ISSUES OF BUSINESS AND LAW VOLUME 1 (2009) ISSN 2029-1094 DOI: 10.2478/v10088-009-0002-0
INTRODUCTION SEQUENCE WITH FUNCTIONALITY THRESHOLD AND REAL OPTION Paul LACOURBE Dr., Assistant Professor at École Supérieure des Sciences Économiques et Commerciales Avenue Hirsch, Cergy 95021, France E-mail:
[email protected]
Abstract. Existing literature on introduction sequence mostly argues against introducing a low-end product before a high-end product. In this paper, we present a simple model to show when it can be optimal to introduce a low-end product first. Based on some observations in industry, high-end consumers are not only wealthier, but also more demanding in quality. With this property, introducing a low-end product first without commitment would not cannibalize the high-end segment because it does not satisfy the quality requirements of the high-end consumers. We also allow for a stochastic environment: the firm may find it valuable to retain flexibility, or the so-called “real options”, rather than make commitment about forthcoming products. With this model setup, we add a different perspective that it can be optimal to introduce a low-quality product first for purely marketing reasons. We show that functionality thresholds can play the same role as Piguovian third degree discrimination.
Keywords: functionality thresholds, introduction sequence, real options, Piguovian third degree discrimination.
Introduction Current literature on introduction sequence (Moorthy, Png, 1992; Krishnan, Gupta, 2001; Bhattachaya et al., 1998) repeatedly finds that, in a deterministic environment, it is not optimal to introduce a low-end product before a high-end product in the absence of “exogenous technological improvement”. Bhattachaya et al., 2003 show that it may be optimal to introduce a low-end product before a high-end product when technology evolves over time. In other words, for purely marketing considerations, introducing a low-end product first cannot be optimal because, by doing so, “the profits from the higher performance product are not only delayed by one period but also reduced because of cannibalization” (Krishnan, Gupta, 2001). This robust result is driven by the assumption that high end consumer derives higher utility than low end consumer from all products. In other words, high end consumers are “better” consumers. With this assumption, high end consumers would buy the low end product in the absence of high end product, and low end product introduced first without credible announcement would cannibalize the high end segment. However, this assumption does not hold for certain products. Consider the following example of an industrial product. Expanded polystyrene foam (EPS) is a raw material for package production (Probert, Schütte, 1999). Two types of package producers are potential clients for the EPS producer: package producers employing vacuum machines (vacuum clients) and those employing manual machines (manual clients). EPS is sold in different qualities to these two types of clients. Vacuum clients cannot use low-quality EPS; it causes machine breakdowns that make production uneconomical. Even if high-quality EPS becomes unavailable, vacuum clients will simply refrain from buying. Manual clients, in contrast, can use EPS of high or low quality (and will decide on the asis of the quality/price ratio). When high-quality EPS is offered, only vacuum clients are willing enough to pay for it; they are the high-end consumers, and manual clients are low-end consumers.
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In this situation, low-quality EPS is sold to low-end consumers, and high-end customers do not buy it regardless of the availability of a high-end product. Another example is provided in Krishnan et al., 1999 and Krishnan and Gupta, 2001 concerning capability of data processing machines: consumers need a specific capability of machines for a particular task, and will not buy machines with a capability below the requirement, regardless of price and availability of other products. This property is referred as strict downward substitutability in Krishnan et al., 1999 and reservation quality in Krishnan and Zhu, 2006. Adner and Levinthal, 2001 define functionality threshold as “the minimum objective performance (independent of price) that a given product must deliver in order for the consumer to consider it”. The existence of functionality threshold adds a new element to the introduction sequence literature: the high-end consumers are not only wealthier, as described in the literature, but they are also more demanding of quality. Therefore, if the low-end machine is introduced first, it is useless to the high-end users, who will not buy it, with or without an announcement about the high-end machine. Moreover, when two products are introduced simultaneously, the low-end product does not pose cannibalization threat and lead to a lower price of the high-end product. According to the literature, the optimal sequence in face of market uncertainty is unclear (Moorthy, Png, 1992). Intuitively, in an uncertain environment, introducing a high-end product after a low-end product delays the profit from the high-end segment; but, such a delay may also increase profit from this segment because of better pricing decision after observing the market’s response to the low-end product. The benefit of delay in the face of technological and market uncertainties is well-documented in marketing literature (Rosenberg, 1978; Kalish, Lilien, 1986), however, these papers do not directly address the issue of relative introduction sequence of products. In particular, in the presence of sink cost, there may be less to lose to introduce a low-end product first, in case market conditions do turn out to be unfavorable. In order to capitalize on information updates after the first product is introduced, the firm cannot make a commitment when introducing products sequentially; rather, it makes decisions on future launches after observing the market’s response to products introduced earlier. As the literature states: “commitment is harder to achieve with uncertainty” (Moorthy, Png, 1992, p. 358). In the presence of high market uncertainties, it is valuable to retain flexibility, or the so-called “real options” (Huchzermeier, Loch, 2001), so that the firm can make better decisions based on their observations of the market. Regarding market payoff variability, the market’s willingness to pay is uncertain and depends on how the market perceives its style, brand, or environmental friendliness, etc, and also on the uncertain wealth level of the market itself. Consider the example used in Moorthy and Png, 1992 concerning hardcover and paperback versions of the same book. If the first version of the book turns out to be very popular, it may be a good idea to charge a relatively high price for the next version. If the book is very unpopular, it may be a good idea to charge a relatively low price or simply cancel its release. Therefore, commitment contradicts the real options thinking prevalent in both academic literature and business practice. In this paper, we study the introduction sequence in an uncertain market with functionality thresholds. We show that a low-end product may be introduced first, for purely marketing reasons, in a stochastic environment. 1. The Stochastic Model of Real Options 1.1. Model Conception In the literature, high-end consumers are considered “better” consumers because they have a higher willingness to pay (WTP). Consequently, a low-end product threatens a high-end product but not vice versa. With functionality thresholds, high-end consumers are not only wealthier (“better”) but also choosier (“worse”). Consequently, low-end consumers cannot afford to buy a high-end product 11
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(same as in literature), but, also, high-end consumers would not buy a low-end product which is useless to them. In the literature, the very fact that high-end consumers are “better” consumers makes it unattractive to introduce a low-end product first: a low-end product that is affordable to low-end consumers in the first period, prevents the firm from exploiting the higher WTP of the high-end consumers (this holds true with or without commitment). With functionality thresholds, it is not as dangerous to introduce a low-end product first. High-end consumers will not buy the lowend product even if no announcement about the high-end product is made. 1.2. Model Setup There are two groups of consumers, high-end consumers and low-end consumers with known f , f f > f l . Consumers will only purchase products that satisfy functionality thresholds h l , where h their functionality thresholds. Since our goal is not to study the introduction sequence in an exhaustive manner, but to demonstrate that it can be optimal to introduce a low-quality product first under certain conditions, we take product qualities as given in this paper. This applies to, for example, a situation in which a firm enters a new market with an existing product, or situations in which product qualities are set by industry standard. The quality of hardcover or paperback books can be seen as given, not decision variables. The quality of certain raw material or the capability of machines is also determined by industry standards the firms must accept. The firm has two products with qualities q h , ql that satisfy the functionality thresholds of the two segments: q h > f h , ql > f l . The two products have unit production cost of c h , cl , respectively.
We will now make several other restrictive but plausible assumptions. We assume q l < f h : the quality of the low-end product does not satisfy the functionality thresholds of the high-end product and, therefore, poses no cannibalization threat to the high-end product. We further assume that the production cost of a high-end product surpasses the purchasing power of all low-end consumers and that no low-end consumer can afford the high-end product even if it is sold at cost. That is, a highend product poses no cannibalization threat to a low-end product, a property agreed to by the literature. Thus, the two segments are decoupled and cannibalization does not happen. The demand for the low-end product is described by the standard demand function Dl = bl − al p l , in which a l is
a a uncertain and can take two values: l with probability J, l with probability 1-J. The uncertainty of al can be caused by uncertain wealth level of the market or uncertain popularity of the products.
a − al constant, a greater l means greater market uncertainty (Huchzermeier and a − al a + al Loch 2001). Keeping l constant, a smaller l means a wealthier market. A greater J means that a firm is more optimistic about the market (Huchzermeier and Loch 2001). The demand D = bh − a h p h , in of the high-end product is also described by the standard demand function h a a which a h is uncertain and can take two values: h with probability J, h with probability 1-J. This model allows demand to change continuously with price, and captures the fact that the consumers within each segment have heterogeneous WTP. The WTP across two segments are perfectly correlated: if the market is poor in the high-end segment, it is poor in the low-end segment as well, and vice versa. If we have imperfect correlation, the conclusions will not change as long as the correlation is sufficiently high. For simplicity in analysis, we also assume that the product sold Keeping
al + al
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at cost would generate positive demand for target market even if the market condition turns out to be unfavourable: Dl = bl − al cl > 0 , Dh = bh − a h c h > 0 .
There are two periods, the first period and the second period. The discount factor is δ . The firm has three choices to introduce two products: (a) simultaneously introduce both products in the first period; (b) introduce the high-end product in the first period, observe the market and decide on a low-end product in the second period; or (c) introduce a low-end product in the first period, observe the market and decide on a high-end product in the second period. In the two sequential approaches, the firm launches a product in the first period based on belief about a , observes the value of a , and decides on the other product in the next period based on the observed value of a . Not only is the model is easy to analyze this way, it is in fact sufficient for the purpose of the paper: to show that it can be optimal to introduce a low-end product first purely for marketing reasons. In a more general model with qualities as decision variables, there will be more results than in current paper. However, results from the current paper will remain valid because we take optimal quality levels from the more general model and define them as the given qualities in this paper. For results in this paper to be robust, the product technology and market space need to remain stable. The model does not apply to industries with rapid technology evolution or rapid change in market space. 2. Profits from the Three Approaches In this section, we calculate the total profits from these three approaches. Since the two segments are now decoupled due to their different quality requirements and WTP, the problem essentially becomes one under Piguovian Third Degree Discrimination (PTDD) in which “the firm decides what marketing program each segment must receive…” (Moorthy, 1984, p. 288). 2.1. Profit from Simultaneous Introduction When the firm introduces both products simultaneously in the first period, the profit is: E (π ) = J [ ( p h − c h )(bh − a h p h ) ] + (1 − J ) [ ( p h − c h )(bh − a h p h ) ] J [ ( pl − cl )(bl − al pl ) ] + (1 − J ) [ ( pl − cl )(bl − al pl ) ]. The optimal price and profit can be written as: bl + 2cl J al + 2cl (1 − J )al bh + 2ch J ah + 2ch (1 − J )ah * * , , pl = ph = 2 J al + 2(1 − J )al 2 J ah + 2(1 − J )ah
πh
*
[b =
h
+ 2c h J a h + 2c h (1 − J )a h 4 J a h + 4(1 − J )a h
], 2
πl
*
[b + 2c J a = l
l
l
+ 2cl (1 − J )al
(1)
]
2
4 J al + 4(1 − J )al
π simu = π h* + π l *
(2)
2.2. Profit from Sequential Introduction with a High-End Product Introduced First
When a high-end product is introduced first, the optimal price of the high-end product is the same as in simultaneous introduction, and the price of the low-end product is determined after observing π = ( pl − cl )(bl − al pl ) the market. If the market turns out to be wealthy, the profit function is l . bl + 2cl al ** pl = . 2a l If the market turns out to be poor, the The optimal price for the wealthy market is 13
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profit function is π l = ( pl − cl )(bl − al pl ) . The optimal price for the wealthy market is bl + 2cl al ** pl = . 2a l Considering the probability of a wealthy market or poor market, the undiscounted profit from the low-end product is 2 2 bl + 2cl al bl + 2cl a l ** + (1 − J ) πl = J 4a l 4a l . (3) Therefore, the total profit is π high = π h * + δπ l ** . (4)
[
]
[
]
2.3. Profit from Sequential Introduction with a Low-End Product Introduced First
When the low-end product is introduced first, with exactly the same procedure used to obtain
π high
, we can obtain the total profit π low = π l * + δπ h **
π h ** = J
[b
h
+ 2c h a h 4a h
Where
]
2
+ (1 − J )
[b
h
+ 2c h a h 4a h
(5)
]
2
.
2.4. The Value of Real Options
The value of real options for a low-end product is: 2 (al − al ) 2 bl J (1 − J ) ** * πl −πl = 4al al J al + (1 − J )al . (6) The value of real options for the high-end product is 2 (a h − a h ) 2 bh J (1 − J ) ** * πh −πh = 4a h a h J a h + (1 − J )a h . (7) Simple algebra reveals that both values increase with market uncertainty and market wealth.
[
]
[
]
3. Comparisons of the Three Approaches
In this section, we will compare these three approaches. We will outline the range of discount factors with which each approach is optimal. The range depends on the first period and second ** * ** * period profits of both products. Since this is essentially a PTDD problem, ( π h , π h ) and ( π l , π l ) become two interchangeable pairs, and the two products are, in a sense, “symmetric”. With simple algebra, we obtain the following result: ** ** * * If π h ≥ π l and π h > π l , the optimality conditions of the three approaches are given as:
π l* π h* δ ≤ min( ** , ** ) ⇔ π simu ≥ max(π high , π low ) πl πh
(8)
π l* π h* − π l* δ ≤ ≤ ⇔ π high ≥ max(π simu , π low ) π l** π h** − π l** (here, the range of δ can be an empty set).
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π h* − π l* π h* δ ≥ max( ** , )⇔ π low ≥ max(π simu , π high ) π h − π l** π h** . If
(9)
π h ≥ π l and π h ≤ π l , the optimality conditions of the three approaches are given as: **
**
*
*
π h* δ ≤ ** ⇔ π simu ≥ max(π high , π low ) πh δ≥
(10)
π ⇔ π low ≥ max(π simu , π high ) π * h ** h
If π h ≤ π l **
δ ≤ min(
**
*
π l* π h* , )⇔ π simu ≥ max(π high , π low ) π l** π h**
(12)
π π −π , )⇔ π high ≥ max(π simu , π low ) π π −π
(13)
δ ≥ max(
* l ** l
* l ** l
π π −π ≤δ ≤ π π −π * h ** h
* l ** l
If π h ≤ π l **
(11)
and π h < π l , the optimality conditions of the three approaches are given as: *
**
* h ** h
* h ** h
⇔
π low ≥ max(π simu , π high )
.
(14)
and π h ≥ π l , the optimality conditions of the three approaches are given as: *
*
δ≤
π l* ⇔ π simu ≥ max(π high , π low ) π l**
δ≥
π ⇔ π high ≥ max(π simu , π low ) π .
(15)
* l ** l
(16) From the analysis, we can see that it can be optimal to introduce a low-end product first regardless whether the low-end product is more profitable or not, in the first period or in the second period. Introducing a low-end product becomes more attractive when π h or π l decreases or π l *
**
*
or
π h increases. If the firm commits all prices in advance (credible announcement), there is no need to wait and the products should be introduced simultaneously. When the low-end product poses no cannibalization threat to the high-end product, then the ability to charge a higher price for the highend product in the absence of a low-end product is no longer relevant. 4. The Impact of Fixed Cost When the firm decides to launch a product, there is a volume independent sink cost, which may be quite important compared to all margins recovered from selling the product. Normally this fixed cost increases with quality, due to investment in superior equipment to accommodate higher quality (Banker et al. 1996). There is a simple way to represent the model with fixed cost. We still use π h ** > π h * and π l ** > π l * to represent the first period and second period profit after deducting the **
fixed cost from profits calculated in Section 4. Since the results in the previous section concerning ** * ** * the optimal approach depend on π h , π h , π l , π l only, all the results will still be valid. There is a key difference though if abandoning option is exercised. When a product is not introduced in the first period, and the profit of this product in the worst case scenario in the second period is negative, the firm should abandon its launch. In that case, the profit from the product launched in the second 15
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period only contains the profit from the best case scenario. The rest of the analysis in the previous section will still hold. Note that if no abandoning option is exercised (profit is positive even in a ** * ** * worst case scenario), then π h − π h or π l − π l is not impacted by the presence of fixed cost. If the abandoning option is exercised, then π h − π h or π l − π l increases with fixed cost. **
*
**
*
Conclusions
This paper uses a simple model to add two important elements to the introduction sequence literature: functionality thresholds and stochastic environment. In the literature, the very fact that high-end consumers are “better” (wealthier) consumers makes it unattractive to introduce a low-end product first; because a low-end product affordable to low-end consumers in the first period, prevents the firm from exploiting the higher WTP of the high-end consumers. With functionality thresholds, high-end consumers are not only wealthier (“better”) but also choosier (“worse”). Consequently, high-end consumers will not buy a low-end product even if no announcement about a high-end product is made. Due to the existence of functionality threshold, the ability to charge a higher price for the high-end product in the absence of a low-end product (Moorthy and Png, 1992; Krishnan and Gupta, 2001) is no longer relevant because the low-end product poses no cannibalization threat. The dominance of simultaneous introduction in the first period over introducing a low-end product before a high-end product (Moorthy and Png, 1992) no longer holds, because the low-end product introduced first does not appeal to the high-end segment. The product launched first provides valuable information for the forthcoming product in a stochastic environment, or the so called real options. With several other restrictive but plausible assumptions, we construct the problem into a PTDD problem. The goal is not to address the introduction sequence problem in an exhaustive manner, but to offer an alternative perspective on when it may be a good idea to introduce a low-end product first for purely marketing reasons. In this model, we take product qualities as given in this paper. This applies to, for example, a situation in which a firm enters a new market with an existing product, or situations in which product qualities are set by an industry standard. When quality is the decision variable, our model states that the firm is able to avoid cannibalization if it chooses to sufficiently differentiate its products (with the models in the literature, the firm is unable to avoid cannibalization). Even though it remains unclear when the firm may find it advantageous to avoid cannibalization, results from the current paper will remain valid if the optimal quality levels indeed exclude cannibalization. We obtain the following results in this paper: In an uncertain environment, the firm may find it advantageous not to make commitment and to maintain flexibility, or so called “real options”, when making introduction sequence decision. Introducing a low-end product first may be the best option if it can provide valuable market information for better decision about a high-end product. The more lucrative the high-end segment is, the more there is to gain from such market information update. If the benefit outweighs the loss of delaying profit from this segment, it is worthwhile to introduce a high-end product after a lowend product. If there is a sink cost that increases with product quality, introducing a low-end product first implies that there is less to lose in case the market condition turns out to be unfavourable. We analyze products differentiated in quality. But since the analysis is essentially a model of PTDD, the results may apply to other situations with PTDD as well, such as launching products across several geographically segmented markets. For example, launch sequence decision, the relative sequence of introducing products into Japan, US and Western Europe, is very important for multinational companies.
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This model may find applications in many real situations. When a firm enters new markets with existing products, there may be high market uncertainty in some emerging markets due to distinctive cultures, very different economy structures, or unreliable statistics. For example, in 2006, China recalculated its GDP and raised it by 16.7%, and in 2007, the World Bank recalculated China’s GPD by purchasing power parity and reduced it by 40%. China also has an economic structure and culture very different from the West. When introducing products into such markets, it may not be a good idea to introduce a high-end product first, since market analysis is very unlikely to be reliable. It is better to use a low-end product to test the waters first, as many multinationals have done. This is also the insight we add to existing papers which propose to delay introduction to learn more about the market: certain market information can only be learned after a product is introduced, no matter how good the market analysis is before introduction. Another application is introduction sequence into isolated markets, that is, several markets with no connection with one another. For example, the US, Europe and Japan are three major markets for iPhone, and product introduced in one market cannot be used in another; however, market information learned from one market can be used for better pricing in the other two markets. iPhone is introduced first in the US, the home market of the firm and the market with the lowest uncertainty. This model has several limitations. First, functionality thresholds, while not uncommon, do not exist for all products (books, for example). Even if functionality thresholds do exist, whether and when firms will use this property to avoid cannibalization remains unknown. Regarding market information provided by another product, in practice, there is no perfect correlation between different products. Therefore, the ability to use one product to provide market information for another product is limited. In addition, the assumption of perfect correlation and the assumption of no cannibalization in a sense contradict each other: the more similar these two products are, the more useful market information will be, but the more likely they are to cannibalize. The issue of reputation is also important: a low-end product introduced first may give the consumers the impression that it is a low-end firm and have a negative impact on future launches. Consumers may buy more than one unit: they may first buy a low-end product to try it out, and buy the high-end one or upgrade to it later on. Despite these limitations, this model shows that a low-end product may be introduced first, even if a high-end product is available at the same time, which is the purpose of this paper. This study assumes no cost relationship among products. If we add a common platform, the results can be different. We exclude technology uncertainty and focus mainly on market uncertainty. Since literature on design flexibility with technological uncertainty (Krishnan and Bhattacharya, 2002; Bhattachaya et al., 1998) is already available, further study on introduction sequence with technological uncertainty is a hopeful direction. References Adner, R.; Levinthal, D. (2001). Demand heterogeneity and technology evolution: implications for product and process innovation. Management Science, 47, 611-628. Banker; Khosla; Sinha. (1998). Quality and competition. Management Science, 44, 1179-1192. Bhattachaya, S.; Krishnan, V.; Mahajan ,V. (1998). Managing new product definition in highly dynamic environments. Management Science, 44, 50-64. Bhattachaya, S.; Krishnan, V.; Mahajan, V. (2003). Operationalizing technology improvement in product development decision-making. European Journal of Operational Research, 149, 102-130. Huchzermeier, A.; Loch, C. (2001). Project management under risk: using the real options approach to evaluate flexibility in R&D. Management Science, 47, 85-101. Kalish, S.; Lilien, G. (1986). A market entry timing model for new technologies. Management Science, 32, 194205. Krishnan, V.; Bhattachaya, S. (2002). Technology selection and commitment in new product development: the role of uncertainty and design flexibility. Management Science, 48, 313-327.
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Krishnan, V.; Gupta, S. (2001). Appropriateness and impact of platform-based product development. Management Science, 47, 52-68. Krishnan, V.; Singh, R.; Tirupati, D. (1999). A model-based approach for planning and developing a family of technology-based products. Manufacturing & Service Operations Management, 1, 132-156. Krishnan, V.; Zhu, W. (2006). Designing a family of development-intensive products. Management Science, 52, 813-825. Moorthy, K. (1984). Market segmentation, self-selection, and product line design. Marketing Science, 3, 288-307. Moorthy, K.; Png, I. (1992). Market segmentation, cannibalization, and the timing of product introductions. Management Science, 38, 345-359. Probert, J.; Schütte, H. (1999). BASF in China: the Marketing of Styropor. INSEAD Case. Rosenberg, N. (1976). On technological expectations. The Economic Journal, 86, 523-535. Tirole, J. (1988). The Theory of Industrial Organization. Cambridge: MIT Press. Short biographical note Paul Lacourbe holds a PhD in Operations Management from INSEAD, and is currently an assistant professor at ESSEC.
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