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A VIEW INTO NON-PRICE

PERSUASIVE ADVERTISEMENT

Abstract

This paper looks at a vertically differentiated Bertrand competition where a firm has the possibility to use marketing to increase the perceived quality a consumer has. In order to analyze the role marketing can play in a quality competition environment a market is considered where two firms are active, one competing through marketing and price management, the second firm through quality and price management. The paper shows the importance of understanding consumer preferences and the consumers’ perceptiveness to marketing before being able to conclude whether marketing can be an effective tool in the competition. Thorough understanding of these variables leads to the result that marketing can be of significant use to fend off the competition.

Bachelor Econometrie Universiteit van Amsterdam

Tomasz Makarewicz Wibrand de Reij

10166610 Bachelor scriptie

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Contents

1. Introduction ... 2 2. The model ... 4 2.1 Consumer side ... 4 2.2 Producer side ... 4 2.3 The market ... 5 3. The game ... 6 3.1 Indifference equilibria ... 6

3.1.1 Firm 1 controls the market ... 6

3.1.2 Firm 2 controls the market ... 7

3.2 Best response... 8

4. Role of consumer preference ...10

4.1 Effect on profit in indifference equilibria ...10

4.2 Effect on best response ...12

5. Conclusion ...14

Declaration of self made work:

Hierbij verklaar ik, Wibrand de Reij, dat ik deze scriptie zelf geschreven heb en dat ik de volledige verantwoordelijkheid op me neem voor de inhoud ervan.

Ik bevestig dat de tekst en het werk dat in deze scriptie gepresenteerd wordt origineel is en dat ik geen gebruik heb gemaakt van andere bronnen dan die welke in de tekst en in de referenties worden genoemd.

De Faculteit Economie en Bedrijskunde is alleen verantwoordelijk voor de begeleiding tot het inleveren van de scriptie, niet voor de inhoud.

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1. Introduction

As the research conducted by Petruzzellis (2010) has shown, marketing goes hand in hand with technological development in the smartphone market. According to the research, marketing is one of the variables to motivate a consumer to choose a certain phone over another. Nowadays the cell phone market is dominated by several big cell phone producers, each one of them engaging in advertisement to a certain level. Firms trying to enter the cell phone market stand before several difficulties in positioning their product due to, for instance the size, budget and brand loyalty of the players that are already in place. Vidale and Wolfe (1957) have also shown that besides product quality, advertisement plays a major role in general product demand. As a firm on the cell phone market, where marketing has an influence on product demand (Petruzzellis, 2010), it is important to understand how persuasive the marketing can be for a consumer, in order to determine the effectiveness of marketing.

A common way to gain ground in an advertising-intensive market is through business stealing, which is not attracting new consumers but merely trying to make consumers switch firms to the competing firm. To do so one player can set up an advertisement campaign in order to convince consumers of their superiority in product quality. An example of this effect is shown in Nichols’ (1951) famous study on the cigarette industry. Cigarette manufactures, from the 1920’s on, competed through advertising rather than price cuts or quality

improvements. This is known as the adverse view of advertising, which supports the idea that advertisements create unreal differentiation. The article Advertising Age (2004), shows that in many of the advertising-intensive markets the products are nearly homogeneous.

Chioveanu (2008) created a model which shows that in these near homogeneous and advertising-intensive markets advertising could be used as a means to redistribute buyers and increase product demand. This turns advertisement into a persuasive tool meant to create subjective product differentiation rather than an informative tool (informative advertisements are meant to increase industry demand whilst persuasive advertisements are used to affect brand demand). The past decade a great amount of literature is spend on the economic

analysis of informative advertising (Bagwell, 2007), but the models for persuasive advertising have received less attention. The model created by Chioveanu (2008) concerns near

homogeneous markets where competition and buyer distribution is explained by persuasive advertising and brand loyalty. The cell phone market is one of the advertisement-intensive markets where advertisements are still used to create subjective product differentiation, but with product differentiation.

This paper models a vertically differentiated product market such as the cell phone market where advertisement has a persuasive role and creates subjective product differentiation in such a way that it can be used to increase demand. In depth the paper studies the strategic effect of non-price advertisement on consumers’ choice in a duopoly simultaneous

advertisement game, in a differentiated product market.

One of the first models for sales response to advertising has been set up by Vidale and Wolfe (1957). Their model is a simple one, due to the simplicity and its possibility to capture the link between advertising and product sales in an intuitively satisfying manner the model always had a wide appeal. Their model states that sales of a product are influenced by two effects: a response to the advertising which acts on the unsold portion of the market (part of

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the market which not yet owns the product created by the market), and loss of the sold portion of the market caused by factors such as rival advertisement. The Vidale and Wolfe model however lacks the competitive element of a real market. Since the introduction of the Vidale and Wolfe model there have been many derivations to include other elements, Deal (1979) for example, has extended the model into a duopoly to include the competitive element. The Lanchester model has also been claimed to be an extension (Little, 1979). The model created by Wang and Wu (1999) further extends the Deal model and the Lanchester model to make it more appropriate for an actual market where the share of two competitors is usually not stable.

Instead of focusing on the common informative side of advertisement like Grossman and Shapiro (1984) and Wang and Wu (1999), this paper takes on a different aspect of product advertisement, looking at the persuasive aspect of advertisement. In the field of homogeneous product markets, there has been significant empirical work on the question of whether

advertisements are informative of persuasive. Results of the research has been contradictory and dependent of the industry the research has been conducted. Nichols’ study into the cigarette industry (1951), Baltagi and Levins’ study into the cigarette industry (1986) and Kelton and Keltons’ research into the brewery industry (1982) support the persuasive view of advertising. The elaborate study of Bagwell (2007) provides a lot of empirical as well as theoretical insight in advertisement up to 2007.

The model created by Chioveanu (2008) on advertisement, brand loyalty and pricing is closely linked to the model in this paper. Chioveanu (2008) considers homogeneous product markets with advertisement-intense features, whereas this paper considers a heterogeneous market where the consumer can choose based on a vertically differentiated market. Her model mainly focusses on the homogeneous product markets where persuasive advertising creates subjective product differentiation (which can lead to different interpretations of quality) and changes the nature of subsequent price competition. In her model firms compete first through non-price advertising and then price competition, in a two-stage oligopoly game. The firms simultaneously choose the advertisement level in the first stage, during the second stage the price competition occurs. Opposed to Baye and Morgan (2004) who use a model where cross effects between price and brand advertising are included, Chioveanu (2008) leaves these links aside. Her model predicts asymmetric advertising outlines even after the initial symmetry of the firms. It shows links between persuasive advertising and a consumers’ product choice.

What is not incorporated in the model by Chioveanu (2008) is the possibility of differentiated products in an advertisement-intensive market. She only assumes the homogeneous products markets where advertisements create subjective product

differentiation. This paper focusses a market with vertical product differentiation, this makes the model more generalizable. It can be applied in several worldwide markets which possess the characteristics described, for instance in the cell phone market, which is defined by vertical differentiation, and it is therefore interesting to model the effect of the persuasive advertisements on the perception consumers have of the products. Let us look at the public image of an Iphone, as being of a high quality in the western part of the world, versus a phone made by Huawei, which is not known to be of a high quality. The hypothesis now is that the right amount of persuasive advertisement the Iphone user will switch to a Huawei phone. This paper uses the model of Chioveanu, but reduces it to the first stage of advertisement to the point where an existing producer can choose its products’ quality level. A second producer in

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the market produces the same product but of a lesser quality (adding the dimension of vertical differentiation to the model) and chooses the amount of persuasive advertisement needed to control the market. This will be modelled in simultaneous duopoly game. Eventually this paper seeks the equilibrium between relative product quality and the level of marketing that creates a balance for the consumers’ choice of supplier. In addition this paper will show the importance of understanding consumer preference to give an exact meaning to what extend marketing can be a useful tool to increase perceived quality for the consumer.

The second section of the paper explains the research method more extensively and discusses the assumptions of the model. The third section derives the equilibrium that

emerges after in the simultaneous game and discusses what a firm without a market share can do to change its situation. The fifth section provides more insight in the setting and the understanding of the market and the sixth section presents some concluding remarks on the findings.

2. The model

This paper looks at vertically differentiated products in a market where advertisement can play a significant role in product choice. In this model a durable product for daily use is assumed, thus creating a full market, where all consumers make use of the product. It is based on the idea of Chioveanu (2008) that firms are able to compete through quality, price and advertisements.

2.1 Consumer side

For the purpose of this paper, consumers are assumed to be homogeneous, this means that every consumer wishes to maximize its utility in the same way and that the consumers

appreciate quality in the same way, so if one consumer chooses one firm, so will all the others. Because of the homogeneity of the consumers it is possible to assume the entire group of consumers as only one consumer. The utility of the consumer is represented like this:

𝑈(𝑞𝑝) = 𝛽 ∗ (𝑞𝑝

𝑖) − 𝑝𝑖

Here 𝛽 is a measure of taste for the consumers, 𝑞𝑝

𝑖 represents the quality perceived by the

consumer if it chooses firm 𝑖 and 𝑝𝑖 denotes the price of the product produced by firm 𝑖. In

the market it is assumed that the consumer wishes to pay the price 𝑝𝑖 up to a maximum price denoted by 𝑝−.

2.2 Producer side

Opposed to Chioveanu (2008), who focusses on a market of n firms, this paper focuses on a market where there are only two firms active. The firms produce the same product at

different levels of quality, this means that there is a level of vertical differentiation between the firms. For simplification purposes the two firms are defined as firm 1 and firm 2 from now on. Firm 1 creates a product at a certain price, 𝑝1, and quality level, say 𝑞1. The firm is able to change its level of quality and its price to compete with the other firm. Firm 2 creates a

product at price 𝑝2 and fixed quality level 𝑞2, instead of alternating the quality level it uses a certain amount of marketing 𝑚 to increase the perceived quality by the consumer. For purposes of researching the effect of marketing I assume that 𝑞1 ∈ [𝑞2, 𝑞−]. This means that quality of firm 1 should always be at least as high as the quality of firm 2, since if the quality

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of firm 1 already is lower than the quality of firm 2 there would be no incentive for the usage of marketing.

The cost for production of a product at quality level 𝑞𝑖 is given by 𝛾1𝑞𝑖2, where 𝛾1> 0. I assume that for both firms the production of the variable quality has the same cost. This assumption is made to be able to evaluate the effect of marketing better. The cost of using marketing 𝑚 is equal to 𝛾2𝑚2 with 𝛾2 > 0. It is important to note that the assumption is not made that the cost of marketing is greater than the cost of producing actual quality, this strongly depends on the industry that is looked at. The defined variables and a demand function 𝐷𝑖 lead to the following profit functions:

𝜋1(𝑝1, 𝐷1, 𝛾1, 𝑞1) = 𝑝1∗ 𝐷1− 𝛾1∗ 𝑞12 (1)

𝜋2(𝑝2, 𝐷2,𝛾1, 𝛾2, 𝑞2, 𝑚) = 𝑝2∗ 𝐷2− 𝛾1∗ 𝑞22− 𝛾

2 ∗ 𝑚2 (2)

2.3 The market

The quality and marketing levels found in the previous section translate to the perceived quality for the consumer in the following way, for firm 1 and for firm 2:

𝑞𝑝 1 = 𝑞1

𝑞𝑝

2 = 𝑞2+ 𝛼 ∗ 𝑚

For firm 1 the only perceived quality it can offer is the actual quality of their product. For firm 2 however the perceived quality has a different form due to the marketing. Here 𝛼 > 0 represents a transformation to show the effectiveness of 𝑚. The perceived quality equations are used to find the utility functions per firm for the consumer:

𝑈(𝑝1, 𝑞1) = 𝛽 ∗ 𝑞1− 𝑝1 𝑈(𝑝2, 𝑞2, 𝑚) = 𝛽 ∗ (𝑞2+ 𝛼𝑚) − 𝑝2

Because of the homogeneity of the consumers the demand for the firms is determined by the consumers’ utility. Consumers are expected to always go for the highest utility they can get as long as the price does not exceed a maximum price given by 𝑝−. This leads to the following demand functions:

𝐷1= 𝐼[𝑈(𝑝1,𝑞1)>𝑈(𝑝2,𝑞2,𝑚)] 𝐷2= 𝐼[𝑈(𝑝2,𝑞2,𝑚)>𝑈(𝑝1,𝑞1)]

In the special case that the consumer is indifferent, this paper assumes that the firm that initially controlled the market stays in control. An indifferent consumer means that the

consumer does not have a preference for either one of the firms anymore, the consumer would receive the same utility from both firms.

Both the firms are aware of the utility the consumer can receive when it chooses the competition. They play a non-cooperative simultaneous game where firm 1 tries to optimize its profit over quality to maintain control of the market and firm 2 uses the variable marketing to achieve the same goal. The next section first describes for both firms how they want to

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optimize their profit for an indifferent consumer and later it discusses what a firm can do to ensure complete control over the market.

3. The game

The game has two general equilibria. For the first equilibrium firm 1 controls the market and wishes to optimize its profit given the price, quality and marketing of firm 2, and for the second equilibrium for firm 2 it is vice versa. For both firms a best response can then be found to react when the competition is in control of the market. The last part of this sections tries to find the best response and analyze if it is a plausible option for the firm trying to make the move.

3.1 Indifference equilibria

The game is split in two scenarios, for the first scenario, firm 1 starts of in control of the market. In this situation price, quality and marketing of firm 2 are given and firm 1 wishes to maintain control but also optimize its profit, so by price and quality management the point is reached where the consumer is indifferent according to the following equation:

𝑈(𝑝1, 𝑞1) = 𝑈(𝑝2, 𝑞2, 𝑚)

Firm 1 first sets its price according to the indifference equation and then optimizes over its quality. In the optimum the firm in control has to take in mind that even though it is in control and the other firm has a revenue of zero, it has a potential profit. For the second scenario exactly the same is done but firm 2 optimizes over marketing.

3.1.1 Firm 1 controls the market

If firm 1 starts in control of the market it will set their price according to the indifference equation to find the price they should set to meet the indifference condition. This leads to the following price equation.

Lemma 3.1

For the consumer to be indifferent between both firms the following condition applies for the price of firm 1:

𝑝1 = 𝛽(𝑞1− 𝛼𝑚 − 𝑞2) + 𝑝2 (3)

To find the optimal quality, the indifference price (3) is then substituted into the profit

function of the firm (1). The profit is then maximized over quality, 𝑞1. For the 𝑞1found to be a maximum the following first and second order conditions have to be satisfied:

𝛿𝜋1(𝛽, 𝑞1, 𝑚, 𝑞2, 𝑝2, 𝐷1)

𝛿𝑞1 = 0

𝛿2𝜋

1(𝛽, 𝑞1, 𝑚, 𝑞2, 𝑝2, 𝐷1)

𝛿𝑞12 < 0

This resulted in only one maximum for the optimal quality, the optimum is defined in the following lemma.

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7 Lemma 3.2

The optimal level of quality for firm 1 according to first and second order conditions is defined by:

𝑞1(𝛽, 𝛾

1) = 2𝛾𝛽

1 (4)

The optimal level for quality is then substituted to find the optimal price level . This leads to the following solution:

𝑝1∗(𝛽, 𝛾1,𝛼, 𝑚, 𝑞2, 𝑝2) = 𝛽 (2𝛾𝛽

1− 𝛼𝑚 − 𝑞2) + 𝑝2 (5)

Now that the optimal levels of price and quality are known, the maximum profit under the indifference condition can be found. To do so the found optima are substituted into the profit function previously defined.

Theorem 3.1

Given that firm 1 starts off the game in control of the market and wishes to stay in control whilst optimizing its profit the following equilibrium will occur in the market, given price, quality and marketing of firm 2. Now firm 1 will decide to enter whilst firm 2, which has a maximum profit of zero, will not enter the market.

𝜋1(𝛼, 𝛽, 𝐷 1,𝑝2, 𝑞2, 𝑚, 𝛾1) = [𝛽 (2𝛾𝛽 1− 𝛼𝑚 − 𝑞2) + 𝑝2] ∗ 1 − 𝛾1∗ ( 𝛽 2𝛾1)2 (6) 𝜋2∗(𝑝2, 𝛾1, 𝛾2, 𝑞2, 𝑚) = 𝑝2∗ 0 − 𝛾1∗ 𝑞22− 𝛾2 ∗ 𝑚2 𝑞1∗(𝛽, 𝛾1) = 𝛽 2𝛾1 𝑝1∗(𝛽, 𝛾1,𝛼, 𝑚, 𝑞2, 𝑝2) = 𝛽 (2𝛾𝛽 1− 𝛼𝑚 − 𝑞2) + 𝑝2

3.1.2 Firm 2 controls the market

For firm 2 the situation is mathematically speaking not very different, the results however, are. First the price equation for the indifference condition is computed.

Lemma 3.4

For the consumer to be indifferent between both firms (1) the following condition applies for the price of firm 2:

𝑝2 = 𝛽(𝑞2+ 𝛼𝑚 − 𝑞1) + 𝑝1 (7)

To find the optimal marketing, the same methodology is applied as for optimal quality for firm 1. The following first and second order conditions have to be satisfied:

𝛿𝜋2(𝛽, 𝑞1,𝑚, 𝑞2, 𝑝1, 𝐷1)

𝛿𝑚 = 0

𝛿2𝜋

2(𝛽, 𝑞1,𝑚, 𝑞2,𝑝1, 𝐷1)

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These conditions resulted in only one optimal level of marketing. Lemma 3.5

The optimal level of marketing for firm 2 is defined by: 𝑚∗(𝛼, 𝛽, 𝛾

2) =2𝛾𝛼𝛽

2 (8)

By using the optimal marketing and substituting it into the best price for firm 2 the following price will optimize the profit for firm 2:

𝑝2(𝛽, 𝑝

1, 𝑞1, 𝑞2,𝛼, 𝛾2) = 𝛽 (𝑞2+ 𝛼2 𝛽2𝛾

2 − 𝑞1) + 𝑝1 (9)

Now that the optimal levels of price, quality and marketing are known, the maximum profit under the indifference condition can be found. To do so the found optima are substituted into the profit function previously defined.

Theorem 3.2

Given that firm 2 starts off the game in control of the market and wishes to stay in control whilst optimizing its profit the following equilibrium will occur in the market given price and quality of firm 1 and quality of firm 2. Firm 2 will now decide to enter the market whilst firm 1, which has a maximum profit of zero, will not enter the market.

𝜋1(𝑝 1, 𝛾1, 𝑞1) = 𝑝1∗ 0 − 𝛾1𝑞12 𝜋2(𝛼, 𝛽, 𝑝 1, 𝑞1,𝑞2, 𝛾1, 𝛾2) = [𝛽 (𝑞2+ 𝛼(2𝛾𝛼𝛽 2) − 𝑞1) + 𝑝1] ∗ 𝐷2− 𝛾1∗ 𝑞2 2− 𝛾 2∗ (2𝛾𝛼𝛽 2) 2 (10) 𝑚∗(𝛼, 𝛽, 𝛾 2) =2𝛾𝛼𝛽 2 𝑝2(𝛽, 𝑝 1, 𝑞1, 𝑞2,𝛼, 𝛾2) = 𝛽 (𝑞2+ 𝛼2 𝛽2𝛾2 − 𝑞1) + 𝑝1 3.2 Best response

Whenever any of the two situations found in the previous section occurs it means that the profit of the firm in control is at least zero whilst the profit of the other firm is never higher than zero. In this situation the firm that is not in control of the market looks for a best response to change the situation. A logical step for the firm not in control is to decrease its price to increase its utility for the consumer, in this way the consumer would always choose the highest utility. But in this case the firm previously in control will do the same thing. Ultimately the prices will be so low that either one of the firms will not make any profit anymore. In this part the best response for the firm which is not in control of the market is computed to show what will happen in the simultaneous game.

To find the best response in each of the situations I proceed from where I ended in the previous section. In this part the profits found for the firm in control of the market in the equilibrium are the ones the competition wishes to manipulate. In the first case firm 1 is in control of the market and its profit is given by (6) in Theorem 3.1, which is dependent of the price of firm 2. Since the game is simultaneous firm 2 can adjust its price at any time and so can firm 1. So in order to find the best response of firm 2, two conditions have to be satisfied.

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The first condition is to ensure that if firm 2 decides to act, the profit of firm 2 will still be equal to or higher than zero if it were to come in control of the market. This would be the minimum price, 𝑝2𝑚𝑖𝑛. The second condition is that the height of the price of firm 2 should minimize the profit of firm 1 to such an extent that firm 1’s profit is either zero or lower if it still would control the market. This condition would be the maximum price, 𝑝2𝑚𝑎𝑥 and makes sure that firm 1 has no incentive to stay on the market.

Lemma 3.6

If firm 1 is in control of the market (Theorem 3.1) and firm 2 wishes to take over and at the same time make sure firm 1 will not have an incentive to attend the market anymore the following conditions apply:

𝑝2𝑚𝑖𝑛 > 𝛾1∗ 𝑞22+ 𝛾 2 ∗ 𝑚2

𝑝2𝑚𝑎𝑥 < 𝛽(𝑞2+ 𝑎𝑚) −4𝛾𝛽2

1

The equilibrium price that occurs here is set so that firm 1 will stay out of the market, and firm 2 will choose its price according to the following equation since this leads to maximum price and profit for the firm.

𝑝2= 𝛽(𝑞

2+ 𝑎𝑚) −

𝛽2

4𝛾1− 𝜀

Where 𝜀 is a random very small number greater than zero. This equilibrium is stable as long as the price is conform the first condition of Lemma 3.6. The profit for firm 1 would be zero whilst for firm 2 the profit would be defined like this:

𝜋2(𝛾 1, 𝛾2, 𝛽, 𝑞2, 𝛼, 𝑚) = [𝛽(𝑞2+ 𝑎𝑚) − 𝛽2 4𝛾1− 𝜀] ∗ 1 − 𝛾1∗ 𝑞2 2− 𝛾 2∗ 𝑚2

In the second situation firm 2 is in control of the market and firm 1 wants to do the same as firm 2 in the previous situation. The same applies for firm 1 so I will immediately proceed to the lemma. Remember the first condition is the minimum price and the second is the maximum price.

Lemma 3.7

If firm 2 is in control of the market (Theorem 3.2) and firm 1 wishes to take over and at the same time make sure firm 2 will have an incentive to enter anymore the following conditions apply: 𝑝1𝑚𝑖𝑛 > 𝛾1𝑞12 𝑝1𝑚𝑎𝑥 < 𝛾1∗ 𝑞22+ 𝛽(𝑞 1− 𝑞2) − (𝑎𝛽)2 4𝛾2

In this case firm 1 would always maximize its profit, so the equilibrium price for firm 1 to make sure firm 2 will not have an incentive to enter the market would be defined like this:

𝑝1= 𝛾

1∗ 𝑞22+ 𝛽(𝑞1− 𝑞2) −

(𝑎𝛽)2

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For the same 𝜀 as before. This equilibrium can only be stable as long as the price also complies with the first condition of Lemma 3.7. The profit of firm 2 would be zero in this situation, the profit of firm 1 would be denoted like this:

𝜋1(𝛾

1,𝛾2, 𝛽, 𝑞1,𝑞2, 𝛼) = [𝛾1∗ 𝑞22+ 𝛽(𝑞1− 𝑞2) −

(𝑎𝛽)2

4𝛾2 − 𝜀] ∗ 1 − 𝛾1∗ 𝑞12 Although these conditions and equilibria might seem plausible the next section will show to what extend these equilibria could be realized.

4. Role of consumer preference

Since the entire model is based on the effectiveness of marketing this section will shed some light on, and illustrate the importance of understanding consumer preference.

4.1 Effect on profit in indifference equilibria

From the optimal profit functions found for the indifference it is clear that the

effectiveness of the use of marketing is dependent of the size of 𝛼. The parameter represents a transformation to the marketing, to show to what extend marketing can be an addition to actual quality, in order to increase the perceived quality of the consumer. In this section the profit of firm 1 is the profit in case it is in control of the market (Theorem 3.1), for profit of firm 2 this means the profit in case firm 2 is in control (Theorem 3.2). Profit of firm 2 in Theorem 3.1 is independent of 𝛼. The same accounts for the profit of firm 1 in case firm 2 is in control. To further look at the influence 𝛼 has on the profit the optimal profit functions were rearranged. 𝜋1(𝛼, 𝛽, 𝑝 2, 𝑞2,𝑚, 𝛾1) = −𝛼𝑚𝛽 + 𝛽 2 4𝛾1− 𝛽𝑞2+ 𝑝2 (11) 𝜋2(𝛼, 𝛽, 𝑝 1, 𝑞1,𝑞2, 𝛾1, 𝛾2) = (𝑎𝛽) 2 4𝛾2 + 𝛽(𝑞2− 𝑞1) + 𝑝1− 𝛾1∗ 𝑞22 (12)

For the effect of 𝛼 we look at the derivative of the profits (11) and (12) to 𝛼. 𝜋1(𝛼, 𝛽, 𝑝 2, 𝑞2, 𝑚, 𝛾1) 𝛼 = −𝑚𝛽 𝜋2(𝛼, 𝛽, 𝑝 1, 𝑞1,𝑞2, 𝛾1, 𝛾2) 𝛼 = 𝑎𝛽2 2𝛾2

The first derivative shows that for firm 1 the profit is only linearly affected by 𝛼 through the marketing and taste parameter 𝛽. For firm 2 however the profit is influenced in a quadratic way by the effectiveness of marketing 𝛼, the taste parameter and the cost of marketing.

To show the importance of understanding the effectiveness of the marketing, the profit of both firms is set out to 𝛼. In figure 4.1.a the effect of 𝛼 on the profit of firm 1 will be shown, 𝛼 will range from zero to two whilst keeping all other parameters constant, 4.1.b will do the same for firm 2. Table 4.1 shows the settings for the figures. The numbers that have been left out are not used in the figures they belong to.

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11 Table 4.1 Figure 𝛼 𝛽 𝛾1 𝛾2 𝑞1 𝑞2 𝑝1 𝑝2 𝑚 4.1.a [0,2] 0.8 1 2 1 2 1 4.1.b [0,2] 0.8 1 0.8 2 1 4 4.2.a [0,2] 0.8 1 0.8 2 1 4.3.b [0,2] 2 0.2 1.5 3 2 5 4 2 4.2.c [0,2] 0.8 1 0.8 2 1 1 4.2.d [0,2] 2 0.2 1.5 3 2 5 4 2

As mentioned above the figures 4.1.a and 4.1.b represent the firms’ profit extend of dependence from the effectiveness of 𝛼.

Figure 4.1.a

Figure 4.1.b

From figure 4.1.a it is clear that 𝛼 has significant influence on the profit of firm 1. In other words, depending on the consumer preferences and their perceptiveness to advertisements, marketing could be used to entirely vaporize the profit of firm 1. To find the size of 𝛼 that is needed to set the profit of firm 1 equal to zero, equation (11) is set to zero to find the

following: Lemma 4.1

In the case described by Theorem 3.1, for any 𝛼 >4𝛾𝛽

1𝑚−

𝑞2

𝑚 +

𝑝2

𝑚𝛽 the profit of firm 1 will

never exceed zero. -1 -0,5 0 0,5 1 1,5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 P rof it fi rm 1 𝛼 0 0,5 1 1,5 2 2,5 3 3,5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 P ro fi t fi rm 2 𝛼

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12

This is dependent of quality, price and marketing of firm 2 since in Theorem 3.1 these are assumed to be fixed in order to find the equilibrium.

Figure 4.1.b illustrates the quadratic relation between 𝛼 and the profit of firm 2. Combining the results in both figures shows that the size of 𝛼 has a significant influence on the profit of both firms. The results show that if marketing can be used as a tool to influence perceived quality it is important to understand the market. The intuitive explanation confirms that for a market where consumer preference is not likely to be altered by marketing it is not expected to be helpful, whilst in a market where consumers are perceptive to marketing it can be very helpful. In a market such as the cell phone market, marketing can add significantly to the perceived quality as Petruzzellis (2010) has shown.

4.2 Effect on best response

After investigating the effect of 𝛼 on the quality and marketing equilibria the same can be done for the best response part of the game. Since the simultaneous game is expected to converge to the equilibria described by the lemmas 3.6 and 3.7, these lemmas can be used to analyze the effect of 𝛼 in the final stages of the game. At the same time this is also a way to demonstrate to what extend it is possible for the firms to drive the profit of their competition low enough to take over the market. Table 4.1 from the previous paragraph also contains the settings for the figures 4.2.a through 4.2.d.

Figure 4.2.a and b Best response firm 1 when firm 2 is in control of the market

Figure 4.2.c and 4.2.d Best response firm 2 when firm 1 is in control of the market 0 1 2 3 4 5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 P ri ce 𝛼 Max P Min P 0 0,5 1 1,5 2 2,5 3 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 P ri ce 𝛼 Max P Min P 0 0,5 1 1,5 2 2,5 0 0,5 1 1,5 2 P ri ce 𝛼 Max P Min P -2 -1 0 1 2 3 4 5 6 7 8 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 P ri ce 𝛼 Max P Min P

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13

In all four figures Max P represents the maximum price the firm can set whilst satisfying the first condition in the lemmas 3.6 and 3.7. Min P represents the minimum price for the firm to make sure the firm remains maintain a profit of 𝜋𝑖 > 0 which is represented in the second conditions in both lemmas. This results in a possible area between both Max P and Min P where the best response can actually lead to a permanent takeover in the simultaneous game. It is obvious that the firm in control wishes to maximize its profit, so it would go with Max P, according to the maximum prices described in lemmas 3.6 and 3.7.

Figure 4.2.a represents the ability of firm 1 to take over from firm 2. Clearly with the chosen settings for the other figures there is no area where firm 1 would be able to control the market fully. Upon choosing other settings, see figure 4.2.b, the difference decreased. But it seems that only for relatively high 𝛽 and low 𝛾1firm 1 is able to control the market. Firm 1 is only competing through price and quality management and apparently this leads to more difficulty to take over the market. To determine numerically for which 𝛼 firm 1 is able to completely control the market the following theorem is set up.

Theorem 4.1

Given that firm 2 starts off the game in control of the market and the market reaches the indifference equilibrium, firm 1’s best response is able to completely take over the market if:

𝑝1𝑚𝑎𝑥 > 𝑝1𝑚𝑖𝑛 For the size of 𝛼 this leads to:

𝛼 < √4𝛾2

𝛽2 (𝛾1(𝑞22− 𝑞12) + 𝛽(𝑞1− 𝑞2)

If 𝛼 complies with this that means that firm 1 is able to take over the market from firm 2. This would lead to the stable equilibrium and profit function for firm 1 found in section 3.2. Figure 4.2.c displays a different image from 4.2.a, strongly depending on the size of 𝛼, it seems easier for firm 2 to respond in the best possible way and take over complete control of the market whilst firm 1 started off in control. This is based on the settings from 4.1 and upon trying other settings it became less likely for the areas of Max P and Min P to overlap but it shows that size of 𝛼 can be of significant influence on the success of the best response. Figure 4.2.d and 4.2.b show that for some settings in the market both of the best responses could be successful. Figure 4.2.c confirms that if marketing can be a tool to influence the perceived quality, it can change the dynamics of the simultaneous game and might even change it to a monopoly depending on the perceptiveness of the consumer towards marketing. Theorem 4.2 explains the size of 𝛼 that is needed for firm 2 to take over the market.

Theorem 4.2

Given that firm 1 starts off the game in control of the market and the market reaches the indifference equilibrium, firm 2’s best response is able to completely take over the market if:

(15)

14 For the size of 𝛼 this leads to:

𝛼 >𝛾1∗ 𝑞2 2+ 𝛾 2∗ 𝑚2− 𝛽𝑞2+ 𝛽 2 4𝛾1 𝛽𝑚

If 𝛼 complies with this that means that firm 1 is able to take over the market from firm 2. This would lead to the stable equilibrium and profit function for firm 1 found in section 3.2.

5. Conclusion

This paper researched the effect non-price persuasive advertisement can have on product demand. Specifically in a vertically differentiated market with Bertrand competition in a duopoly form of a simultaneous game. One of the firms, firm 1, uses price and quality to compete whilst the other firm, firm 2, competes through quality and price. Since the model looks at persuasive advertisement to influence product demand it is comparable to the model created by Chioveanu (2008). She also looked at the influence of persuasive advertisement on the way consumers were distributed, she however only looked at markets with near homogeneous products. This model distinguishes itself because it takes into account the possibility of vertical differentiation and looks at marketing as a tool to create unreal differentiation in such a way that it is possible to increase the perceived quality for the consumer. The model led to a clear conclusion: if marketing can be a substitute for perceived quality competition dynamics change and marketing can help in several ways, but it is strongly dependent of the consumers’ perceptiveness to marketing.

After finding the optimal levels of marketing and quality for both firms I was able to find the equilibria which occur when the consumer is indifferent towards both firms. Secondly this paper looked at the best response for the firm which was not in control in either one of the equilibria found under the indifference equation. The best response was meant to see whether or not the competing firm could adjust price levels to such an extent that the firm in control no longer had an incentive to enter the market, leaving it open for the competing firm. These results already showed that the profits were strongly dependent on consumer preferences, which defines whether or not and to what extent the consumer is perceptive to marketing. Further research showed that increased consumer perceptiveness to marketing led to quadratic increase in the profit for firm 2, whilst only a linear decrease in profit for firm 1 competing through quality. For the best response it seemed that for firm 1, not using marketing it is highly unlikely to be able to succeed at performing the best response. With marketing however, firm 2 seemed to be a lot more likely to perform the best response and take over the market by making sure firm 1 had no more incentive to enter. The results confirm the hypothesis that if marketing can be a substitute for perceived quality, it can be of significant use to the firm. But before deciding to use marketing it is of great importance to understand consumer preferences and the cost structure, this became clear from all of the results.

This model is restricted by the fact that it assumes homogeneous consumers and only two firms. It also assumes that all advertisements and marketing reach all consumers, and that marketing is only used as persuasive tool, not informative at all. This can be a problem when comparing it to a real life example, but this model be a good basis for further elaboration on the subject. Other researchers can expand the model to consider a market of a larger number of producers as well.

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15

References

Advertising Age, June 28, 2004. 100 leading national advertisers

Bagwell, K., 2007. The economic analysis of advertising. In: Armstrong, M., Porter, R. (Eds.), Handbook of Industrial Organization, vol. 3. North-Holland, Amsterdam, pp. 1701–1844.

Baltagi, B.H., Levin, D., 1986. Estimating dynamic demand for cigarettes using panel data: The effects of bootlegging, taxation and advertising reconsidered. Rev. Econ. Statist. 68, 148 –155.

Baye, M., Morgan, J., 2004. Brand and price advertising in online markets. Mimeo.

Butters, G., 1977. Equilibrium distributions of sales and advertising prices. Rev. Econ. Stud. 44, 465–491

Chioveanu, I., 2008. Advertising, brand loyalty and pricing. Games and economic behavior 64, 68 -80. Deal, K.R., 1979. Optimising advertising expenditures in a dynamic duopoly. Operations Research 27 (4), 682±692.

Kaldor, N.V., 1950. The economic aspects of advertising. Rev. Econ. Stud. 18, 1 –27.

Kelton, C., Kelton, D., 1982. Advertising and intraindustry brand shift in the US brewing industry. J. Ind. Econ. 30, 293–303.

Little, J.D.C., 1979. Aggregate advertising models: the state of the art. Operations Research 27, 629±667. Nichols, W. H., 1951. Price policies in the cigarette industry. Vanderbilt University Press.

Petruzzellis, L., 2010. Mobile phone choice: technology versus marketing. The brand effect in the Italian market. European Journal of Marketing 44, 610 - 634

Vidale, M.L., Wolfe, H.B., 1957. An operations research study of sales response to advertising. Operations Research 5, 370±381

Wang, Q., Wu, Z., 1999. A duopolistic model of dynamic competitive advertising, Operations research 128, 213 – 226

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