國立高雄大學經營管理研究所
碩士論文
Advertisement Spillover Effect on Location Choice
廣告外溢效果對廠商區位選擇之影響
研究生：王瑾瑜 撰
指導教授：鄭育仁 博士
中華民國 一 O O 年 六 月
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致謝詞
終於到了寫謝誌的時刻，能夠走到現在真的要感謝太多人的教誨與幫助，讓 我能順利完成研究所的學習。首先要感謝的就是指導教授鄭育仁老師。由論文題 目的發想，到實地分析與撰寫，無數次的 meeting，儘管我的想法有時表達的不 夠完整，老師都不厭其煩的教導與提點，清楚地指出我該走的方向，讓我有動力 能夠完成這份論文。 感謝兩位口試委員楊雅博老師與童桂馨老師在百忙之中，仍願意擔任這份論 文的口試委員，同時以豐富的學術涵養與嚴謹的研究態度，給予這份論文精闢的 見解與寶貴的建議，使得這份論文能夠更為完整。 感謝共同努力的同門師兄弟姊妹哲豪、蘇三、陳葳、許大哥、方恩、莉芳， 和時常友情相助的億靜、祐萱、皖華及景隆，因為有你們跟我一起努力，讓艱辛 的研究所學習過程變得較為有趣，因為有你們的笑聲，研究室才不會顯得過於安 靜。在此感謝冠婷姐在行政事務上的幫助，也感謝棠祺學姐在我遭遇困難時能夠 給予鼓勵與建議。 最後，特別要感謝我的父母與姊姊，給予我幸福美滿、衣食無缺的環境，讓 我能順利完成碩士學位，感謝您們對我的照顧與包容。 感謝之意時時放在心底，但若有因為我的疏忽而有所遺漏的，請見諒，在我 心裡其實抱著十二萬分的感謝。 瑾 瑜 謹誌 2011.06ii
Advertisement Spillover Effect on Location Choice
Advisor: Dr. Yu-Jen ChengInstitute of Business and Management National University of Kaohsiung
Student: Chin-Yu Wang
Institute of Business and Management National University of Kaohsiung
ABSTRACT
When firms compete with their rivals, they invest in advertisement to provide consumers information for enhancing consumers’ awareness of their product quality. But informative advertisement has the spillover phenomena in nature. When a firm advertises its product quality, advertisement effect will diffuse to its rival’s product.
Consumers have two ways to obtain the advertisement product: (1) Consumers pay the transportation costs for purchasing products. (2) The firms spend the distribution costs delivering the products to consumers’ locations. We adopt Hotelling model and set up a three-stage game model for investigating the advertisement effects on firms’ location choices. The results of both cases show the advertisement spillover effect will positively influence the two firms’ clustering considerations. Though the two cases have the same result, the conclusions can be used in different application. When the transportation cost is paid by consumer, the firms will cluster because of higher spillover effect; when the distribution cost is paid by firm, the number of firms will decrease since the spillover effect is higher.
We further compare this paper with Nelson’s research. Nelson made a distinction between qualities of advertisement goods: search goods and experience goods and concluded that stores sell search goods cluster more than stores sell experience goods. We consider advertisement for search goods can be transmitted easily and then search goods have greater advertisement spillover effect than experience goods. Our finding of advertisement spillover effect is identical with Nelson’s conclusion.
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廣告外溢效果對廠商區位選擇之影響
指導教授：鄭育仁博士 國立高雄大學經營管理所 學生：王瑾瑜 國立高雄大學經營管理所 摘要 當廠商和其他廠商競爭時，會投資廣告提供消費者商品資訊，以提升消費者 對商品品質的認知。然而，傳遞資訊的廣告有外溢效果。即一家廠商廣告自家商 品品質，廣告效果會擴散至競爭廠商的商品。 本文從外溢效果的角度，將消費者取得廣告商品的方式分為兩種，一為消費 者支付運輸成本至廠商所在處購買商品，二為廠商負擔配銷成本將商品送到消費 者所在處。採用 Hotelling model 架構一個三階段賽局，分別討論在這兩種情況 下，廣告外溢效果對廠商區位選擇之影響。研究發現，不論是消費者支付運輸成 本取得商品，或廠商負擔配銷成本提供外送服務，廣告外溢效果對兩廠商聚集之 決策呈正向的影響。即使兩模型得出相同的結果，但可做不同的解釋。在消費者 負擔運輸成本的模型裡，廣告外溢效果很大會吸引廠商聚集；在廠商支付配銷成 本的模型裡，廣告外溢效果很大會使的廠商數量減少。尤其，當廣告效果完全外 溢，總公司只會授權一家廠商代理負責整個市場的營運和需求。 本文更進一步與 Nelson 的文章做比較。Nelson 將廣告商品分為搜尋品與體 驗品。我們認為搜尋品品質資訊較體驗品品質資訊容易傳遞，屬於廣告外溢效果 較大的廣告商品類型，體驗品屬於廣告外溢效果較小的商品。並提出銷售搜尋品 的廠商會比銷售體驗品的廠商容易聚集。本研究結果與 Nelson 結論相符。 關鍵字：區位選擇、外溢效果、廣告與廣告效果、Hotelling 模型iv
Catalog
Chapter 1 Introduction ... 1
Chapter 2 Literature Review ... 5
2.1 Location choices ... 5
2.2 Spillover effect ... 6
2.3 Advertisement and the effect of advertisement ... 8
Chapter 3 The Basic Model ... 12
3.1 Preamble ... 12
3.2 Transportation cost is paid by the consumer ... 12
3.3 Distribution cost is paid by the firm ... 23
3.4 Conclusion ... 32
Chapter 4 Concluding remarks ... 33
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List of Figures
Fig. 1 Research Procedure ... 4
Fig. 2 Hotelling model ... 13
Fig. 3 The procedure of the three-stage game ... 15
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1. Introduction
In metropolitan area, most firms with similar nature run their businesses in the neighborhood; some even open their stores just next to their competitors. The clustering phenomenon further locates the merchant of a kind into limited boundary.1 For example, a “wedding gown street” crowds with many wedding service stores; the “food street” attracts various kinds of restaurants; the shopping district collects many department stores nearby and so on. Whereas, some firms choose to operate businesses dispersedly, such as shopping mall usually tend to initiate operation in a distinct.
There might be several reasons for firms clustering in the neighbor area. Firstly, clusters form shopping district, which enables customers to find the products they need easily and reduce consumers’ searching cost. For example, in 3C stores consumers can rapidly purchase the products they need as well as those do not in their purchasing lists originally.2 Secondly, clustering provides flexibility for consumers to obtain ideal products. Cinemas, for instance, located in a neighboring area with same films but variety schedules enables consumers to choose their available time. Hence, every cinema can allot a market share. Thirdly, clustering can also attract streams of people. In contrast, those firms, who are afraid that consumers perceive too much information about similar products and decrease their willingness to buy or willingness to pay, may decide to operate their businesses dispersedly.
When a firm launches commercial activities, it introduces product information to consumers through media of languages, words, images or videos. Thus, consumers
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Clustering: A geographically proximate group of interconnected companies and associated institutions in a particular field (Porter, 2000).
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are impressed with its product and obtain a better awareness of the product quality. This is what we call “the advertisement effect.” However, even other firms doing similar businesses do not advertise or advertise less, consumers may understand their product information simultaneously. This is called “the advertisement spillover effect.” For example, by receiving the advertisement of Mercedes Benz, consumers’ knowledge about autos of other brands is meanwhile better improved.
From the perspective of firms’ advertisement that provides product information to consumers, this research discusses the characteristic of advertisement spillover effect. We consider that consumers’ product quality awareness will be enhanced by knowing the specification and the product quality while receiving the advertisement with greater spillover effect. At the same time, consumers’ knowledge about similar products of other firms is improved as well; whereas, the firm’s advertisement with trivial spillover effect can only inform consumers the existence of the product. Consumers can not further understand the firm’s and its competitor’s real product quality.
After receiving advertisement information, consumers have two ways to obtain the products: (1) Consumers purchase the product at the firm s’ place. It means consumers have to pay the transportation costs for acquiring the products. We discuss this case from the perspective of consumers. (2) The firms pay the distribution costs for delivering the goods to consumer s’ locations when consumers order the products and ask for deliver service. We discuss the case from the perspective of firms.
Under the above two cases, we will naturally ask the question. What kinds of characteristics do advertisement have that can affect firms’ location choice? For answering the question, we adopt Hotelling model to investigate the firms’ location choices as the advertisement has spillover effect. The original Hotelling (1929) model
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exists an unique equilibrium located at the center of the market, but d'Aspremont, et. al. (1979) followed Hotelling’s product homogeneous assumption but modified the transportation cost as the quadratic form, and they showed that there exist infinite equilibriums. d'Aspremont, et. al. (1979) further suggested that product differentiation must be important in the competitive market. Hence, in this paper we create a framework that the products in the market are differentiated according to the firms’ informative advertisement with spillover effect which will alter consumers’ awareness to their product quality. We will discuss how the advertisement effect and spillover effect influence firms’ location choices. The research purposes are listed below: 1. The effect on the following subjects while the transportation costs are paid by
consumers:
a. To understand how the equilibrium product price is set after firms’ advertising and price competing.
b. To know the effect of a firm’ advertising that provides product information on consumers and competitors.
c. To discuss the equilibrium expenditure on advertisement when the product advertisement has the characteristic of spillover effect.
d. To discuss how the direct effect and spillover effect of advertisement affect consumers’ awareness of product quality.
e. By displaying the model of spillover effect of advertisement, to explain how the direct effect and spillover effect of advertisement affect firm’s location choice. 2. The effect on the subjects mentioned above while the distribution costs are paid by
firms.
The research procedure is shown as Fig. 1. And this paper is organized as follows. In chapter 2, we review the past literatures concerned about location choices, spillover effect and the advertisement effect. In chapter 3, we discuss the advertisement spillover effect on firms’ location choices in two scenarios: transportation costs are paid by consumers and distribution costs are incurred by firms. Chapter 4 is the concluding remarks.
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Select research topics
Survey relative literatures
Propose research objectives and problems
Is the basic model sufficient to describe and explain the objectives and
problems?
No
Fig 1. Research Procedure 1. Analyze the basic model
2. Enrich the basic model for extensive analysis
1. Arrange the research outcomes
2. Explain and conclude their economic and policy implications.
Complete the thesis Yes
Design and modify the basic model
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2. Literature Review
The issue of advertisement has been discussed in a variety of strands. In this paper, we focus on the topic of location choice when informative advertisement with spillover effects. Hence, we review the following related fields.
2.1 Location choices
The phenomenon of agglomeration has been examined in many studies (Wolinsky, 1983; Dudey, 1990; Fischer and Harrington, 1996). Agglomeration can be categorized into two recognitions. Firstly, the geographical approach of industries and services are referred to urbanization economies (Hoover, 1937). Secondly, the geographical agglomeration or cluster of related economic activities is referred to localization economies on firms’ locations. For example, high-tech industries concentrate in Silicon Valley and the auto industry in Detroit (Ellison and Glaeser, 1997; Belleflamme, Picard, and Thisse, 2000). Past researches considered agglomeration is equivalent to cluster. Porter (2000) defined cluster as “a geographically proximate
group of interconnected companies and associated institutions in a particular field, linked by commonalities and complementarities.”
Maskell (2001) considered the existing literature provide different cognition about the phenomenon of related firms’ cluster. Some scholars analyzed how clusters have originated and accompanied by the subsequent evolution (Bischi, Dawid, and Kopel, 2003). Another undertook to specify the possible reasons which may attract firms to locate in a cluster. The latter aspect suggested that if firms are heterogeneous they will have incentives to cluster and receive different benefits from clustering (Fischer and Harrington, 1996; Ellison and Glaeser, 1997; Shaver and Flyer, 2000).
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There are several mechanisms that persuade firms into clustering. Firstly, clusters may be about location and associated exogenous forces like resources, specialized suppliers, demand, and infrastructure. Secondly, firms may access to skilled labor easily. Thirdly, there are inter-firm knowledge spillovers. Fourthly, clusters of firms attract consumers by facilitating price comparison (Dudey, 1990; Tallman et al. 2004). Substantial attention has been paid to knowledge spillovers within economic researches recently (Shaver and Flyer, 2000; Belleflamme et al., 2000; Tallman et al., 2004). For example, the physical proximity and knowledge spillovers are positively related. Firms are more likely to imitate other firms that are proximate geographically (Jaffe, Trajtenberg, and Henderson, 1993).
Economides (1986) considered that firms compete when their products are defined by two characteristics and then develop a two-dimensional equivalent model based on the assumptions of Hotelling model. He further compared the one-characteristic model with the two-characteristic model and showed that there exist the Nash equilibrium prices for all symmetric varieties. The finding is opposite to one-characteristic model that there are no Nash equilibrium prices for adjacent locations comparatively.
2.2 Spillover effect
The phenomenon of spillover is proposed by Schmookler (1966). The R&D efforts of one firm may enable other firms to achieve the same goal without exerting any effort (Griliches, 1979; Jaffe, 1986). The possible sources of knowledge spillovers are as follows: (1) reverse engineering, patent citations, informal communications among personnel at different firms, seminars where information is discussed (Mansfield, 1985; Alsleben, 2005) (2) the mobility of employees from one firm to
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another (Mansfield, 1985; Fosfuri and Ronde, 2004) (3) cooperation between firms (Brod and Shivakumar, 1997) (4) FDI, international trade, and joint ventures (Bernstein and Yan, 1997; Porterie and Lichtenberg, 2001; Girma, et. al., 2008).
There are different explanations about spillovers. Romer (1986, 1990) embodies knowledge in the forms of physical capital and human capital. The external effects of knowledge lead to cost reductions and increase marginal output. Romer show that the new knowledge created by one firm may influence other firms positively because knowledge can’t keep secret or be patented completely. On the other hand, some scholars focus on the aspect of technology diffusion. Keller (2002) used a set of panel data which includes most of the world's innovative activity between 1970 and 1995 and found that technology is to a certain degree of local, but global. The benefits from spillovers decline with distance. Henderson (2007) concluded that the leakage of knowledge can be involuntary and voluntary while there is a non-rivalrous component to knowledge.
The clusters of similar firms are widespread. Silicon Valley and Hollywood are probably the most famous examples of clusters (Maskell, 2001). Ellison and Glaeser (1997) analyzed the common phenomenon that several different US industries are geographically concentrated, e.g. high-tech industries in Silicon Valley and the auto industries in Detroit. Adams and Jaffe (1996) found that the effects of a firm’s R&D on plant-level productivity are decreased by both the geographic and technological distance. It demonstrates that knowledge is tacit, so it is not easy to spread and the cost of transmitting knowledge increases with distance. Information flows and knowledge spillovers may be limited by geographic division. The principal motive of these firms clustering is to get technological and knowledge spillovers from similar firms which are located nearby. Acquiring others’ technology and knowledge, firms
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can reduce cost. Consequently, location choice is a main strategy that firms can reach for potential knowledge spillovers. Spillover is advantageous to nearby firms and firms prefer to cite the knowledge of firms which are proximate geographically (Krugman, 1991; Jaffe, Trajtenberg, and Henderson, 1993; Alcacer and Chung, 2007).
Most literatures about knowledge spillovers often assume and conclude that there exist many benefits for firms to cluster. But there may be some loss of sharing knowledge with other firms. For example, German manufacturing firms and high-tech industries do not cluster in a region (Alecke, et. al., 2004). Alsleben (2005) sketched a duopoly model of location choice by firms and based on the premise that knowledge spillovers take place when firms poach labors from other firms. Firms will raise salary of their employees for the sake of preventing themselves from poaching by their rivals. Because the expense of sharing knowledge spillovers is too big, firms prefer to separate. The other reason that firms do not cluster may be the diverse conditions of firms. Shaver and Flyer (2000) analyzed firms’ location choice empirically. They conducted the sample which consists of FDI activities into the US in 1987. If the firms are heterogeneous, the benefits they have received from clustering are different. The firms with better quality (e.g. technologies, human capital) will obtain little from the others and tend to disperse when their knowledge, employees spillover to their rivals. The firms with weaker quality are likely to cluster with other firms in order to reach for potential spillovers.
2.3 Advertisement and the effect of advertisement
Advertisement means a specific sponsor invests in communicating with the target group and promoting the product, belief, or service by languages, words, pictures, and images (Cheng, 2006). According to the function of advertisement, advertisement can
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be classified as informative advertisement, persuasive advertisement, and reminder advertisement. The literature about informative advertisement views advertisement as an implement for information spread, broadcasting the existence of a product, available locations, major characteristics, quality, etc. (Grossman and Shapiro, 1984). Informative advertisement provides more accurate information to consumers (LeBlanc, 1998). This function enables consumers to make sensible selection by supplying adequate information. The literature about persuasive advertisement regards advertisement as a tool to induce consumers to notice the unusual product, increase demand for the product. Some scholars adopted Hotelling model to discuss the advertisement effect which might alter consumers’ preference between two firms. (Francis and Delphine, 1999). This function is a means which can persuade consumers by creating mental difference (Nichols, 1985). Advertisement which is used to remind consumers of the product that has been supplied and sold for a long time is reminder advertisement, like Coca-Cola (Cheng, 2006).
In this paper, we focus on the informative advertisement in what follows. Consumers often know little about the price and attributes of products when firms do not advertise. Nelson (1970, 1974) showed that advertisement information originates from consumer power in the product market and characterizes the process that consumers receive information about price and quality as search. In addition, Nelson made a distinction between qualities of goods: search goods and experience goods.3 Advertisement for search goods provides consumers with specification of the qualities of the particular product. However, advertisement for experience goods supplies
3
Nelson (1970) categorized products being advertised into two types. (1) Search goods: consumers know the characteristics of the product before they purchase and the product quality can be easily found. (2) Experience goods: consumers will not know the product quality unless they buy it and experience it by themselves. Therefore, advertising for different types of products will have different spillover effects.
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consumers the direct information. The primary goal of advertisement for experience goods is to increase the reputation (reputability) of the product. It’s impossible to know the quality of the product before purchasing (Milgrom and Roberts, 1986; Linnemer, 2002). Consequently, consumers receiving search goods advertisement will compare the firms’ product quality and purchase the product from the firms they prefer. The firms will choose to diminish their distance for consumers. Nelson concluded that stores sell search goods will cluster more than stores sell experience goods.
Grossman and Shapiro (1984) studied informative advertisement in markets with differentiated products and considered that firms employ advertisement to attract consumers’ attention when they deal with commercial activities and compete with rivals. Firms offer consumers the information of their own products and increase consumers’ awareness of products (Bibek and Bandyopadhyay, 2003). It is called the direct effect of advertisement. But, it may generate spillover effect for the advertisement simultaneously. Consumers who have received one firm’s advertisement information would partially understand other firms’ product information. For instance, the advertisement of autos, mobile phones, and computers will reveal not only the specifications of their products but also exert the implicit comparison with their rivals’ product qualities. Consequently, the advertisement practiced by one firm may drive consumers to purchase similar products from its rivals (Cellini and Lambertini, 2003; Nakata, 2006; Brady, 2007).
A strand of literatures studied the relationship between consumers’ awareness and advertisement. Fluet and Garella (2002) discussed whether firms advertise in order to signal quality and whether advertisement has competitive effects. They showed that advertising is a necessary part of telling consumers the product information when
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there is insignificantly quality difference under the price competition. Sridhar and Zhao (2000) inspected the relationship between advertisement expense and perceived product quality. They measured consumers’ awareness of quality by two surveys. The first survey was conducted among 40 part-time MBA students at a leading university in the northeastern US in the first quarter of 1993. The second survey was conducted among 44 staff members at the same university in the third quarter of 1994. The two surveys do not exhibit differently. Sridhar and Zhao concluded that the relationship between perceived quality and advertisement spending is positively related. In this circumstance, advertisement information seems to inform consumers of product qualities indirectly. Consumers can infer implicit quality of the product from explicit advertisement (Kihlstrom and Riordan, 1984).
From the above discussion, we can know that informative advertisement provides more accurate information to consumers. But the advertisement effect will diffuse from the advertising firm to the non-advertising firm. The literatures concerning R&D spillover effects explain the benefits from spillovers decline with distance. Hence, we would like to investigate the advertisement spillover effect on firms’ location choices in this paper.
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3. The Model
3.1 Preamble
Assume that consumers do not fully understand the product quality before firms offer advertisement. Therefore, the firms will utilize the informative feature of advertisement for enhancing consumers’ awareness towards the product quality. Yet, the effort that one firm advertises to improve consumers’ awareness for its own product may also benefit the rival firms. Past literatures investigate R&D have concluded that the closer are the firms to each other, the more advantages they receive from their competitors’ endeavors. In order to understand whether the advertisement has similar effect under firms’ location choices, we adopt Hotelling model and formulate a three-stage game model. In the first stage, firms make their location decisions. In the second stage, firms determine their expenditures on advertisement. In the third stage, firms engage in price competition. We discuss the advertisement spillover effect on the firms’ location choices in two conditions respectively: (1) transportation costs are paid by consumers, and (2) distribution costs are incurred by firms.
3.2 Transportation cost is paid by consumer
We consider a linear city model with two firms, Firm 1 and Firm 2, supplying differentiated products. The two firms locate in a line segment of unit distance. Consumers are uniformly distributed along the segment. Firm i locates at yi∈
[ ]
0,1, with y1≤ y2, i , j =1, 2, i≠ (see Fig. 2). Let j p1 and p2 denote the prices ofFirm 1 and Firm 2. Each consumer is characterized by her location x in the segment. The highest price a consumer is willing to pay for a good is called the reservation
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price, γ . Assume that every consumer purchases one unit of the product, provided that the price does not surpass her reservation price.
Advertisement has the ability for conveying the informative message.4 Lack of advertisement, consumers may be vague about the firms’ products quality. The surplus of the consumer x purchasing from Firm i under no advertisement is given by:
2 ) ( i i i p t x y CS =γ − − − (1)
where t >0 is the parameter of the rate of transportation fee. The term of x− yi
denotes the distance between the consumer x and Firm i . We apply the quadratic form of (x−yi)2 for signifying the fact that the transportation cost is getting greater
as the distance increases. Hence, the consumer x has to pay t(x−yi)2 for buying a unit of product produced by Firm i .
Firms invest in advertisements to provide consumers information for enhancing consumers’ awareness of their product quality. But part of advertisement information may spill over to the other firm’s product information. That means a certain degree of
4
Informative advertising is an implement for information spread, broadcasting the existence of a product, available locations, major characteristics, quality, etc. (Grossman and Shapiro, 1984; LeBlanc, 1998; Cheng, 2006).
Fig. 2 Hotelling model
0 1 The location of Firm1 The location of Firm 2 1 y 2 y
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advertisement effect will spill over to its competitor’s product quality. Let β be the degree of the spillover effect, 0≤β ≤1. β =0 represents that consumers cannot understand the product information of the firm who does not advertise; whereas, when
1 =
β , consumers’ products quality awareness towards the firm with advertisement and the rival firm without advertisement are the same. In most situations, β often sits between 0 and 1.
The aggregated advertisement effects which consumers receive about Firm i ’s
product is given by E , i
j i
i e e
E = +β (2)
where e and i e denote Firm i and Firm j j s’ advertisement effects.
Advertisement helps consumers to further understand the product quality, reduce the risk of consumption, and increase consumers’ willingness to pay. If consumers have received a unit of advertisement effect, their reservation prices will increase by E . i
The surplus that the consumer decides to buy a unit of product from Firm i after
receiving advertisement information is given by:
2 ) ( i i i i E p t x y CS =γ + − − − (3)
We setup a three-stage game when the benefits of the informative advertisement may spill over to its competitor’s product quality. First, the two firms choose their locations. Then, the two firms decide their expenditures on advertisement. Finally, the two firms engage in price competition (see Fig. 3). We apply the backward induction to solve for the subgame-perfect equilibrium of this game.
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Stage 3: The price subgame
In the price subgame, the two firms engage in price competition. The first step is to derive the demands for the two firms. Assume that there exists a critical consumer locates at s∈
[ ]
0,1. It is indifferent for the critical consumer to purchase the product from Firm 1 at p1 or Firm 2 at p2. Buying a unit product from Firm 1 and Firm 2, the critical consumer’s surplus are denoted as2 1 1 1 1 E p t(s y ) CS =γ + − − − (4) 2 2 2 2 2 E p t(s y ) CS =γ + − − − (5)
Since the critical consumer is indifferent to buy a unit of product from Firm 1 or Firm 2, therefore, Eq. (4) equals Eq. (5).
2 2 2 2 2 1 1 1 p t(s y) E p t(s y ) E − − − = + − − − + γ γ
According to Eq. (2) and the above equality yields s ,
) ( 2 ) )( 1 ( ) ( 2 ) ( 1 2 1 2 1 2 1 2 y y t e e p p y y s − − − − − + + = β (6)
The consumers locate between 0 and s will buy the product from Firm 1 for receiving greater surplus than buy the product from Firm 2. The other consumers
Stage 1
time
The two firms choose locations simultaneously.
Fig. 3 The procedure of the three-stage game
Stage 2 Stage 3
The two firms decide their expenditures on advertisement.
The two firms engage in price competition.
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between s and 1 will buy the product from Firm 2. According to the previous assumption that every consumer purchases one unit of the product, s is the market demands of Firm 1 and (1− is those of Firm 2. s)
The profit functions for Firm 1 and Firm 2 are
2 1 1 1 1 1 2e s p a s p ρ π = − = − (7) 2 2 2 2 2 2 2 ) 1 ( ) 1 ( s a p s e p ρ π = − − = − − (8)
where ρ is the parameter of conveying informative message. If ρ is great, consumers can hardly understand the advertisement information. Then they will have difficulties in realizing the product quality. Therefore, the greater of ρ , the higher the cost of information transmission has to be paid by the firm. In contrast, while ρ is trivial, consumers can acknowledge the advertisement information and will know the product quality easily. The firm’s information transmission cost becomes lower. In this paper, we utilize ρ to switch the effect of transmitting the quality information to advertisement expenditure. Let the advertisement expenditures of the two firms be the quadratic form, 2
2 i
i e
a = ρ , to emphasize that the cost of information transmission increases with the difficulty in conveying message. We neglect the operation costs of both firms in this model without loss of generality. From the first-order-condition of Eqs. (7) and (8), we solve the equilibrium prices as:
)] )( 1 ( ) 2 )( ( [ 3 1 1 2 1 2 1 2 * 1 t y y y y e e p = − + + − −β − (9) )] )( 1 ( ) 4 )( ( [ 3 1 1 2 1 2 1 2 2 t y y y y e e p ∗= − − − + −β − (10)
From the comparative static analysis, the advertisement effects on the equilibrium prices are as follows:
17 0 3 ) 1 ( ≥ − = ∂ ∂ ∗ β i i e p (11) 0 3 ) 1 ( − ≤ − = ∂ ∂ ∗ β i j e p (12)
Eq. (11) reveals that the more advertisement effects consumers received from Firm i ’s product, the higher price of Firm i’s product is. In contrast, Eq. (12) shows
that more advertisement from Firm i will lower Firm j’s price.
Stage 2: The advertisement subgame
In Stage 2, the two firms decide their advertisement expenditures taking their locations as given. Substituting Eqs. (9) and (10) into Eqs. (7) and (8), we obtain:
2 1 1 2 2 1 2 1 2 1 2 1 2 ] ) ( 18 )] )( 1 ( ) 2 )( ( [ e y y t e e y y y y t β ρ π − − − − − + + − = (13) 2 2 1 2 2 1 2 1 2 1 2 2 2 ) ( 18 )] )( 1 ( ) 4 )( ( [ e y y t e e y y y y t β ρ π − − − − + − − − = (14)
Taking first-order-condition of the profit functions, Eqs. (13) and (14), we obtain the response functions of advertisement effect:
2 1 2 2 2 1 1 2 2 1 ) 1 ( ) ( 9 ] ) 1 ( ) 2 )( ( )[ 1 ( ) ( β ρ β β − − − − − + + − − = y y t e y y y y t e e (15) 2 1 2 1 2 1 1 2 1 2 ) 1 ( ) ( 9 ] ) 1 ( ) 4 )( ( )[ 1 ( ) ( β ρ β β − − − − − − − − − = y y t e y y y y t e e (16)
and the equilibrium advertisement effects,
] ) ( 9 ) 1 ( 2 [ 3 ] ) 2 )( ( 3 ) 1 ( 2 )[ 1 ( 1 2 2 2 1 1 2 2 1 ρ β ρ ρ β β y y t y y y y t e − − − + + − − − − = ∗ (17) ] ) ( 9 ) 1 ( 2 [ 3 ] ) 4 )( ( 3 ) 1 ( 2 )[ 1 ( 1 2 2 2 1 1 2 2 2 ρ β ρ ρ β β y y t y y y y t e − − − − − − − − − = ∗ (18)
18
We can check the change of the two firms’ distance will not affect the advertisement effect in Eq. (19).5
0 = ∆ ∂ ∂ ∗ y ei (19)
Then, the equilibrium advertisement expenditures as:
2 1 2 2 2 3 2 1 1 2 2 1 1 ] ) ( 9 ) 1 ( 2 [ 18 ] ) 1 ( 2 ) 1 )( 2 )( ( 3 [ 2 ρ β ρ β ρ β ρ y y t y y y y t e a − − − − − − + + − = = ∗ ∗ (20) 2 1 2 2 2 3 2 1 1 2 2 2 2 ] ) ( 9 ) 1 ( 2 [ 18 ] ) 1 ( 2 ) 1 )( 4 )( ( 3 [ 2 ρ β ρ β ρ β ρ y y t y y y y t e a − − − − − − − − − = = ∗ ∗ (21)
Stage 1: The location game
In the first stage, the two firms choose their locations, y , expecting how these i
decisions will influence their subsequent choices of advertisement expenditures and prices. Substituting Eqs. (17) and (18) into Eqs. (13) and (14), we get the profits:
2 1 2 2 2 2 1 1 2 2 2 1 2 1 ] ) ( 9 ) 1 ( 2 [ 18 ] ) 2 )( ( 3 ) 1 ( 2 ][ ) 1 ( ) ( 9 [ ρ β ρ ρ β β ρ π y y t y y y y t y y t − − − + + − − − − − − = (22) 2 1 2 2 2 2 1 1 2 2 2 1 2 2 ] ) ( 9 ) 1 ( 2 [ 18 ] ) 4 )( ( 3 ) 1 ( 2 ][ ) 1 ( ) ( 9 [ ρ β ρ ρ β β ρ π y y t y y y y t y y t − − − − − − − − − − − = (23)
Taking first-order-condition of the expressions for profit, Eqs. (22) and (23), we obtain the equilibrium locations:
ρ β β ρ β ρ ρ t t t t y 72 ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 9 2 2 2 4 2 1 − − − + − − + = ∗ (24) ρ β β ρ β ρ ρ t t t t y 72 ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 63 2 2 2 4 2 2 − + − + − − − = ∗ (25) 5
In Stage 1, we will prove that 1 + 2 =1
∗ ∗ y y (Eq. (26)). Substitute 1 + 2 =1 ∗ ∗ y
y into Eqs. (17) and (18) we can also calculate the equilibrium advertisement effects as a constant value:
ρ β ρ β ρ ρ β β)[2(1 ) 9 ]/3 [2(1 ) 9 ] (1 )/3 1 ( 2 2 * 2 * 1 =e = − − − t ∆y − − t ∆y = − e , therefore, ∂ei*/∂∆y=0.
19
From Eqs. (24) and (25), we can compute that the critical consumer locates at 1 2. And the sum of y and 1∗ y is 2∗
1 72 72 2 1 + = = ∗ ∗ ρ ρ t t y y (26)
Further, we figure out the equilibrium advertisement expenditures and the equilibrium prices in the followings:
ρ β 18 ) 1 ( − 2 = ∗ i a (27) ρ β β ρ β ρ ρ 36 ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 27 − 2 2− − 2 + − 4 + − 2 = ∗ t t t pi (28)
From Eq. (26), we can see that the two firms cover the whole market. And substitute Eqs. (26), (27), and (28) into Eq. (6), we can derive s=1 2 and then conclude that the two firms locate symmetrically on the two halves of [0,1] respectively. From Eqs. (24) and (25), the distance between the two firms, ∆ , is y
ρ β β ρ β ρ ρ t t t t y y y 36 ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 27 2 2 2 4 2 1 2 − + − + − − − = − = ∆ ∗ ∗ (29)
Consider Eq. (29), if β =1 (i.e., the advertisement spillover effect is perfect), we have ∆y=0. That means the two firms will choose the same location exactly at 1 2. We then obtain Proposition 1.
Proposition 1. When the degree of advertisement spillover effect approaches to one, the two firms will choose the same location at 1/2.
We then check whether the change of the rate of transportation fee and the advertisement spillover effect will influence the distance of the two firms.
20 0 ) 1 ( 4 ) 1 ( 324 729 18 ] ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 81 [ ) 1 ( 4 2 2 2 2 2 4 2 2 2 2 ≤ − + − − − − − + − − + − − = ∂ ∆ ∂ β ρ β ρ ρ β β ρ β ρ ρ β t t t t t t t y (30) 0 ) 1 ( 4 ) 1 ( 324 729 9 ] ) 1 ( 2 ) 1 ( 4 ) 1 ( 324 729 81 )[ 1 ( 4 2 2 2 2 4 2 2 2 ≤ − + − − − − − + − − + − − = ∂ ∆ ∂ β ρ β ρ ρ β β ρ β ρ ρ β β t t t t t t y (31)
From Eqs. (30) and (31), we can see that the rate of transportation fee and advertisement spillover effect will negatively affect the two firms’ location distance. Eq. (30) indicates that as the rate of transportation fee decreases, consumers bear less transportation costs. They might compare the prices between the two firms. Once the price margin exceeds the transportation cost, consumers will purchase the product from the firm where they can receive greater surplus. Hence, the firms will locate at the places dispersed from the midpoint where the critical consumer locates. In contrast, when the rate of transportation fee increases, consumers have to pay more transportation cost. The transportation cost might exceed the price margin if they want to search and buy the product from the firm where they can receive greater surplus. In this circumstance, the firms will cluster for enhancing the competitiveness.
Nelson (1970) show if consumers are attracted by the advertisement for a search good, they will not only search for the firm’s product information, but also explore other firms’ informative message even if the other firms do not invest in advertisement activities. Consequently, consumers desiring these kinds of products will compare the firms’ product quality. The expenses on transporting are significant for consumers. It will tempt the firms into clustering. On the other hand, consumers who have received the advertisement for an experience good would never know what the quality is until they consume and use it. The distance between two firms is not important for consumers.
In this paper, we consider the search goods have identical size, quality and characteristics. When the firms sell search goods and advertise their products,
21
consumers accept the advertisement information readily. Moreover, consumers can understand the product quality easily and then purchase the product from the firms they prefer. On the contrary, no matter which firms advertise experience goods, consumers would hardly understand the product information. Hence, we believe that the search goods information can be transmitted to consumers easier than the experience goods information. While receiving one firm’s search goods advertisement, consumers can partially know the other firm’s product quality; acquiring one firm’s experience goods advertisement, consumers can less comprehend the rival firm’s quality information. That is to say, the spillover effect on search goods is greater than that of experience goods. From Eq. (31), we can figure that when the spillover effect is great, the firms would compete in nearby area and form a commercial district to attract consumers, like clothing stores; when the spillover effect is trivial, the firms would disperse, like amusement parks.
In order to explore the above results further, we simulate the relation among the rate of the transportation fee, the spillover effect, and the two firms’ distance in Fig. 4 for ρ =5. The horizontal axis denotes the rate of transportation fee and the vertical axis is the distance between the two firms. The set of contours represent different spillover effect. In Fig. 4, let ρ =5. It symbolizes that the quality information may be transmitted with difficulty when the firm provides informative advertisement. After receiving the advertisement information, consumers can barely understand the product quality. From Fig. 4, the result shows that when the degree of spillover effect is constant, the higher the rate of transportation fee, the closer the firms locate; when the rate of transportation fee is fixed, the greater the degree of spillover effect, the closer the firms locate. Fig. 4 also reveals that the rate of transportation fee and the spillover effect will accelerate the closeness of the two firms.
22
From the above discussions, we can conclude the results as Proposition 2.
Proposition 2. On the case of the transportation cost is paid by consumers, the following variable(s) will positively impact the two firms’ clustering considerations when we consider (1) the rate of transportation fee alone (β is fixed), (2) the advertisement spillover effect alone ( t is fixed), and (3) the rate of transportation fee and the advertisement spillover effect simultaneously.
The comparative static analysis of the advertisement spillover effect on the equilibrium advertisement expenditure is:
0 9 ) 1 ( − ≤ − = ∂ ∂ ∗ ρ β βi a (32)
The rate of transportation fee is not included in the equilibrium advertisement expenditures, Eq. (27). But from Eq. (32), we find that the advertisement spillover effect and the advertisement expenditure are negatively related. When the firms advertise their product information and the degree of advertisement spillover effect is
0 = β 2 . 0 = β 4 . 0 = β 6 . 0 = β 8 . 0 = β y ∆ t
Fig. 4 The distance between the two firms (ρ =5)
23
great, consumers can not only receive and realize the firm’s product quality but also know the rival firm’s quality information. Hence, the firms are reluctant to expend on advertisement under the condition that some benefits of each firm’s advertisement will spill over to its competitor. On the contrary, when one firm promotes its products quality and the degree of advertisement spillover effect is trivial, consumers only know the firm’s advertisement information. They can barely receive the other firm’s product information. In this circumstance, the firms are more willing to expend on advertisement for raising consumers’ awareness towards the product. Hence, we summarize the statement above in Proposition 3.
Proposition 3. The equilibrium advertisement expenditure is independent of the rate of transportation fee. But the advertisement spillover effect will negatively influence the advertisement expenditures.
3.3 Distribution cost is paid by firm
In the previous case, consumers have to purchase the products at the firms’ places after receiving informative advertisement. Consumers pay both the product price and the transportation cost. In this section, we discuss the condition from the perspectives of the firms and modify our model into a different scenario. Consider the industries like furniture or pizza, consumers order the products and ask for the delivery service after receiving advertisement information. The firms have to deliver the products to consumers’ locations and cover the distribution costs. The other assumptions of this case are identical with those of the previous case. The two firms locate in a line segment of unit distance,
[ ]
0,1 . Consumers are uniformly distributed along the segment of unit distance. Each consumer is characterized by the location xˆ in the segment. Every consumer purchases one unit of the product.24
Assume that there is a headquarter who delegates two firms (subsidiaries) to operate in the market. Though most of the advertisement of the two firms is made by the headquarter directly, the two firms still utilize other ways to advertise their product quality.
The lowest price a firm expects to obtain from the consumer is called desired value, v . If Firm i does not provide advertisement information but distributes the product to the consumer’s location, a consumer xˆ purchases one unit of the product from Firm i , Firm i ’s surplus is given by:
2 ) ˆ ˆ ( ˆi i i p d x y PS = −ν − − (33)
where d >0 is the parameter of the rate of distribution fee. The distance between Firm i and consumer is xˆ− . The quadratic form of distance, yˆi 2
) ˆ ˆ
(x−yi , shows that the distribution costs become greater while the distance increases. Hence, Firm i has to spend d(xˆ−yˆi)2 when delivering one unit of the product.
When the two firms compete with each other, they provide consumers informative advertisement for promoting their product quality. The aggregated advertisement effects received by consumers about Firm i’s product quality is given by Eˆi
j i
i e e
Eˆ = ˆ +βˆˆ (34)
After advertising the product quality, the firms expect to obtain more revenues. The firm’s desired value will increase by Eˆi. When the consumer xˆ purchases from
Firm i , the surplus of Firm i is
2 ) ˆ ˆ ( ) ˆ ( ˆi i i i p E d x y PS = − ν + − − (35)
25
We setup a three-stage game to discuss the advertisement spillover effect on firms’ location choices. In the first stage, the two firms choose their locations. In the second stage, the two firms decide their advertisement expenditures. In the third stage, the two firms engage in price competition. We adopt backward induction to solve the subgame-perfect equilibrium. The procedure of this case is the same as Fig. 3.
Stage 3: The price subgame
In stage 3, the two firms engage in price competition. Suppose that there is a critical consumer locates at k∈[0,1]. No matter who sell and deliver the product to the critical consumer, the two firms receive the identical surplus. As Firm i delivers
its product to the critical consumer, the surplus of Firm i is given as:
2 ) ˆ ( ) ˆ ( ˆi i i i p E d k y PS = − ν + − − (36) Therefore, we have 2 2 2 2 2 1 1 1 ( ˆ ) ( ˆ ) ˆ ( ˆ ) ( ˆ ) ˆ E d k y p E d k y p − ν + − − = − ν + − − (37)
From Eq. (37), we can derive k
) ˆ ˆ ( 2 ) ˆ ˆ ( ) ˆ ˆ )( ˆ 1 ( 2 ) ˆ ˆ ( 1 2 1 2 1 2 1 2 y y d p p e e y y k − − − − − + + = β (38)
Delivering the product to consumer who locates between 0 and k , Firm 1 can receive greater surplus than Firm 2; delivering the product to the consumer between
k and 1, Firm 2 can receive greater surplus than Firm 1. Therefore, Firm 1 dominates
in the segment of
[ ]
0,k and Firm 2 dominates in the segment of[ ]
k,1 . As the assumption of every consumer purchases one unit of the product, the market demand of Firm 1 is k and that of Firm 2 is (1−k).26
The profit functions of Firm 1 and Firm 2 are then given by6
2 1 1 1 1 1 ˆ 2 ˆ ˆ ˆ ˆ ˆ pk a pk ρe π = − = − (39) 2 2 2 2 2 2 ˆ 2 ˆ ) 1 ( ˆ ˆ ) 1 ( ˆ ˆ p k a p k ρe π = − − = − − (40)
where ρˆ represents the parameter of conveying informative message. If ρˆ is great, there are difficulties in conveying product information. Therefore, the cost that the firm spends on promoting the product quality gets higher. If ρˆ is trivial, the informative advertisement is easier to transmit. The cost that the firm spends on transmitting the product quality becomes lower. We consider the cost spent on advertising the product quality is the advertisement expenditure, aˆ . The quadratic i
form, ˆ2 2 ˆ i e ρ
, is used to illustrate that the advertisement cost increases with the difficulty in conveying informative message. Without loss of generality, the operation costs are omitted in this model.
From the first-order-condition of Eqs. (39) and (40), we solve the equilibrium prices as: )] ˆ ˆ )( ˆ 1 ( ) ˆ ˆ 2 )( ˆ ˆ ( [ 3 1 ˆ1 d y1 y2 y2 y1 e2 e1 p∗ = − + + − −β − (41) )] ˆ ˆ )( ˆ 1 ( ) ˆ ˆ 4 )( ˆ ˆ ( [ 3 1 ˆ2 d y1 y2 y2 y1 e2 e1 p ∗= − − − + −β − (42)
We then check whether the advertisement effects will influence the equilibrium prices.
6
In Eq. (38), Firm i’s average distribution distance per unit product isk 2. And we will prove that k is a constant of 12 later in p.29. The distribution cost is also a constant of ( 2)2 16
d k
d = . Because the constant distribution cost will not affect the response function of Firm i’s profit function, the distribution costs are omitted for simplifying the following calculations.
27 0 3 ) ˆ 1 ( ˆ ˆ ≥ − = ∂ ∂ ∗ β i i e p (43) 0 3 ) ˆ 1 ( ˆ ˆ ≤ − − = ∂ ∂ ∗ β i j e p (44)
Eq. (43) reveals that the more advertisement effects consumers received from Firm i ’s product, the higher price of Firm i’s product is. In contrast, Eq. (44) shows
that more advertisement from Firm i will lower Firm j’s price.
Stage 2: The advertisement subgame
In Stage 2, the two firms decide their advertisement expenditures respectively supposing locations as given. Substituting the equilibrium prices, Eqs. (41) and (42) into Eqs. (39) and (40), we obtain
2 1 2 1 2 1 2 1 2 2 1 1 ˆ 2 ˆ ] ) ˆ ˆ ( 18 )] ˆ ˆ )( ˆ 1 ( ) ˆ ˆ 2 )( ˆ ˆ ( [ ˆ e y y d e e y y y y d β ρ π − − − − − + + − = (45) 2 2 2 1 2 1 2 1 2 2 1 2 ˆ 2 ˆ ) ˆ ˆ ( 18 )] ˆ ˆ )( ˆ 1 ( ) ˆ ˆ 4 )( ˆ ˆ ( [ ˆ e y y d e e y y y y d β ρ π − − − − + − − − = (46)
From the first-order-condition of Eqs. (45) and (46), we get the response functions of advertisement effect: 2 2 1 2 2 1 1 2 2 1 ) ˆ 1 ( ˆ ) ˆ ˆ ( 9 ] ˆ ) ˆ 1 ( ) ˆ ˆ 2 )( ˆ ˆ ( )[ ˆ 1 ( ) ˆ ( ˆ β ρ β β − − − − − + + − − = y y d e y y y y d e e (47) 2 2 1 1 2 1 2 1 1 2 ) ˆ 1 ( ˆ ) ˆ ˆ ( 9 ] ˆ ) ˆ 1 ( ) ˆ ˆ 4 )( ˆ ˆ ( )[ ˆ 1 ( ) ˆ ( ˆ β ρ β β − − − − − − − − − = y y d e y y y y d e e (48)
28 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 3 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 2 )( ˆ ˆ ( 3 )[ ˆ 1 ( ˆ 2 2 1 2 2 1 2 1 1 β ρ ρ β ρ β − − − − − + + − − = ∗ y y d y y y y d e (49) ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 3 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 4 )( ˆ ˆ ( 3 )[ ˆ 1 ( ˆ 2 2 1 2 2 1 2 1 2 β ρ ρ β ρ β − − − − − − − − − = ∗ y y d y y y y d e (50)
From the comparative static analysis, we find that the two firms’ distance will not influence the advertisement effects.
0 ˆ ˆ = ∆ ∂ ∂ ∗ y ei (51)
Then, solve the equilibrium advertisement expenditures as:
2 2 2 1 2 2 2 1 2 1 2 2 1 1 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 18 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 2 )( ˆ ˆ ( 3 [ ) ˆ 1 ( ˆ 2 ˆ ˆ β ρ ρ β ρ β ρ − − − − − + + − − = = ∗ ∗ y y d y y y y d e a (52) 2 2 2 1 2 2 2 1 1 2 2 2 2 2 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 18 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 4 )( ˆ ˆ ( 3 [ ) ˆ 1 ( ˆ 2 ˆ ˆ β ρ ρ β ρ β ρ − − − − − − − − − = = ∗ ∗ y y d y y y y d e a (53)
Stage 1: The location game
The two firms choose their locations, yˆ in Stage 1. Substituting Eqs. (49) and i
(50) into Eqs. (45) and (46), we get the profits:
2 2 2 1 2 2 2 1 2 1 2 2 1 1 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 18 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 2 )( ˆ ˆ ( 3 ][ ) ˆ 1 ( ˆ ) ˆ ˆ ( 9 [ ˆ β ρ ρ β ρ β ρ π − − − − − + + − − − − = y y d y y y y d y y d (54) 2 2 2 1 2 2 2 1 2 1 2 2 1 2 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ ( 9 [ ˆ 18 ] ) ˆ 1 ( 2 ˆ ) ˆ ˆ 4 )( ˆ ˆ ( 3 ][ ) ˆ 1 ( ˆ ) ˆ ˆ ( 9 [ ˆ β ρ ρ β ρ β ρ π − − − − − − − − − − − = y y d y y y y d y y d (55)
Taking first-order-condition of Eqs. (54) and (55), we solve the equilibrium locations:
29 ρ β β ρ β ρ ρ ˆ 72 ) ˆ 1 ( 2 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 9 ˆ 2 4 2 2 2 1 d d d d y∗ = + + − + − + − (56) ρ β β ρ β ρ ρ ˆ 72 ) ˆ 1 ( 2 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 63 ˆ 2 4 2 2 2 2 d d d d y ∗ = − + − + − − − (57)
From Eqs. (56) and (57), we derive the equations below.
1 ˆ 72 ˆ 72 ˆ ˆ1∗+ 2∗ = = ρ ρ d d y y (58)
Applying the equilibrium locations, the equilibrium advertisement expenditures and the equilibrium prices are as follows:
ρ β ˆ 18 ) ˆ 1 ( ˆ 2 − = ∗ i a (59) ρ ρ β β ρ β ρ ˆ 36 ˆ 27 ) ˆ 1 ( 2 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 2 4 2 2 2 d d d pi∗ = + − + − + − − (60)
Eq. (58) shows the sum of ˆy and 1∗ ∗ 2
ˆy equals to one, we can check that the two firms cover the whole market. Moreover, the firms have symmetric advertisement expenditures and product prices. Substitute Eqs. (58), (59) and (60) into Eq. (38), we can know that the second term of Eq. (38) equals to zero. Hence, the critical consumer
kˆ is the person who locates at 1/2. That means, each firm owns a half of the market demand and the two firms sit symmetrically on the two halves of [0,1]. Let
∗ ∗−
=
∆yˆ yˆ2 yˆ1 , we get the distance between Firm 1 and Firm 2 as:
ρ ρ β β ρ β ρ ˆ 36 ˆ 27 ) ˆ 1 ( 2 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ ˆ ˆ 2 4 2 2 2 1 2 d d d d y y y= − = + − + − + − − ∆ ∗ ∗ (61)
From Eq. (61), we further find that the two firms will choose the same location at
2
30
necessary to delegate two subsidiaries or two exclusive agents to operate in the district. This finding is described as proposition 4.
Proposition 4. When the degree of advertisement spillover effect approaches to one, the headquarter will delegate just one firm.
From the comparative static analysis, the effect of the rate of distribution fee and the advertisement spillover effect on the distance of the two firms are as follows:
0 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 18 ] ) ˆ 1 ( 2 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 81 [ ) ˆ 1 ( ˆ 4 2 2 2 2 2 4 2 2 2 2 ≤ − + − + − + − + − + + − − = ∂ ∆ ∂ β ρ β ρ ρ β β ρ β ρ ρ β d d d d d d d y (62) 0 ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ˆ 9 ] ) ˆ 1 ( 4 ˆ ) ˆ 1 ( 324 ˆ 729 ) ˆ 1 ( 2 ˆ 81 )[ ˆ 1 ( ˆ ˆ 4 2 2 2 4 2 2 2 2 ≤ − + − + − + − + + − + − − = ∂ ∆ ∂ β ρ β ρ ρ β ρ β ρ β ρ β β d d d d d d y (63)
Eq. (62) shows that the higher the rate of distribution fee, the closer the firms will locate and vice versa. That means as the rate of distribution fee increase, the two firms will more cluster for eliminating the cost difference and increasing their surplus. In contrast, the two firms will locate apart from each other while the rate of distribution fee decreases because the distribution cost is trivial. Eq. (63) reveals that the two firms will choose their locations approximately while the degree of advertisement spillover effect increases. Additionally, from Eq. (63) we can know that the degree of advertisement spillover effect will negatively impact the two firms’ distance results in the two firms getting more cluster. In the real world, we take the exclusive agent or geographic division management for example. The headquarter delegate the two firms to operate within a responsibility district by choosing their locations and advertisement expenditures. If the advertisement effect perfectly spill over to each other’s product quality, the two firms will choose the same location. The headquarter should create only one agent or subsidiary instead of two. Naturally, this result is
31
concluded in the situation that the distribution cost is the only consideration. The other factors such as delivery time and service quality are beyond our discussion.
The results are summarized in Proposition 5.
Proposition 5. In the case of distribution cost is paid by firms, the following variable(s) will positively impact the two firms’ clustering considerations respectively when we consider (1) the rate of distribution fee alone (β is fixed), (2) the advertisement spillover effect alone ( d is fixed), and (3) the rate of distribution fee and the advertisement spillover effect simultaneously.
From the comparative static analysis, the spillover effect on the equilibrium advertisement expenditure is given:
0 ˆ 9 ) ˆ 1 ( ˆ ˆ ≤ − − = ∂ ∂ ρ β β i a (64)
We observe Eq. (59), the advertisement expenditure is not the function of the rate of distribution fee. But in Eq. (64), the advertisement spillover effect will negatively impact the advertisement expenditure. The firm exerting advertisement expects to increase consumers’ awareness of its own product quality and then attracts consumers to purchase its product. If the degree of spillover effect is great, consumers can understand the rival’s product quality, thereby, the firm is hesitating to spend on advertisement in advance. On the other hand, when the degree of advertisement spillover effect is trivial, consumers can hardly understand the rival firm’s product quality. Hence, the firm is willing to spend on advertising its product quality for raising consumers’ awareness. The conclusion of the advertisement spillover effect on advertisement expenditure is shown in Proposition 6.
32
Proposition 6. The rate of distribution fee does not impact the firm’s advertisement expenditure. The advertisement spillover effect will negatively influence the firm’s advertisement expenditure.
3.4 Conclusion
In our model, we discuss the advertisement spillover effect on firms’ location choices from the perspectives of consumers and firms individually. In the first case, we consider consumers’ surplus while consumers need to spend the transportation costs for purchasing the product after receiving the informative advertisement. In the second case, we consider firms’ surplus while the firms have to expend distribution costs delivering the products to consumers’ places after consumers receive the advertisement and order the products.
We finds that no matter the transportation cost is paid by consumer or the distribution cost is paid by firm, the results of both cases show that while the firms compete with each other, each firm owns a half of market demand. And the two firms will locate symmetrically on the two halves of the line segment of unit distance. Finally, the advertisement spillover effect will positively influence the clustering decisions of the two firms.
33
4. Concluding remarks
This paper has shown that the advertisement spillover effect may impact the distance between the two firms. At first, we signify the importance of advertisement information in affecting consumers’ awareness. Extending the advertisement effect to firms running similar businesses has generated other advertisement effect: the advertisement spillover effect. It represents consumers receive one firm’s informative advertisement will realize the other firms’ product quality simultaneously. That is, the advertisement provided by one firm may encourage consumers to purchase similar products from its rivals.
We develop a three-stage game model with informative advertisement and spillover effect based on Hotelling model. Then, we discuss the advertisement spillover effect on firms’ location choices in two ways: (1) The transportation costs are incurred by consumers. After receiving informative message, consumers’ awareness of the product quality will increase. Consumers will purchase the products at firms’ locations and choose to buy from the firm where they can receive greater surplus. (2) The distribution costs are paid by the firms. After consumers receive the advertisement information, they order the products from the firms and ask for deliver service. The firms have to spend the distribution cost delivering the products to consumers’ locations. The firms only deliver the products to consumers’ locations where they can receive greater surplus.
We find that no matter who pay the transportation/distribution costs, both of the results are identical. The two firms’ distance increases while the rate of transportation/distribution fee decreases. The advertisement spillover effect and the distance between the two firms are negatively related. This implies that the firms are
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willing to cluster for the spillover effect is getting greater. Though the two cases we discuss in this paper obtain the same conclusion. But, the conclusion can be used in different applications in location choice. For example, in the case of consumers pay the transportation cost, higher spillover effect forces the firms to cluster. Yet, in the case of firms pay the distribution cost, higher spillover effect will reduce the number of firms. Extremely, if the advertisement with perfect spillover effect, the headquarter will cancel the system of dual exclusive agents or subsidiaries into one.
Nelson (1970, 1974) made a distinction between qualities of goods: search goods and experience goods. He showed that advertisement for search goods provides consumers with specification of the product qualities and characteristics. Consequently, consumers desire the advertisement search goods will compare the firms’ product quality and purchase from the firms who they prefer. The firms will tend to minimize the transportation distance for consumers. In contrast, advertisement for experience goods notice consumers the existence of the product. Consumers do not know the product quality until they experience it. The transportation costs are not important comparatively. Nelson further concluded that stores sell search goods cluster more than stores sell experience goods. In this paper, we consider that search goods are the products with greater advertisement spillover effect since the products with more clear specifications will be easier to be understood through informative advertisement; whereas, experience goods are the product with trivial advertisement spillover effect because consumers can hardly know one firm’s product information from the other firm’s advertisement. Hence, our finding of advertisement spillover effect will enhance the firms to cluster is complementary to Nelson’s conclusion and provides a new support from the perspective of spillover effect.
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