Allocating expenditures across keywords in search advertising

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Allocating expenditures across keywords in search advertising ¨ zgu¨r O ¨ zlu¨k and Susan Cholette O Received (in revised form): 11th July, 2007 Department of Decision Sciences, College of Business, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132, USA Tel: 415-817-4353; Fax: 415-405-0364; E-mail: [email protected]

O¨zgu¨r O¨zlu¨k is an assistant professor of decision sciences in the College of Business at San Francisco State University. His research interests are in business applications of mathematical programming, practices of revenue management and spreadsheet engineering. He obtained his PhD in operations research from UNC Chapel Hill in 1999. After getting his PhD degree, he spent three years working for an airline scheduling company and at a revenue management consulting firm.

determines ad placement, which in turn affects the response function, defined as the click-through rate. Advertisers typically have a fixed daily budget that should not be exceeded, so an advertiser must allocate the budget as productively as possible by selecting which keywords to use and then deciding how much to allocate for each keyword. We construct and examine a model for this selection and allocation process.

Susan Cholette is an assistant professor of decision sciences in the College of Business at San Francisco State University. Her research interests include supply chain management, especially as applied to the wine industry, and she is currently supervising a federal grant to optimally match wineries to distributors. Prior to her university appointment, she served as a project manager for several supply chain management solution providers. She earned her PhD in operations research from Stanford University and her BSE in electrical engineering from Princeton University.

INTRODUCTION An increasingly popular venue for advertisers is keyword advertising on the web pages of search engines such as Google, Yahoo and MSN. Keyword ads, also known as search-based advertisements (ads), appear side by side with ‘organic’ unsponsored search results, and the advertiser is charged only if a user clicks on the ad, taking the user to the advertiser’s web page. US advertisers are projected to spend nearly $8.3bn on keyword ads in 2007, nearly a 25 per cent increase from 2006 and a 43 per cent share of all US internet-marketing expenditures (eMarketer, 2007). Search-based ads provide national, even worldwide, access to potential consumers. The ability to set up and run campaigns of any size allows one-person businesses to compete side by side with much larger companies. Keyword searches have special appeal for businesses that cater to small, niche markets such as shoes for people with very big

ABSTRACT KEYWORDS: search-based advertising, keyword advertising, keyword bidding, internet marketing, resource allocation, budget optimisation

An increasingly popular venue for advertisers is the keyword advertising on the web pages of search engines. Advertisers bid for keywords, where bid price

Journal of Revenue and Pricing Management (2007) 6, 347–356. doi:10.1057/palgrave.rpm.5160110

& 2007 Palgrave Macmillan Ltd, 1476-6930 $30.00 Vol. 6, 4 347–356 Journal of Revenue and Pricing Management 347

Allocating expenditures across keywords

feet. Yet keyword advertising is a relatively new medium. The first search-based ads appeared in 1998 in Overture, and Google did not adopt the current format until 2001 (Vise and Malseed, 2005). Thus all advertisers are still learning how to take advantage of these opportunities. Our research focusses on maximising the value that a firm receives from placing keyword ads. Advertisers typically have a fixed daily budget that should not be exceeded, so an advertiser must allocate the budget as productively as possible by selecting which keywords to use and then deciding how much funding to allocate to each keyword. We construct and examine a model for this selection and allocation process. LITERATURE REVIEW Given the recent development and adoption of search-based ads, academic publications examining keyword ads are not as common as in other channels. In this section, we survey the existing literature on keyword advertising and briefly examine papers concerned with resource allocation in other types of internet advertising and in early generalised advertising research. One of the first operations research papers on advertising, Vidale and Wolfe’s (1957) much-cited work formalises the question of how to best allocate advertising expenditures given a fixed budget. They introduce the concept of a response function by defining a response constant and also discuss the saturation effect. No shortage of papers addressing the resource allocation problem exists by the 1970s. In addition to presenting their own models, Zoltners and Sinha (1980) provide a detailed overview of 24 other papers that have defined sales response functions. The majority of the functional forms presented are concave, although a few researchers attempt other techniques, such as developing heuristics for S-shaped response curves. These prior papers and doubtless many others bemoan the difficulty of collecting accurate data for determining the effectiveness of an ad campaign. Today, this effectiveness can be

measured more accurately. The advent of internet advertising allowed for the use of metrics such as impressions generated and clicks recorded. Furthermore, the time needed to collect data and evaluate effectiveness has decreased dramatically. Budget and resource allocation horizons shifted from quarterly or yearly down to daily allocations. Much of the early internet-advertising research is concerned with banner ads, a form that predates keywords. Chatterjee et al. (2003) explore the likelihood of generating clicks, given the placement of banner advertising and a variety of other variables. They determine that earlier placement in a sequence of web pages is more likely to generate clicks and discuss the difference between results for general audience and targeted niche banner ads. Findings for the latter category are likely to be more applicable to keyword advertising. Mangani (2004) constructs a theoretical model of net revenues obtained from banner ads by using simple nonlinear functions. He explores the trade-offs in using the Cost-perImpression pricing model against the thenemerging Cost-per-Click (CPC) paradigm. He introduces the concept of elasticity of access with respect to the quantity of advertising and shows that the optimal budget allocation depends on the relation between these elasticities, a finding akin to our results. Zhao and Nagurney (2005) consider allocating ad expenditures between several websites. Like Mangani, they also evaluate alternative pricing schemes, even including pricing based on generated revenue, which was a novel approach in 2004. They explain the paradox of why click rates are decreasing as internet usage increases given a concave response function. Although this research does not concern keyword ads specifically, many of their results would appear to be relevant to that venue. Nakamura and Abe (2005) continue the examination of banner ad placement by constructing a linear programming model that maximises the clicks for a palette of banner ads. They define website categories, such as sports

348 Journal of Revenue and Pricing Management Vol. 6, 4 347–356 & 2007 Palgrave Macmillan Ltd, 1476-6930 $30.00

¨ zlu¨k and Cholette O

versus nonsports sites, and investigate how other variables affect the response function. Their findings are, however, best suited to broad-based advertising and are not as applicable to the niche markets served by keyword advertising. Fruchter and Dou (2005) research keywordactivated banner ads. These are ads that will appear only when the user has searched for a relevant keyword. For instance, clothing retailers might be more interested in displaying banner ads on pages selected by consumers who have searched for terms like ‘fashion’. They assume a concave response function — in particular, they utilise a power function. They then formulate the problem as an optimal control problem. Their investigation of keywordspecific banners rather than generalised banners suggests a crossover to research on search-based advertising. Their results suggesting that more generalised ads at generic portals yield higher click-through rates (CTRs) would not seem appropriate to be applied to keyword ad decision making. Other authors examine managing internet advertising from the point of view of improving advertising revenues for websites that sell advertising space. Chickering and Heckerman (2003) present a linear programming model created for MSN to optimise revenues from ad sales given the constraint of a fixed quota of space to sell. They use a two-stage approach, first implementing a pilot to collect data and refine model parameters and then optimising scheduling and placement of ads with the objective of maximising total clicks. The focus of their study remains on banner ads. While some targeting is involved in scheduling ads to specific subject areas of the MSN website, the underlying model does not naturally lend itself to search-based advertising with its large and growing number of possible keywords. Menon and Amiri (2004) likewise espouse the publisher website’s view and consider how to best schedule the placement of banner ads given a finite amount of space. They interpret this problem as a variant of the bin-packing problem and compare Lagrangian decomposi-

tion to a column generation procedure. Once again, the approach is intriguing, but not as applicable to our research question. Additionally, while ads that generate a greater number of clicks for advertisers also increase revenues for the search engines and other websites that sell the space, it should be cautioned that the best solution for a search engine is not necessarily the one that most benefits the advertiser. Only recently (2006) do we find published research dedicated to search-based advertising and the aspects of it, such as real-time auctions for keywords, which differentiates it from other forms of internet advertising. The following papers all address the specific question of optimising the value obtained from keyword ads given the constraints of a fixed daily advertising budget. Rusmeivichientong and Williamson (2006) consider selecting from a palette of keywords by using an adaptive approximation algorithm that prioritises keywords by sorting them based on their profit-to-cost ratio. Selecting from a palette of keywords can be considered analogous to deciding which of the levers of a multi-armed slot machine to pull where the gambler has no initial knowledge about the reward of different levers. One traditional heuristic is to use a greedy algorithm to select the lever with the best payoff from the subset of observed levers (1e) per cent and to engage in exploration the remaining e% of the trials. Rusmeivichientong and Williamson use simulations to show their algorithm performs better than typical multi-armed bandit approaches. Muthukrishnan et al. (2006) specifically address both the auction nature of keyword bidding and the rampant uncertainties associated with the response functions for keywords. They postulate that a search engine selling keywords can predict probability distributions associated with these keywords and then attempt to solve the advertiser’s allocation problem through the application of stochastic models. We will utilise some of the assumptions they make, such as lack of interaction between keywords.



The auction method used by Google and most other search engines to sell keywords to advertisers is also coming to the attention of researchers. This mechanism is the generalised second price auction (GSP) where advertisers do not pay their bid price but that of their competitor one slot below. Edelman et al. (2007) and Cary et al. (2007) attempt to determine optimal bidding strategies from a game theoretic standpoint. GSPs are nontruthful, and it may behoove bidders not to reveal their valuations of keyword ad placements. Zhou and Lukose (2006) show such behaviour has been observed in practice, including vindictive bidding. This gaming element of optimising keyword strategies is beyond the scope of our research effort. Although both Rusmeivichientong and Williamson (2006) and Muthukrishnan et al. (2006) present complex solution techniques, Feldman et al. (2006) propose an alternative approach to keyword selection and bidding that is likely to be more practical to apply. They introduce the concept of click price curves, where clicks increase as the CPC increases. They also show that a simple randomised hybrid of two uniform bid strategies works well and comes close to reaching the theoretical maximum possible clicks. As several of these authors are employed by Google, they have access to auction data to empirically test their strategies. The arena of search-based advertising is so new that solution approaches, let alone vocabulary terms, have not yet been standardised. In the next few years, there will doubtless be a plethora papers on keyword ads offering an even greater variety of models and methodologies. This paper will present one such approach. AN OVERVIEW OF KEYWORD ADVERTISING Keyword advertising is not implemented identically across all search engines. We primarily consider Google, the dominant player with over a 50 per cent share of the keyword advertising market by several metrics

(Karbasfrooshan, 2007). We note that other sites such as Yahoo!, MSN, Ask and AOL may differ, but we believe that the differences are sufficiently minor so that our research can be generalised to all search engines. Given a keyword that is bid on by multiple advertisers, a search engine holds an instantaneous, automated auction to determine which of the advertisers currently bidding on that keyword are allocated advertising slots. Depending on the strength of the advertiser’s bid relative to other bids for the same keyword, the search engine assigns the advertiser’s ad a position that is continually updated throughout the day, subject to new or revised bids by advertisers. Larger bids result in better placement than smaller ones, although the advertiser usually cannot directly specify the exact ad position. Ads placed higher on the page are more desirable than lower placements. In fact, exact positioning is not known in advance and changes dynamically as competitors bid for keywords. Indeed, Google’s reports provided to its advertisers denote ad position as a noninteger average value (Google, 2007). This average value is calculated over a user-specified report duration and can be as frequently as daily. When a user of the search engine types the keyword that the advertiser has bid on, the advertiser’s ad is displayed, resulting in an impression at the position the search engine has predetermined. If the user clicks on the ad, the advertiser is charged a fee based on the bid price. While not all clicks may result in sales, the advertiser expects that a portion of the users who click through the displayed ad will make a purchase of the advertised product(s) or that the advertiser will otherwise benefit from the user’s click. Thus the advertiser wishes to maximise this benefit while not spending beyond the budget. Figure 1 illustrates this flow. While Yahoo’s positioning is based solely on bid price, Google analyses the traffic for all advertisers competing for the same keyword and gives higher positions to the ads that generate more clicks over those who offer a similar bid



Bid price

Ad Position

Impressions

Clicks

Revenue

Given these two factors, we define the revenue generated from a keyword and the expenditure on that keyword using the following multiplicative models:

Spending

Revenue ¼ ImpressionsCTR Figure 1: Influences on revenue and spending for keyword searches

Revenue-per-Click Spending ¼ ImpressionsCTR Cost-per-Click

price but that generate fewer clicks. In addition to placing ads that have greater draw in a more convenient space for the user, this preferential treatment towards more popular ads has the effect of maximising Google’s revenues. Our model assumes the advertiser has constructed the ad to be as appealing as possible, so relevance is taken as exogenous to the advertiser’s decision process in this model. In determining the best strategy for an advertiser, two key factors must be considered: the bid price and the rate at which a search engine user is likely to click on the published ad. The bid price is commonly referred to as the CPC. While in reality, for GSPs actual CPC is less than the bid price, we assume that this difference is negligible and will use these terms interchangeably. Bid prices must be positive and are set by most search engines to be at least $0.05 per click. In this model, we focus on bids that are sufficiently large to lead to placement on the first page of the search engine’s results, typically positions 1–10, with 1 being the highest. The rate at which a search engine user is likely to click on the published ad is called as the CTR. Because bid price determines ad placement, CTR is a function of bid price and is assumed to be continually differentiable over the region of interest. There are actually two dynamics in play here; first bid price determines ad position, and then ad position determines CTR. Both of these effects are combined into a single monotonically increasing function in our model. Feldman et al. (2006) confirm that better positioning yields better CTRs.

Impressions denote how often the ad is displayed and depend on the popularity of the product that the keyword references. Revenueper-Click accounts for widely diverse values that keywords may generate and is function of the underlying profitability of the product being searched or the likelihood of a user’s click converting into a sale or other valueadded action for the advertiser. Impressions and Revenue-per-Click are both assumed to be exogenously determined in our research. FORMAL MODEL: TWO KEYWORDS Suppose that we consider an advertiser with a fixed budget who would like to decide how much to bid on two separate keywords. Then the problem can be defined as follows:

Maximise Revenue ¼ m1 r1 f ðxÞ þ m2 r2 gðyÞ subject to m1 xf ðxÞ þ m2 ygðyÞpB x; yX0

where the decision variables are x: bid price for keyword 1 y: bid price for keyword 2 with f (x): CTR for keyword 1 given x g(y): CTR for keyword 2 given y r1: revenue-per-click for keyword 1 r2: revenue-per-click for keyword 2 m1: number of impressions for keyword 1 m2: number of impressions for keyword 2 B: total advertising budget This model assumes that no interaction exists between an advertiser’s set of keywords. As



explained by Feldman et al. (2006), keywords can overlap, resulting in inadvertent selfcompetition. Such interaction can be illustrated by an advertiser who bids on both ‘Platform’ and ‘sandals’, since a query for ‘platform sandals’ meets the specification for both keywords. Grappone and Couzin (2006) in their practitioner book oriented towards potential advertisers suggest that the best strategy is to bid for focussed keywords that target the ‘long tail’ of advertising opportunity rather than for generic terms, like ‘shoes’. By definition, such focussed keywords will have less likelihood of overlapping with others, especially if the advertiser manages the keyword set wisely. In particular, our underlying exposure to this market has been with an advertiser whose keywords were primarily shoe brands, such as ‘Prada’ and ‘Stuart Weiztman’. Such brands are inherently nonoverlapping. In the case of a hypothetical online shopper interested in both Prada and Steward Weiztman shoes, no interaction occurs if the said shopper performs her queries sequentially, rather than creating a joint, single query. Grappone and Couzin (2006) suggest that users will enter a series of short queries rather than a long one. Therefore, we can reasonably assume that the selection of such targeted keywords will have no interactions. The model also supposes that the value generated for the advertiser from each click can be represented by an average value that is independent of the ad position and the traffic generated by the ad. Without loss of generality, we incorporate the number of impressions generated for each keyword into the functions f and g themselves as multiplicative constants. We thus define the response function as the CTR multiplied by the number of impressions. Then, the model becomes

The monotonically increasing response function means that spending additional money will always increase clicks. So long as the revenue or value obtained from a click is greater than its bid price, the budget is exhausted in the optimal solution. Maximise Revenue ¼ subject to

r1 f ðxÞ þ r2 gðyÞ xf ðxÞ þ ygðyÞ ¼ B x; yX0

‘‘By examining the Karush-Kuhn-Tucker (KKT) conditions for optimality in this optimization problem we get the following Lagrangian. L ¼ r1 f (x) þ r2 g(x)l(xf(x) þ yg(y)B)’’ Taking the derivative of the Lagrangian with respect to each variable and setting to 0 yields rL dr1 f ðxÞ df ðxÞ ¼ l f ðxÞ þ x rx dx dx ¼0

ð1Þ

rL dr2 gðyÞ dgðyÞ ¼ l gðyÞ þ y ¼ 0 ð2Þ ry dy dy Rearranging the terms of (1) to express as a function of x yields df ðxÞ ðr1 lxÞ ¼ 0 dx df ðxÞ df ðxÞ ¼ r1 lf ðxÞ lx dx dx r1 f ðxÞ x¼ l df ðxÞ dx Similarly, r2 gðyÞ y¼ l dgðyÞ dy lf ðxÞ þ

Thus Maximise subject to

Revenue ¼ r1 f ðxÞ þ r2 gðyÞ xf ðxÞ þ ygðyÞpB x; yX0

yþ 1 ¼ l

gðyÞ f ðxÞ dgðyÞ x þ df ðxÞ dy dx ¼ r1 r2



Rearranging to separate the terms dealing with each decision variable provides the following: 0

1

1

0

1B f ðxÞ C 1 B gðyÞ C A ¼ @y þ A @x þ df ðxÞ dgðyÞ r1 r2 dx dy Borrowing from economic theory, a variant of price elasticity of demand can be applied to the keyword market. In particular, the elasticity of the response function is defined as the change in the CTR with respect to with respect to the change in bid price Ef ;x ¼

x df ðxÞ ; f ðxÞ dx

Eg;y ¼

y dgðyÞ gðyÞ dy

Re-writing the equation in terms of the elasticity of the response functions yields the following: x 1 y 1 1þ 1þ ¼ r1 Ef ;x r2 Eg;y

ð3Þ

Equation (3) shows that at this extremum point, the trade-off between spending more on a bid price in one market relative to another is dependent on the ratio of values of each keyword and also the elasticities. That is, if the value of keyword x increases — all else remaining unchanged — the ratio of bid prices will shift to favour a higher bid price for x. It should be noted that neither the total budget nor any other detail about response function, save its elasticity, will affect the ratio of spending between two keywords. Likewise, if the elasticity at a particular bid price for a keyword x increases (showing greater response to increased investment), the ratio of bid prices should likewise shift. This result is true for any f(x) and g(y) that are continuously differentiable and monotonously increasing over the bounds specified for the bid price. We next show that this extremum is indeed the global optimum. In order to show this, we

assume that the response function can be modelled by a function that is concave and not just monotonically increasing over bid price. Concavity reflects diminishing returns, an assumption made in other internet-advertising research efforts, such as Fruchter and Dou (2005), Mangani (2004) and the majority of researchers cited in Zoltners and Sinha (1980). It is to be expected that competition increases for placing ads in top positions, and the overall cost to reach the top spot for a market in equilibrium should outpace the increased clicks generated, assuming all bidders place the same value on these clicks. We also note concavity reflects the fact that no matter how high the advertiser bids, the highest position that can be achieved is the top of the first page on the search engine website. A more realistic mathematical model could be an S-curve, which incorporates convexity in the lower price range, as too-small expenditures are likely to have a minimal impact. Our simplification is mitigated by the fact that the model is restricted to apply only to the first page of search results. This avoids discontinuity effects between positions on the bottom of one page and top of the next. Additionally, in order for an advertiser to reach the first page, the required bid price for a keyword in a stable, competitive market is likely to be sufficient to belong in the concave portion of the S-curve. For concave f (x), g(y), f (x) þ g(y) are concave. In Appendix A, xf (x) is shown to be convex on x. Thus, any combination of ad expenditures are also convex, and as total spending must be less than or equal to the budget, the feasible region is a convex set. Local optima obtained from maximising a concave function over a convex feasible region are also global. Therefore, under stated conditions, the optimisation problem turns into finding the solution to equation (3).

GENERALISATION TO N KEYWORDS The results we have found so far can be easily generalised to N keywords. For N keywords,



the model becomes Maximise

Revenue ¼

N P

ri fi ðxi Þ

i¼1

subject to N P

xi fi ðxi Þ ¼ B

i¼1

xi X0 Since there are no interaction terms, it is easy to see that using KKT conditions, we get ri fi ðxi Þ xi ¼ df ðx Þ i i l dxi

which implies that for any pair of keywords (i, j), we have ! xj xi 1 1 ð4Þ 1þ 1þ ¼ Efi ;xi Efj ;xj ri rj Now assume that we have N keywords and we have the optimal bid prices for these as ~ x ðN Þ ¼ ðx1 ; x2 ; . . . ; xN Þ with optimal revenue R(N). Consider what happens when we would like to consider a new keyword, keyword N þ 1. First, it is interesting to observe that adding a new keyword to the mix will never worsen the optimal revenue in our model. This follows from the fact that the solution ~ xðN þ 1Þ ¼ ðx1 ; x2 ; . . . ; xN ; 0Þ is a feasible solution for the instance of the optimisation problem with N þ 1 keywords. This implies R(N þ 1)XR(N). An interesting research question for an advertiser would be to determine when to increase the number of keywords used from N to N þ 1. Common sense suggests that the advertiser should go ahead with the N þ 1st keyword if the increase in revenue offsets the additional overhead of managing an additional keyword. Mathematically, this could be determined if the magnitude of the difference R(N þ 1)R(N) exceeds a predefined thresh-

old T. If it does not, then the advertiser should not adopt the N þ 1st keyword. Finding R(N þ 1) given the optimal solution to the N keyword problem may amount to solving a new optimisation problem for general form of response functions. If response functions are, however, power functions in the form fi ðxi Þ ¼ ai xni where 0onio1, this process becomes simpler. To see this, first we have to note that the elasticity of a power function is constant, that is Efi ;xi ¼ ni . Fruchter and Dou (2005) utilise power functions in their work, and Nerlove and Arrow (1962) utilise a constant elasticity response function in their seminal work. Thus, equation (4) above can be rewritten as xj xi 1 1 ¼ 1þ 1þ ni nj ri rj

ð5Þ

This new equality implies that the optimisation problem for N keywords can be reduced to the following one-dimensional optimisation problem in terms of x1 without loss of generality Maximise Revenue ¼

N P

ri fi ðdi x1 Þ

i¼1

subject to N P

x1 fi ðdi x1 Þ i¼1 x1 X0

¼B

where di ¼ r1/ri(1 þ 1/ni)(1 þ 1/n1)1 Equation (5) also implies that in the case of constant elasticity, the ratio of optimal bid prices is independent of the number of keywords. So if ~ x ðN Þ ¼ ðx1 ; x2 ; . . . ; xN Þ is the optimal solution for the N keyword problem, then ~ x ðN þ 1Þ ¼ ðax1 ; ax2 ; . . . ; axN ; bÞ is the optimal solution for the N þ 1 keyword problem for some 0oao1 and b>0. In this case, instead of solving optimisation problem for N þ 1 keywords, we only need to solve the



following equation N X

axi fi ðaxi Þ þ bfN þ1 ðbÞ ¼ B

i¼1

for a with b ¼ x1 rN þ 1 /r1 ð1 þ 1/n1 Þ ð1 þ 1/nN þ 1 Þ1 Thus, the advertiser would decrease bid price on each of the prior keywords by (1a)%, which would then decrease the overall budget allocated to those keywords. The unspent funds would then be allocated to the N þ 1st keyword. It should be noted that use of a concave response function implies that the advertiser benefits from further spreading limited financial resources over more keywords. We assume the advertiser offers products or services that allow for a variety of relevant keyword ads to be created, such as our example of an online shoe retailer that sells hundreds of brands and styles. We also maintain our restriction that the bid prices stay sufficiently high that placement remains on the first page of search results for all keywords. As bid prices decrease with a new keyword addition, this condition may no longer hold. A practical check would be to remove any keyword that has an average position higher 10 and resolve for bid prices and funding allocations accordingly. Repeating this process would allow an advertiser to evaluate and refine a palette of keyword ads over time. CONCLUDING REMARKS As internet advertising, especially search-based advertising, continues to become more popular, advertisers would like to spend their limited budget more wisely. In this paper, we briefly present the status quo of the literature on keyword advertising and other relevant advertising allocation studies. We formalise the advertiser’s problem of deciding how to allocate an advertising budget among multiple keywords.

We show that the trade-off for bidding more for a particular keyword versus another is dependent on the ratio of the click-through values of these keywords and the price elasticities of the response functions. In particular, the more value a particular keyword generates for the advertiser, the higher its bid price should be relative to other keywords’ bid prices. In addition, neither the budget nor the specific form of the response function, except for its elasticity, has any effect on the ratio of bid prices between keywords. Furthermore, we address the question of when an advertiser should increase the number of keywords used. If the keywords chosen are sufficiently focussed so as to prevent marketplace interactions, we show that adding more keywords into the portfolio is always beneficial in increasing profitability, subject to certain thresholds. We also provide theoretical results to show how the impact of an additional keyword can be calculated fairly easily under the assumption of constant elasticity. With keyword advertising being a new field, our underlying model presents many opportunities for future research. In addition to empirical studies to validate the model structure, we also suggest some avenues for theory development. One important area would be to incorporate the impact of temporal market changes on the allocation scheme — that is, has the market for a particular keyword stabilised or is it either growing or declining? How should an advertiser manage bid prices given these temporal shifts? Another possibility would be extending the scope of this model to include the fraction of clicks that convert to sales or another measurable and beneficial action. With consideration of the average value of the sale or action, the advertiser could then allocate advertising funds more effectively between keywords. This extension would also aid in comparing efficacy of a CPC campaign against one where payment occurs upon action, an even newer pricing paradigm. We look forward to continuing to solve such problems and



reading about the research of others in this dynamic and evolving arena.

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APPENDIX A AD EXPENDITURE ON A KEYWORD, XF (X), IS CONVEX ON X For any concave, monotonically increasing function f(x), b can be found such that

f ðxÞXb for any x40; where b40: Multiplying by x, for all x>0, yields xf (x)Xbx. As xf (x) is also monotonically increasing, and it is greater than bx for all x, it must be convex. Were it concave, there would be a point y at which by>yf (y).
