Problem Set #12-Key. Minimum Price. Maximum Price

Transcription

1 Mean Price Per Bottle Sonoma State University Business 580-Business Intelligence Problem Set #12-Key Dr. Cuellar Market Segmentation and Price Discrimination: Retail Channel Price Differentials 1. Summary Statistics. a. Construct a table showing the mean, minimum, maximum, standard deviation and the number of observations of price across channels. market Mean Price Minimum Price Maximum Price Standard Deviation Observations DRUG $ ,479 FOOD $ ,664 LIQUOR $ ,692 b. Construct a bar graph showing the mean price across channels c. Are the mean price differentials statistically significant? Explain fully. d. Construct a 99% confidence interval on the mean price differentials. Explain your answer. Yes, the coefficients on Drug and Liquor are statistically significant. Price Lower 99% CI Upper 99% CI DRUG [18.56]** LIQUOR [7.57]** Constant [359.58]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

2 e. Construct a histogram showing the distribution of prices across channels. Describe your graph. 0 Price Per Bottle Percent DRUG FOOD LIQUOR Price Per Bottle f. Construct a box and whiskers graph to show the distribution of prices across channels. Describe your graph.

3 0.5 Mean Price Per Bottle g. Construct a bar graph showing the log price across channels h. Are the log price differentials statistically significant? Explain fully. See regression coefficients. Yes, they are statistically significant. i. Construct a 99% confidence interval on the log price differentials. Explain your answer. See 99% confidence interval in the regression table below. lnprice Lower 99% CI Upper 99% CI DRUG [23.11]** LIQUOR [11.72]** Constant [844.24]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

4 j. Construct a histogram showing the distribution of log prices across channels. Describe your graph Percent DRUG FOOD LIQUOR log Price Per Bottle k. Construct a box and whiskers graph to show the distribution of log prices across channels. Describe your graph. l. Based on the above, what can you say about the retail channel price differentials? There does appear to be retail channel price differentials and they are statistically significant.

5 2. Estimating the Price Elasticity of Demand. a. Construct a model to estimate the price elasticity of demand across all three retail channels. Show your model. lncases i = β 0 + β 1 lnprice i + δchannel + ΠChannel*lnPrice i + ΩMonth + u i Where: Channel is a vector of dummy variables for the Liquor and Drug channels. Channel*Price is a vector of interactions of channel and price. Month is a vector of dummies for months 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 [27.88]** DRUG [39.42]** LIQUOR [43.34]** Drug*lnprice Drug store prices are statistically less than grocery store prices [14.02]** Liquor*lnprice Liquor store prices are statistically greater than grocery store prices [22.07]** February [8.07]** March [7.44]** April [7.09]** May [11.64]** June [11.10]** July [11.12]** August [9.84]** September [9.42]** October [9.59]** November [9.35]** December [1.95] Constant [180.33]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

6 Cases Sold Per Month Price Elasticities Drug Food Liquor c. Are the estimated price elasticities consistent with the price differentials? Explain. Yes, Price Drug < Price Food < Price Liquor ε Drug > ε Food > ε Liquor a. 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 Ravenswood California Cabernet Sauvignon, which is sold across all three retail channels. a. Construct a scatter diagram showing the relationship between price and quantity for Ravenswood California Cabernet Sauvignon by retail channel. Describe your graph. Does the law of demand appear to hold? DRUG FOOD LIQUOR Price Per Bottle Yes, the law of demand appears to hold. The price elasticities appear to be consistent with the retail channel hypothesis: Drug store appear to have the flattest demand, liquor stores the steepest and food stores somewhere in between the two.

7 b. Set up a model estimating the price elasticity of demand for Ravenswood California Cabernet Sauvignon across all three retail channels. Be sure to account for differential effects that may occur across channels. lncases i = β 0 + β 1 lnprice i + δchannel + ΠChannel*lnPrice i + ΩMonth + u i Where: Channel is a vector of dummy variables for the Liquor and Drug channels. Channel*Price is a vector of interactions of channel and price. Month is a vector of dummies for months c. Are the price elasticities across channel different? Are they statistically significant? Cases Log Cases Price -1, [8.64]** [2.75]** DRUG -23, [9.59]** [1.29] LIQUOR -20, [4.50]** [0.05] Drug*price 1, statistically less than grocery store ces [7.26]** [3.30]** Liquor*price 1, statistically less than grocery [3.76]** [0.30] February [1.69] [1.90] March [2.57]* [3.32]** April [3.14]** [4.48]** May -1, [5.75]** [7.72]** June -1, [5.90]** [8.13]** July -1, [5.84]** [8.12]** August -1, [5.60]** [8.47]** September -1, [5.59]** [6.38]** October [3.94]** [4.70]** November [2.24]* [3.43]** December [0.84] [1.87] Constant 24, [11.74]** [8.99]** Observations Adjusted R Absolute value of t-statistics in brackets * significant at 5% level; ** significant at 1% level

8 5. Inventory Management a. Find the average price and quantity sold across all three channels in January 2010 of Ravenswood California Cabernet Sauvignon, the last month of the data for this item. Market Mean Price $8.00 $8.66 $9.29 Mean Cases b. Suppose that Ravenswood wanted to set a uniform price across all three channels of $8.99. How many cases should they ship to each channel? Explain fully. Market Proposed Price $8.99 $8.99 $8.99 Estimated Cases 1,030 6,179 2,503 Log Cases Cases 249 7,491 2, Price Optimization. a. For the quantities sold in January 2010 (part a above), find the optimum price across each channel. Market Proposed Cases Estimated Price -$ $8.54 $5.59 Log Price Price $8.25 $9.28 $8.29 b. Compare the optimum prices with the actual prices across all three channels. 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. Calendar Using the unit regression equation, there does not appear to be any opportunities to increase price.