coefficient is for the month of January only. Alternatively, you can run a simpler regression such as: Casesi = β0+ β1i + β2drug + β3liquor + β4drug*i + β5liquor* +ui Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level Unit Regression Cases Double Log Regression lncases FOOD 33, [0.22] LIQUOR 7, [0.23] [0.63] [0.52] [0.84] FOOD*price -2, [0.97] LIQUOR*price [0.33] Constant 1, [0.45] Observations Adjusted R-squared Estimated Elasticity Retail Channel Unit Regression Double Log Regression Food Drug Liquor

12 5. Inventory Management a. Find the average price and quantity sold across all three channels in August 2010 of Chateau St. Michelle Cabernet Sauvignon, the last month of the data. month DRUG FOOD LIQUOR Jan. $11.20 $12.19 $ Feb. $11.31 $12.54 $ March $12.75 $12.82 $ April $11.47 $12.53 $ May $12.30 $12.72 $ June $12.82 $12.59 $ July $12.62 $12.41 $ Aug. $13.08 $12.17 $ b. Suppose that Chateau St. Michelle wanted to set a uniform price across all three channels of $ How many cases should they ship to each channel? Explain fully Drug Estimated Cases Sold Food Estimated Cases Sold Liquor Estimated Cases Sold August 131 4,583 1, Optimization. a. For the quantities sold in August 2010 (above), find the optimum price across each channel. August Actuals 154 $13.08 Drug Estimated Optimal 5,597 $12.17 Food Estimated Optimal 1,037 $13.10 Liquor Estimated Optimal August $12.37 $12.18 $12.10 b. Compare the optimum price with the actual price. Is there an opportunity for strategic pricing across market segments (i.e., channel) to increase revenue? If so, how much revenue can be gained? Explain fully. In this case, there does not appear to be any opportunity to raise price to increase revenue.