A Path To Consumer Surplus & Loyalty∗ How Path Dependent Products Result in Lower Prices and Order-Dependent Consumer Loyalty
Sherzod B. Akhundjanov†, Ben O. Smith‡, Max St. Brown§ February 5, 2018
Abstract In the technology and design industries, one product builds on another: a smart television enhances a smart phone. However, due to complimentary features, the utility gained by owning both products from the same firm is greater than the sum of the two products’ utility if purchased from separate firms. Aftermarkets suggest the margins of the second product would increase. Instead, we show that the firms’ complementary utility offset each other resulting in reduced prices. Further, consumer loyalty is a function of the product release order; given a different release schedule some consumers would be loyal to a different company. Keywords: Aftermarkets, Bounded Rationality, Complementary Goods, Hotelling, Path Dependence JEL: L11, L13, D82, D43
∗
Authors listed alphabetically. The authors thank Southern Economics Conference participants, Leif Lundmark, and Dustin White for their valuable feedback. This paper reflects the views of the authors and are not necessarily those of the Oregon Public Utility Commission. † Department of Applied Economics, Utah State University,
[email protected], 4835 Old Main Hill, Logan, UT 84322. ‡ College of Business Administration, University of Nebraska at Omaha,
[email protected], 6708 Pine Street, Omaha, NE 68182. § The Oregon Public Utility Commission,
[email protected], 201 High Street SE Suite 100, Salem, OR 97301.
1. Introduction Apple customers love Apple products. Whether it is a new phone, tablet, smart TV, or, most recently, watch, some customers seem to buy whatever the company produces next – regardless of the competition. Customer loyalty is not surprising. New technology goods from the same firm are often complements. As an example, you can make calls with your phone and you can watch TV with your smart TV, but initially only when both are made by the same company can you play music from your phone on your TV. When the smart phone was released, firms anticipated that there would be a complementary television product, but the consumers did not. This ‘bonus utility’ exists for a large number of technological and design products.1 Even if the feature set is not expanded, it is often less costly for a customer to learn a new product from the same firm, especially since the interface is more likely to resemble that of the firm’s previous products. Similarly, many customers prefer designed products, such as dishes or furniture, to match the design of their existing purchases – something that can only be achieved by purchasing the product from same firm. Over time, the bonus utility creates a path dependence where a customer’s product choice is determined by the order of the products’ release dates – something the firms take into account. These firm level, path dependent, complementary goods are something different than we have seen in the previous literature. They are not a ‘less pronounced version’ of aftermarket goods – which would suggest that later products have higher margins.2 If this were the case, we would expect gross margins to increase dramatically over time3 – a story that is inconsistent with the recent financials of Apple, Sony, Samsung and Google. The goods are also not fully independent or standard order-independent complementary 1
See Section 3 for more examples from different industries. For a literature review of aftermarkets, see Ellison (2005). 3 The authors are aware that gross margins are at best anecdotal. They are a complex story involving product mix, changing commodity prices and many other factors. The gross margins can be found online for Apple (https://goo.gl/sdoKrz), Sony (https://goo.gl/b3eero), Samsung (https:// goo.gl/ckDFoL), and Google (https://goo.gl/6d643i). 2
2
goods. Because the consumer is only aware of the released products, they do not take later products into account. The firms, recognizing they are creating path dependence, subsidize the first market in an attempt to capture later sales. In this paper, we develop a simple two-period, two-product complete information game in the linear city model framework. Both periods represent the horizontal product differentiation where firms compete in prices, with the first period corresponding to price competition in the market for the first product, while the second period corresponding to price competition in the market for the second, order-dependent product. A firm’s location in our model measures the differentiation by these firms. Each consumer buys at most one unit of a product in each period. The two products provide the same base utility when they are consumed, but there is additional utility if the two products come from the same firm. The main result is that firms competing for market share end up subsidizing the market for the initial good as they anticipate the bonus utility in the second good market for the consumers who buy from them initially. We show that the order-dependent complementary goods can result in an overall decrease in prices. A large difference in market power only occurs if there is a large difference in bonus utility created by the two firms. Otherwise, the bonus utilities offset each other and create a benefit to the consumer. Further, the choices made by individual consumers are a function of the product release order. Given the same preferences, some consumers would have purchased from a different firm if the products were released in a different order. Finally, we show that the presence of a market leader (informational advantage) for a subsequent complementary good creates a premium for that product. Our study relates to the literature on consumer switching costs and lock-in (Klemperer, 1987a,b, 1995; Farrell and Shapiro, 1988, 1989; Beggs and Klemperer, 1992). These studies contend that switching costs (e.g., transaction costs, learning costs, contractual costs, and discounts on repeat purchases) make firms’ demand less elastic, and thereby
3
reduce competition and give firms a degree of market power. Chen (1997), studying discounts offered to new customers in markets with switching costs, shows that firms are worse off engaging in discriminatory pricing, whereby they charge different prices to existing and new customers. Further, Shaffer and Zhang (2000) demonstrate that price discrimination in such settings can lead to lower prices to all customers. Similarly, in our study, firms, despite subsidizing the first market in an effort to attract more customers, do not ultimately benefit in the second market; while consumers enjoy lower prices. Unlike a standard switching cost literature, which considers repeat purchases of the same product, our paper focuses on path dependent, complementary goods (e.g., a smart phone and a smart TV), which are clearly not the same product. Importantly, when bonus utilities for firms are symmetric, the framework developed in this paper provides results that are comparable to those obtained from certain stylized switching cost models.4 However, when bonus utilities are asymmetric, our findings diverge from those in the standard literature. Therefore, our paper contributes to the literature by shedding light on expected pricing and purchasing patterns of path dependent, complementary goods. Further, our paper differs from the standard aftermarket literature (Borenstein et al., 2000; Ellison, 2005) in that customers are not prohibited from switching firms in the second market, and hence are not locked-in in the first purchase brand. Nonetheless, Cabral (2014), studying aftermarkets, tells a similar story to ours; consumers can be better off because firms price more competitively in the first market. The paper also relates to a strand of literature on product mix and multiproduct firms (Dixit and Stiglitz, 1977; Raubitschek, 1987; Shaked and Sutton, 1990; Anderson and de Palma, 1992; Bernard et al., 2010). The additional utility or satisfaction that arise from consumption of different products from the same brand (e.g., brand-reputation effect) have been widely explored in the literature (Oliver, 1999). The bonus utility considered in our study varies from the brand effect in that it emerges from additional 4
In particular, a two-period model of switching cost with (i) myopic consumers; (ii) forward looking firms; and (iii) full independence of product preferences (Villas-Boas, 2015).
4
enhancements or conveniences provided solely by the joint consumption of the two standalone products of a firm, such as a smart phone and a smart TV. In the latter case, the firm can influence the level of bonus satisfaction by providing various tangible features that are only available when the two products are used together. However, when considering features such as a common user interface or design, this additional satisfaction is inherent to the products and cannot be influenced by the firm. The remainder of the paper is organized as follows. In the next section, we present the model, solve for the equilibrium, and provide analysis. Section 3 discusses potential applications of our model, while Section 4 provides concluding remarks.
2. Model Consider a duopoly model where two firms create a two product solution: product A sold in a first market and product B sold in a second market. There is an additional benefit from owning both products from the same firm. We will define this benefit – bonus utility – as µ and γ for firm 1 and 2, respectively. For our purposes, we assume the value of µ and γ are governed by the nature of products and are not chosen by the firm. While consumers are incentivized to purchase both products from the same firm, it is possible to own one product from each of the two firms. At the time of the first product’s release, the firms know the second product will exist, but the consumers do not. For concreteness, think about product A as a smart phone and product B as a smart TV product. Each market is described by a linear city of length one (Hotelling, 1929). Consumers are distributed uniformly and independently, along each city, with total population equaling one for each market. Each potential consumer eventually buys one unit of both products. Firms 1 and 2 are located at positions zero and one, respectively, in both markets. We assume that both firms have constant identical marginal costs to focus on the effect of the bonus utility.
5
0
1 Firm One Customers
Firm Two Customers
xA
Firm One
Firm Two
Figure 1: Here we show a linear city from zero to one. Consumers are uniformly distributed in preferences between zero and one. The consumer who is indifferent between the two firms is referred to as the indifferent consumer (labeled xA ). In the market for product A, any consumer located before xA will buy from firm 1, while any consumer after xA will purchase from firm 2. The firms are implicitly choosing xA by choosing prices.
2.1.
The Equilibrium
A linear city model is solved by finding the consumer who is indifferent between the two firms’ products as any consumer leading up to that point will obtain more utility from the firm located at zero (see Figure 1). Consequently, if U1A is the utility the consumer receives from purchasing product A from firm 1 and U2A is the utility the consumer receives from purchasing the good from firm 2, then the following will determine the indifferent consumer for the first market: sA − p1A − tA xA = sA − p2A − tA (1 − xA ) | {z } | {z } U1A
U2A
−p1A + p2A + tA xA = 2tA
(1)
where sA is the gross consumer benefit from product A, tA is the the transportation cost of each unit of travel, and the prices charged by each firm for product A are p1A and p2A for firm 1 and 2, respectively.5 For product B, xA consumers obtain bonus utility µ if they purchase good B from firm 1, while 1 − xA obtain bonus utility γ if they purchase from firm 2. In both cases, the bonus utility is a function of purchasing product A and B from the same firm. The position of an individual consumer in the market for product B is independent of his 5
Using quadratic transport costs, we find no qualitative difference in our main result: like the model presented here, the final prices for the model with quadratic costs are p∗1A = p∗2A = cA + tA − µ, and p∗1B = p∗2B = cB + tB . The indifferent consumer final solutions in equations 1, 2, and 3 are identical regardless of whether the transport costs are specified linearly or quadratically.
6
0
1 Firm One Customers
Firm Two Customers
xBμ
Firm One
Firm Two
Figure 2: In the market for product A, xA consumers purchased from firm 1. Therefore, xA proportion of consumers in market B get an additional amount of utility by owning both A and B from the same company (µ). The indifferent consumer in the market for product B given the consumer purchased product A from firm 1 is represented by xBµ .
position in market for product A. Further, the bonus utility (µ or γ) is independent of the consumer’s position as it is generated from the use of product A (either training or complementary features). We first determine the indifferent consumer in the second market of those who purchased product A from firm 1. We set the utility of purchasing product B from firm 1 (U1Bµ ) equal to the utility of purchasing product B from firm 2 (U2B ): sB + µ − tB xBµ − p1B = sB − tB (1 − xBµ ) − p2B {z } | {z } | U1Bµ
U2B
xBµ
tB + µ − p1B + p2B = 2tB
(2)
where sB is the gross consumer benefit from product B, tB is the transportation cost for each unit of travel, and the prices charged by each firm for product B are p1B and p2B for firm 1 and 2, respectively. The solution in 2, xBµ , describes the proportion of xA consumers who will also purchase product B from firm 1. Alternatively, 1 − xBµ represents the proportion of xA consumers who purchase product B from firm 2, despite having purchased product A from firm 1 (see Figure 2). Similar to firm 1, 1 − xA consumers, who purchase product A from firm 2, obtain bonus utility γ if they purchase good B from the same firm. We can obtain the indifferent consumer by setting the utility of purchasing product B from firm 1 (U1B ) equal to the utility of purchasing product B from firm 2 (U2Bγ ):
7
0
1 Firm One Customers
Firm Two Customers
Firm One
xBγ
Firm Two
Figure 3: In the market for product A, 1 − xA consumers purchased from firm 2. Therefore, 1 − xA proportion of consumers in market B get an additional amount of utility by owning both A and B from the same company (γ). The indifferent consumer in the market for product B given the consumer purchased product A from firm 2 is represented by xBγ .
sB − tB xBγ − p1B = sB + γ − tB (1 − xBγ ) − p2B | {z } | {z } U1B
U2Bγ
xBγ
tB − γ − p1B + p2B = 2tB
(3)
where 1 − xBγ describes the proportion of the 1 − xA consumers who will also purchase product B from firm 2, while xBγ purchase good B from firm 1 after purchasing good A from firm 2 (see Figure 3). Given firms’ outputs in two markets, firms’ profits are defined as follows: π1 = xA (p1A − cA ) + (p1B − cB )(xA xBµ + (1 − xA )xBγ )
(4)
π2 = (1 − xA )(p2A − cA ) + (p2B − cB )(xA (1 − xBµ ) + (1 − xA )(1 − xBγ )) where cA and cB are the cost per unit of product A and B, respectively. Because the proportion of consumers who receive the bonus utility is a function of sales of product A, the indifferent consumer solutions, xBµ and xBγ , are weighted by the product A sales of the two firms: xA and 1 − xA . Each firm chooses prices in both markets taking the other firm’s expected behavior as given.6 We find the first order conditions using the equations in 4 and solve for the best response functions: 6
In our model, firms choose prices for both markets at the beginning of the game. In reality, the firms might not have perfect knowledge of market B prices. However, they would have an expectation about prices (and thus margins), otherwise they could not take the market into account. We make the simplifying assumption that these expectations are correct. A suggested alternative to this model is to assume both firms are unaware of market B until product B appears in the second period. Under this model, the firms would not subsidize the first market (p1A = p2A = cA + tA ), and pricing
8
2tB (cA + p2A + tA ) − (γ + µ)(p1B − cB ) 4tB 2tB (cA + p1A + tA ) − (γ + µ)(p2B − cB ) p2A (p1A , p2B ) = 4tB tA (2cB + 2tB + 2p2B + µ − γ) + (γ + µ)(p2A − p1A ) p1B (p2B , p2A , p1A ) = 4tA tA (2cB + 2tB + 2p1B + γ − µ) + (γ + µ)(p1A − p2A ) p2B (p1B , p1A , p2A ) = 4tA p1A (p2A , p1B ) =
(5)
The price of product A charged by a given firm is increasing in rival firm’s price 1A ( ∂p > 0 and ∂p2A
∂p2A ∂p1A
∂p1A > 0) and decreasing in the price of good B ( ∂p < 0 and 1B
∂p2A ∂p2B
< 0).
∂p1B Similarly, the price of product B for either firm increases in the rival’s price ( ∂p > 0 and 2B ∂p2B ∂p1B
1B > 0), while it is decreasing in the firm’s price for product A ( ∂p < 0 and ∂p1A
∂p2B ∂p2A
< 0).
Intuitively, if the price of product B goes up, the firm lowers the price it charges for product A to attract more customers and increase the sales of its complementary product. Simultaneously solving the system of four equations in 5 yields Nash equilibrium price levels:
p∗1A =
1 2cA + tA − µ − γ + 2
p∗2A =
1 2cA + tA − µ − γ + 2
z(
z (
Ω }| { ) 2tA (9tA tB − µ(µ + γ)) 18tA tB − (µ + γ)2 Φ }| ){ 2tA (9tA tB − γ(µ + γ)) 18tA tB − (µ + γ)2
(6)
3tA tB (µ − γ) + tB 18tA tB − (γ + µ)2 3tA tB (γ − µ) = cB + + tB 18tA tB − (γ + µ)2
p∗1B = cB + p∗2B
The firms are subsidizing the market for product A knowing that they will create bonus utility in the market for product B.7 But, because both are creating additional utility, in market B would be determined by the difference in bonus utility (i.e., p1B = cB + tB + µ/6 − γ/6, p2B = cB + tB − µ/6 + γ/6). 7 The first period subsidy is not obvious given Ω and Φ in equation 6. However, Ω + Φ simplifies to 2tA . Therefore, given the remainder of price equation, the firms are net subsidizing market A. This holds true both for a simple average of market A prices and a market share weighted average of prices as more consumers will purchase from the less expensive firm.
9
the utility difference is what determines the price in the second market. If the degree of bonus utility is identical (γ = µ) the prices simplify to: p∗1A = p∗2A = cA + tA − µ p∗1B
=
p∗2B
(7)
= cB + tB
The firm anticipates the bonus utility and subsidizes the first market. However, because the bonus utility offsets each other, the two firms charge the same amount for product B as if there was no bonus utility. Clearly, consumers benefit because they receive the subsidy in the market for product A, but do not pay more in the second market. Prices are decreasing in the first market in the value of the bonus utility. This is similar to Fabra and Garcia (2015), where prices are decreasing in the value of the switching cost due to poaching of customers. 2.2.
Unequal Bonus Utility
While offsetting bonus utilities result in a benefit to consumers at the expense of producers, a firm can still benefit from increased bonus utility over its competitor (i.e., µ ≶ γ). Consider the case when γ = 0 (no bonus utility from consumption of both products from firm 2) and µ > 0. Using the equations from 6, prices can be restated as: 9tB t2A 18tB tA − µ2 9tB t2A = cA + 18tB tA − µ2 3tB µtA = cB + 18tB tA − µ2 3tB µtA = cB − 18tB tA − µ2
p∗1A = cA − p∗2A p∗1B p∗2B
From 8, we can derive the profit difference:
10
µ 3tA + 2 2 µ tA − + 2 2 −
+ tB + tB
(8)
tB (18tB tA − µ2 + 18t2A − 3µtA ) 1 π1 − π2 = − 36tB tA − 2µ2 2
(
3tB µtA + tB − µ + tA 18tB tA − µ2
)
φ
z}|{ z }| { µ(12tB tA +µtA − µ2 ) = 2(18tB tA − µ2 ) | {z } ϕ
(9)
ω
The sign of the profit difference can be recovered as follows. Substituting 8 into 1 results in x∗A = tB ≥
µ2 9tA
9tB tA , 18tB tA −µ2
which is bounded between zero and one. This constraint indicates that
or, rearranged, 9tA tB ≥ µ2 . Therefore, ϕ ≥ φ and ω > 0, and hence π1 − π2 > 0.
Intuitively, this implies that an increase in firm 1’s bonus utility µ results in an increased profit difference between firm 1 and firm 2, with firm 1 reaping greater profits compared to firm 2 (π1 > π2 ). For concreteness, we provide numeric results in Table 1. In this example, tA = tB = 2 and cA = cB = c. As indicated by equation 9, when µ > γ, firm 1 experiences higher profit. Further, while firm 1 subsidizes the market for product A more when µ > γ, firm 2 must lower the price of product A due to the competition. In market B, firm 1 charges slightly more than firm 2 when µ > γ, but despite charging more, firm 1 serves more customers than firm 2; the difference is neutralized once γ = µ. Note that total producer surplus (π1 + π2 ) is identical in all three scenarios. 2.3.
Path Dependence and Complementary Goods
While the prices for product B may be identical when the the two products (A and B) are sold independently, the customer base is not. Despite independent preferences for products A and B, purchasing product A from a given firm makes the consumer more likely to purchase product B from that same firm. Consider the difference between the indifferent consumer for product B given they purchased product A from firm 1 (xBµ ) and the indifferent consumer for product B given
11
Table 1: Numerical Example for Symmetric and Asymmetric Bonus Utilities µ γ Firm Firm Firm Firm p1A p2A p1B p2B π1 π2
1 product A overall market share 1 product B overall market share 1’s B share | purchased A from firm 1 1’s B share | purchased A from firm 2
Scenario 1
Scenario 2
Scenario 3
0.4000 0.0000 50.11% 51.67% 56.66% 46.66% c + 1.7978 c + 1.8022 c + 2.0668 c + 1.9332 1.9688 1.8334
0.3000 0.1000 50.06% 50.84% 55.83% 45.83% c + 1.7989 c + 1.8011 c + 2.0334 c + 1.9666 1.9341 1.8664
0.2000 0.2000 50.00% 50.00% 55.00% 45.00% c + 1.8000 c + 1.8000 c + 2.0000 c + 2.0000 1.9000 1.9000
they purchased product A from firm 2 (xBγ ): ∆xB = xBµ − xBγ tB + µ − p1B + p2B tB − γ − p1B + p2B − 2tB 2tB µ+γ ∆xB = 2tB ∆xB =
(10)
This suggests that as the indifferent consumers separate, the choice of firm in the market for product B becomes increasingly dependent on the first market (see Figure 4). This separation is order dependent, indicating that a given consumer might not make the same choices if product B was released before product A. Example. Assume γ = µ = 1 and the travel cost for both markets is tA = tB = 2. Therefore, the indifferent consumers are defined as follows: xA = 1/2, xBµ = 3/4, and xBγ = 1/4. Suppose there is a consumer who is positioned between 1/4 and 1/2 for 0
1
Firm One
ΔxB
Firm Two
Figure 4: As the bonus utility increases the difference between the quantity sold to ‘existing customers’ (customers who purchased product A) and new customers increases.
12
product A and 1/2 and 3/4 for product B. Given the current product release order, our consumer would purchase product A and B from firm 1. However, if product B came first, the bonus utility would be actualized with the purchase of product A. Therefore, the new indifferent consumers would be as follows: xB = 1/2, xAµ = 3/4, and xAγ = 1/4. Thus, if product B was released before product A, our example consumer would purchase both products from firm 2. 2.4.
Leadership in Market B
The primary result of this paper suggests that the lack of a premium in market B is a function of the two firms competing for customers who purchased good A from their competitor. However, while consumers are myopic, both firms are fully informed of the future existence of product B. In this section, we show that if one firm is aware of market B at the beginning of time, but the other is not, a premium in the second market will be maintained. Specifically, the firm with an informational advantage will charge more in the second market and this additional rent will be a function of the bonus utility. Consider two high tech firms producing product A in the first time period. Firm 1 is aware that it will release product B in next period. Further, Firm 1 also knows there is bonus utility associated with owning products A and B from the same firm. Firm 2 does not know product B exists in the first period, but it will produce a competing product after firm 1 releases its version of product B. Firm 1 knows firm 2 will release a version of product B and thus takes its rival’s action into account. Further, we assume the bonus utility is equal for both firms, for simplicity. We will describe this additional utility as µ. This alteration to our multistage game can be solved by considering the last stage and migrating backwards in time. In the last stage, firm 2 maximizes its profits from product B given both firm 1’s pricing and the result of the first stage of the game. In particular, firm 2’s second stage profit can be described as follows: π2B = (p2B − cB )(xA (1 − xBµ ) + (1 − xA )(1 − xBγ ))
13
(11)
where the solutions for xA , xBµ , and xBγ are the previously defined indifferent consumers (equations 1, 2, and 3). In this stage, firm 2 chooses p2B . For succinctness, we will skip the first order condition and move on to the best response function: p2B (p1B , p1A , p2A ) =
tA (cB + tB + p1B ) + µ(p1A − p2A ) 2tA
(12)
In the first stage, firm 2 is myopic and is unaware of the second stage. Therefore, firm 2 constructs its best response function based on the actions of firm 1 but without consideration of the second market. This response function is based on profit maximization of the firm’s first stage profit: π2A = (1 − xA )(p2A − cA )
(13)
where the solutions for xA , xBµ , and xBγ are the previously defined indifferent consumers. Firm 2 chooses p2A given firm 1’s choice of p1A . For succinctness, we will skip the first order condition and present the firm’s best response function: 1 p2A (p1A ) = (cA + p1A + tA ) 2
(14)
Finally, firm 1 maximizes its original profit equation with the exception that, given firm 1 knows the actions of firm 2, the firm replaces all instances of p2B with equation 12. We denote this new profit equation as π1 |p2B (i.e., π1 given p2B ), which is specified as follows: π1 |p2B = xA (p1A − cA ) + (p1B − cB )(xA xBµ + (1 − xA )xBγ )
(15)
With this setup, firm 1 maximizes equation 15 by simultaneously choosing p1A and p1B . This results in the following best response functions: 4tB tA (cA + p2A + tA ) − 3tB µtA + µ2 (−p2A ) 8tB tA − µ2 2tB (6tB tA − µ(cA − p2A + tA )) p1B (p2A ) = + cB 8tB tA − µ2 p1A (p2A ) =
(16)
Using the best response functions from equations 14 and 16, we can solve for the final
14
prices in the model: 6tB µtA + tA µ2 − 12tB tA 3tB µtA = cA + 2 + tA µ − 12tB tA 18t2 tA = cB − 2 B µ − 12tB tA ) ( 9tB tA +2 = cB + tB µ2 − 12tB tA
p∗1A = cA + p∗2A p∗1B p∗2B Notably, x∗A =
3tB µ + 12 , 2(12tB tA −µ2 )
(17)
which is bounded between zero and one. This constraint
indicates that as long as µ < 4tA then µ(3tB + µ) < 12tA tB . As 3tB µ is always positive, 12tB tA > µ2 . Therefore, both firms’ market A prices are less than when the markets are profit maximized independently (cA + tA ), but firm 1 subsidizes the market twice as much as firm 2. In market B, firm 1 always charges more than if the markets were profit maximized independently, but this is not always true of firm 2. Subtracting cB + tB (the pricing when the markets are profit maximized independently) from p1B results in tB (6tB tA +µ2 ) 9t2B tA + , which is always positive. Subtracting cB + tB from p2B results in µ2 −12t 12tB tA −µ2 A tB tB , which is only positive when 3tA tB > µ2 . The price difference between firms can be expressed as follows: 3tB µtA − 12tB tA ) ( 27tB tA = tB −2 12tA tB − µ2
∆pA = p1A − p2A = ∆pB = p1B − p2B
µ2
(18)
Equation 18 indicates the different market B pricing is a function of the bonus utility (µ). In essence, the leader’s knowledge of the connected markets allows them to set higher prices in market B. This matches the pattern of behavior we see in the high tech industry where strategically complementary goods are often more expensive from the firm that first releases the product.
15
2.5.
Non-Covered Market
Section 2.3 suggests that customers are more likely than not to purchase product B from the same firm as product A. However, we can show our main result is driven by the competition amongst firms in the second good’s market. Suppose that product B was purchased by only some customers such that the two firms did not directly compete in the second market. In this case, we would redefine equation 2 as follows: sB − tB xBµ + µ − p1B = 0 {z } | U1Bµ
µ − p1B + sB tB −p1B + sB = x1Bµ = |{z} tB x1Bµ =
x1Bγ
(19)
where µ=0
Similarly, equation 3 would be expressed as: 0 = sB + γ − tB (1 − x2Bγ ) − p2B | {z } U2Bγ
−γ + tB + p2B − sB tB tB + p2B − sB = x2Bγ = |{z} tB x2Bγ =
x2Bµ
(20)
where γ=0
where x1Bµ is the proportion of firm 1 product A consumers purchasing product B from firm 1. Similarly, x1Bγ is the proportion of firm 2 product A customers purchasing product B firm 1. x2Bγ and x2Bµ are defined in a corresponding manner. Since consumers are purchasing products A and B from different firms, then µ = γ = 0 in x1Bγ and x2Bµ . In this setup, the firm finds the customer who is indifferent between purchasing product B from them or not at all. Therefore, the firm does not take into account the behavior of the other firm and effectively behaves like a monopolist in the second market. Using the indifferent consumer solution for product A from equation 1 and our solutions for x1Bµ , x1Bγ , x2Bµ and x2Bγ from 19 and 20, we can define the profit equations as:
16
π1 = xA (p1A − cA ) + (p1B − cB )(xA x1Bµ + (1 − xA )x1Bγ )
(21)
π2 = (1 − xA )(p2A − cA ) + (p2B − cB )(xA (1 − x2Bµ ) + (1 − xA )(1 − x2Bγ )) Similar to profit equations in 4, the indifferent consumers for product B are weighted by the sales of product A. For simplicity, we will assume that γ = µ. We obtain first order conditions from equations 21, and solve for the Nash equilibrium prices: µ µ (sB + − cB ) 2tB 2 cB µ s B = + + 2 4 2
p∗1A = p∗2A = cA + tA − p∗1B
=
p∗2B
(22)
Unlike in equation 7, prices for product B increase in µ – much like an add-on product. Intuitively, this suggests that the competition amongst the two firms in the second market is a necessary condition for the market behavior discussed in this manuscript.
3. Applications In this section, we briefly discuss several real-life examples where the model analyzed in this study, along with its findings, can be particularly applicable. 3.1.
Technology
When the iPhone was introduced in early 2007, there was no indication that the product would become a complementary good to tablets, television products and wearables. Similarly, Google Android’s 2008 release suggested nothing more than a phone operating system and initial reference device. Today, both firms are major players in all of the aforementioned product areas. Yet, while we may not always know the future path, we know there is a future path of product categories. Samsung, an existing phone manufacturer, are preferentially creating
17
hooks to their own new home automation tools.8 Amazon’s phone and tablets preferentially create bonus utility to their online services and new products like the Amazon Echo. As long as new product categories exist, firms might prefer (through complimentary features) their own product within that new category. Even if they did not, consumers would benefit from the firms’ common user interface across products. 3.2.
Design
Dish-ware designers such as Lenox and Noritake commonly release new styles of place settings in phases. Place settings are enhanced by new dishes about once a year. While additions are initially predictable, the additions become increasingly exotic as the years go on. This means the firms are offering divergent features where a consumer may prefer a competitor’s product, but they obtain additional utility because the new product matches the style of their existing place-settings. Path dependent book releases are another example captured by our model. Critical acclaim equal, when selecting between two authors’ first books, you will likely purchase the book with the most interesting topic. When the authors release second books, you might not switch to the other author even if that book’s topic interests you more, due to the bonus utility of being familiar with the first author’s vocabulary, writing style or plot of the series. 3.3.
Recreational Education and Professional Development
Recreational education courses such as amateur painting, sculpting, and woodworking classes feature instructors with a particular personality and teaching style. While the painting (or other creative work) is known to the customer when they sign up for the class, future classes are only known a few months in advance. A customer might select a pottery class based on the design of the work. However, once the student wishes to sign8
See https://www.cnet.com/news/smartthings-to-control-samsungs-smart-appliances/.
18
up for another class, they are already accustomed to the teaching style of their former pottery instructor. This creates bonus utility if they take a class from the same instructor. The additional utility will result in some path dependent customers along with some who will switch based on the designs offered by other studios. Similarly, corporate customers experience bonus utility as they repeatedly purchase services from the same professional education firm. Firms often invest in education services for their labor force (either for individual employees or groups). Once the corporate learners are accustomed to the instructional style of the education company, the firm has a higher propensity to purchase future services. However, it is not known what classes the professional development company might offer in the future.
4. Conclusion In this manuscript, we discuss the implications of path dependent complements. Whether by technological interoperability, a common user interface or a matching design pattern, some goods produce additional utility when purchased from the same firm. While the firms know that these products will be released in the future, the customer does not (or at least they do not know the details) and cannot take them into account when purchasing the initial product. This results in a subsidy in the first market. This ‘bonus utility’ results in two important implications. First, while the first market will be subsidized, due to the competition in the second market, the firm will not gain substantial market power. This result differs from the traditional add-on literature in that some customers who initially purchased a competing product might still prefer the firm’s second product. It is these customers who could switch firms that drive down the prices in the second market. Second, choices made by individual consumers can be influenced by the product release order. Because the bonus utility is actualized upon the purchase of the second good, customers might purchase a product from a firm where, if not for the bonus utility, they would prefer the competitor’s product.
19
This pattern of behavior is particularly prevalent in the technology industry where user interfaces and design languages are common to a firm’s products. This common design produces a bonus utility that the customers enjoy as they are already used to the interface. This suggests that we might be misinterpreting the propensity of existing customers to purchase new products from the same firm as a match in preferences. It might be the case that a portion of that apparent loyalty is a function of bonus utility and the customer would have purchased the products from a different firm had the products been released in a different order. Further, customers who purchase products from the same firm benefit from the existence of customers willing to purchase goods from multiple firms. Future research can further extend our understanding of path-dependent, complimentary products by building on the analysis presented here. A natural extension is to consider a setting where the firm pursues non-linear pricing or bundling. This would help to understand, for instance, hardware foremarket and software aftermarket, whereby a firm sells a bundle in the first market that covers future software launches. Further, in our analysis bonus utility is treated as exogenous and same for all consumers. Future studies can extend our analysis by allowing for endogenous bonus utility and/or relating consumer heterogeneity to bonus utility. Finally, investigating the potential antitrust effects of bonus utility in the context of market predation (Ordover and Willig, 1981; Salop and Scheffman, 1983, 1987) is of interest to understand the welfare implications of path-dependent products.
20
References Anderson, Simon and André de Palma. 1992. “Multiproduct Firms: A Nested Logit Approach”. Journal of Industrial Economics 40(3): 261–276. Beggs, Alan and Paul Klemperer. 1992. “Multi-Period Competition with Switching Costs”. Econometrica 60(1): 651–666. Bernard, Andrew B., Stephen J. Redding, and Peter K. Schott. 2010. “Multiple-Product Firms and Product Switching”. American Economic Review 100(1): 70–97. Borenstein, Severin, Jeffrey K. Mackie-Mason, and Janet S. Netz. 2000. “Exercising market power in proprietary aftermarket”. Journal of Industrial Economics 9: 157– 188. Cabral, Luis. 2014. “Aftermarket power and foremarket competition”. International Journal of Industrial Organization 35(July): 60–69. Chen, Yongmin. 1997. “Paying Customers to Switch”. Journal of Economics and Management Strategy 6(4): 877–897. Dixit, Avinash K. and Joseph E. Stiglitz. 1977. “Monopolistic Competition and Optimum Product Diversity”. American Economic Review 67(3): 297–308. Ellison, Glenn. 2005. “A Model of Add-On Pricing”. The Quarterly Journal of Economics 120(2): 585–637. Fabra, Natalia and Alfredo Garcia. 2015. “Dynamic Price Competition with Switching Costs”. Dynamic Games and Applications 5(4): 540–567. Farrell, Joseph and Carl Shapiro. 1988. “Dynamic competition with switching costs”. RAND Journal of Economics 19(1): 123–137. Farrell, Joseph and Carl Shapiro. 1989. “Optimal Contracts with Lock-In”. American Economic Review 79(1): 51–68. Hotelling, Harold. 1929. “Stability in Competition”. The Economic Journal 39: 41–57. Klemperer, Paul. 1987a. “Markets with Consumer Switching Costs”. The Quarterly Journal of Economics 102(2): 375–394. Klemperer, Paul. 1987b. “The Competitiveness of Markets with Switching Costs”. RAND Journal of Economics 18: 138–150. Klemperer, Paul. 1995. “Competition When Consumers Have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade”. Review of Economic Studies 62: 515–539. Oliver, Richard L. 1999. “Whence Consumer Loyalty?” Journal of Marketing 63: 33–44.
21
Ordover, Janusz A. and Robert D. Willig. 1981. “An economic definition of predation: Pricing and product innovation”. The Yale Law Journal 91(1): 8–53. Raubitschek, Ruth S. 1987. “A Model of Product Proliferation with Multiproduct Firms”. Journal of Industrial Economics 35(3): 269–279. Salop, Steven C. and David T. Scheffman. 1983. “Raising rivals’ costs”. American Economic Review 73(2): 267–271. Salop, Steven C. and David T. Scheffman. 1987. “Cost-raising strategies”. Journal of Industrial Economics 36(1): 19–34. Shaffer, Greg and John Z. Zhang. 2000. “Pay to Switch or Pay to Stay: Preference-Based Price Discrimination in Markets with Switching Costs”. Journal of Economics and Management Strategy 9(3): 397–424. Shaked, Avner and John Sutton. 1990. “Multiproduct Firms and Market Structure”. RAND Journal of Economics 21(1): 45–62. Villas-Boas, Miguel J. 2015. “A short survey on switching costs and dynamic competition”. International Journal of Research in Marketing 32: 219–222.
22
