Barry Nalebuff is an entrepreneur who has recently launched a bottled organic tea brand called Honest Tea (which can be bought online). He has decided to bid on the Google keyword, “Healthy Beverage,” and would like to know how much to bid on this keyword. For this purpose, he decides to use the PROSAD decision support system. Barry learns from Google that 25,000 daily searches happen, on average, on the Google keyword, “Healthy Beverage.” Suppose that

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0.5% of the people who search on the keyword “Healthy Beverage” on a given day and then click on Barry’s sponsored ad are successfully acquired (i.e., become customers of Honest Tea). Suppose further that the annual profit contribution to Barry per acquired customer is $500.

a.What would be the highest value that Barry would be willing to bid for the Google keyword, “Healthy Beverage”? Why?

b.Over the first quarter of launch, Barry subjectively revises his bids on the Google keyword, “Healthy Beverage” on a daily basis. As his bids change, his sponsored ad’s rank changes and, therefore, the clicks on his sponsored ad change as well. Based on the data collected during the first quarter (using Google Analytics software), Barry estimates the relationship between clickâ€through rate (CTR) and sponsored ad rank, and it is as follows: ln (CTR) = â€1.8819 â€ 0.5265 * RANK. Barry also estimates the relationship between costâ€perâ€click (CPC) and sponsored ad rank, and it is as follows: ln (CPC) = 0.9009 – 0.0638 * RANK. Which increases at a faster rate going from an inferior rank (say, X+1) to a superior rank (say, X): clickâ€throughâ€rate or costâ€perâ€click? Does this imply that Barry’s optimal bid for the keyword “Healthy Beverage” would be closer to his highest value (calculated in question 1 above) or to his lowest value ($0)? Why?

c.Does Barry want Honest Tea to be the first ranked brand among the sponsored ads that are listed by Google for the search keyword, “Healthy Beverage”? Why or why not?

d.What is the transactional profit that Barry obtains from the above rank? How much transactional profit would Barry obtain if he were listed at the next lower position?

2. The store manager at the Ladue Schnucks store has estimated Scan*Pro demand models for 3 competing peanut butter brands â€â€ Jif, Skippy, Peter Pan â€â€ using weekly scanner data over the past 2 years. The estimated demand models are as shown below.

Ln (QJif) = 2.64 – 4.99 * ln (PJif) + 0.24 * ln (PSkippy) + 0.08 * ln (PPeterPan),

Ln (QSkippy) = 3.04 + 0.16 * ln (PJif) â€ 5.51 * ln (PSkippy) + 0.11 * ln (PPeterPan),

Ln (QPeterPan) = 2.36 + 0.12 * ln (PJif) + 0.15 * ln (PSkippy) – 4.96 * ln (PPeterPan),

where Q refers to weekly demand (in units sold), and P refers to weekly price (in $).

a Suppose you are the store manager at the Ladue Schnucks store. If Jif, Skippy and Peter Pan are selling their brands to your store at wholesale prices of $0.49, $0.51 and $0.53, respectively, what retail prices must you set for the 3 brands at your store? What would be your resulting retail profits in the peanut butter category? Which brand accounts for the greatest share of this retail profit? (Hint: Assume that your objective is to maximize your retail profit from the peanut butter category).

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b Suppose, instead, that you are the brand manager for Peter Pan. Your marginal cost of production for Peter Pan is $0.38. Taking the calculated retail prices in (a) which the Ladue Schnucks store sets for your brand and your 2 competing brands, calculate your resulting brand profit as a manufacturer from the Ladue Schnucks store. Is this larger or smaller than the retail profit that Ladue Schnucks obtains from your brand?

c Suppose that you are still the brand manager for Peter Pan and that you want to change your wholesale price of Peter Pan from $0.53 to some other value. Assume that the retailer uses a markâ€up of 25 % over your wholesale price to set the retail price for your brand, i.e., retail price for Peter Pan = 1.25 times the wholesale price for Peter Pan. Under this assumption, what wholesale price must you charge the retailer? How much larger is your resulting profit compared to that calculated in Q (b)? (Hint: Assume that Jif and Skippy’s wholesale prices remain at their current values of $0.49 and $0.51, and that the Ladue Schnucks store’s retail prices for those 2 brands remain at the calculated values in (a); assume further that your objective is to maximize your brand profit).

dSuppose that you are still the brand manager for Peter Pan. You suddenly realize that Jif and Skippy will not stay put if you changed your wholesale price as calculated in (c). They will change their wholesale price in order to optimally respond to your new wholesale price. Given their changed wholesale prices, you will further change your wholesale price as an optimal response to their changed wholesale prices, and so on. Where will the 3 wholesale prices finally settle down? In this calculation, assume that the retailer uses a markâ€up of 25 % over the wholesale price to set the retail price for each brand, i.e., retail price for a brand = 1.25 times the wholesale price for the brand. Also assume that the marginal cost of production for Jif and Skippy are $0.39 and $0.51, respectively. (Hint: Assume that the objective of each brand manager is to maximize their brand profit).

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