Multiproduct Pricing and Product Line Decisions with Status Externalities

I. Introduction

Socrates is credited with saying that a good reputation is "the richest jewel you can possibly be possessed of." The importance of reputation is underlined in the economics literature, which focuses on two approaches to reputation (Cabral, 2005). The first approach, with hidden action, models repeated interaction and typically features moral hazard. It explores situations where a particular agent is expected to do something, such as breach a price fixing agreement. The second approach, with hidden information, models situations where a particular agent is thought to be something, such as a producer of high quality products, and typically features adverse selection (Cabral, 2005).

In contrast to the above two strategies, we approach reputation as an idea involving status. Specifically, we explore the reputation of luxury brands and consider the effects of status externalities on the product line and pricing decisions of a monopolist selling status goods. There exists a demand for status goods, because for some it is desirable to be associated with wealth. According to Young, Nunes, and Dr´eze (2010), Thorsten Veblen argues in ‘The Theory of the Leisure Class' (1899) that status is not exposed through the accumulation of wealth, but through its wasteful exhibition, described as "conspicuous consumption."

In order for conspicuous consumption to be effective, branding is utilized so that other consumers are able to recognize the status of the product. Young, Nunes and Drèze define brand prominence as "the extent to which a product has visible markings that help ensure observers recognize the brand." Products are attributed to having conspicuous or discrete branding. The relative conspicuousness of the branding attracts different types of customers and reflects the different signaling intentions of the consumer (Young, Nunes, and Drèze, 2010).

Young, Nunes and Drèze (2010) propose a taxonomy which assigns consumers into four groups, based on wealth and need for status. The set consists of patricians, parvenus, poseurs and proletarians. Patricians have wealth and a low need for status. They want to be associated with other patricians and pay a premium for inconspicuously branded products that use signals interpretable by only other patricians. Parvenus have wealth, and due to their need for high status they engage in conspicuous signaling. Their main concern is to be dissociated from the have-nots, whilst being associated with the wealthy. A luxury brand must make parvenus believe that proletarians and poseurs will know the brand and will recognize its consumer as wealthy. Poseurs have no wealth, but high need for status. They want to be associated with those recognizably wealthy, the parvenus, and dissociated from the have-nots. However, they cannot afford authentic luxury goods and therefore purchase counterfeit luxury products that act as inexpensive substitutes. The proletarians have no wealth and no need for status. They neither want to associate nor dissociate with any of the other groups (Young, Nunes, and Drèze, 2010). By varying the price and conspicuousness of their brand, luxury goods manufacturers can target different types of consumers.

The demand for consumer goods and services can be broken down into functional and nonfunctional demand. Whilst functional demand is the part of the demand for a commodity which is due to the qualities inherent in the commodity itself, nonfunctional demand is that portion of the demand for a commodity which is due to factors other than the qualities inherent in the commodity (Leibenstein, 1950).

We categorize two types of nonfunctional demand. The first type is concerned with the Veblen effect, a phenomenon of conspicuous consumption, where there exists a willingness to pay a higher price for a functionally equivalent good with the intent to signal status (Bagwell and Bernheim, 1996). Whilst the Veblen effect is a function of price, the second type of nonfunctional demand is concerned with the "bandwagon" and "snob" effects, in which the utility derived from the commodity is respectively enhanced or decreased due to others consuming that commodity (Leibenstein, 1950).

The bandwagon effect causes an individual's demand for a commodity to increase when consumers in general or a specific group of individuals in the market demand more of the commodity. It represents the desire of people to purchase a commodity in order to be fashionable and to imitate people they want to be associated with. The snob effect is the reverse, in that the individual consumer's demand is negatively correlated with the total market demand. This represents the desire of people to be exclusive (Leibenstein, 1950). These effects have in common that the consumption behavior of any individual is not independent of the consumption of others.

Similar effects are described in the public policy literature. Positional goods are goods for which consumers are primarily concerned about relative consumption, and they are contrasted with nonpositional goods for which the consumer's main concern is his or her absolute consumption. Frank (2005) suggests that economic models in which individual utility depends only on absolute consumption imply optimal allocation of positional and nonpositional goods. He argues, however, that economic models in which individual utility depends not only on absolute consumption, but also on relative consumption, predict in equilibrium too much expenditure on positional goods and too little on nonpositional goods, due to the expenditure arms races focused on positional goods (Frank, 2005).

This paper analyses a situation where demand is a function of the consumption of others. This leads to the idea of "non-additivity", as discussed in Frank (2005), which occurs when the market demand curve is not the lateral summation of the individual demand curves. We explore the product line and pricing decisions under the assumption of two status externalities. Specifically, the firm sells a low-end product and a high-end product to two segmented consumer groups and must decide whether to brand the products jointly or separately. If the firm sells the products under the same brand, sales of the high-end product positively affect the demand for the low-end product, whereas the sales of the low-end product negatively affect the demand for the high-end product. These effects arise due to the existence of status externalities, which arise under the assumption that sales of different products under the same brand have heterogeneous effects on the status reputation of the brand. Whilst a luxury brand may have high short-term sales by establishing a lower price line, this will diminish the exclusiveness associated with the brand. The following two examples explore benefits and costs of introducing low-end products.

Through the simultaneous introduction of the iPhone 5S and 5C, which occurred on the same day, Apple signaled a link between the two products. This link is further strengthened by the numerical component of the product names. However, as is apparent by the alphabetic component of their names, the two products are also differentiated. The more expensive 5S has more features, such as a fingerprint scanner. However, from a branding perspective the most important difference in the products is their appearance. Apple's decision to utilize two separate materials and color schemes makes them distinguishable to the consumers. The 5S has an aluminum case and is available in the colors gray, silver and gold, which are traditionally associated with luxury. The less expensive 5C is built with a plastic case and is available in the colors blue, green, pink, yellow and white.

Apple is hoping to use the 5C to address emerging markets, especially China, where the majority of smartphone growth is projected to be in the low-end market. Apple entered a multiyear agreement with China Mobile, the world's largest mobile services provider by network scale and subscriber base, which serves over 760 million customers. As a result, the 5S and the 5C will be available in China Mobile and Apple retail stores across mainland China beginning in early 2014. This illustrates the increasing relevance of the Chinese market, which Apple CEO Tim Cook has described to be "extremely important" (Apple, Inc., 2013).

However, by moving towards the low-end market, Apple will possibly encounter difficulties. On the one hand there may be challenges capturing the Chinese low-end market because the 5C's price of $739 is relatively high compared with smartphones currently available in China, such as those from Huawei, Coolpad and ZTE, which are offered for less than $100 (Pfanner and Chen, 2013). On the other hand, since the 5C is relatively inexpensive compared to Apple's other products, its introduction may deter customers who value Apple's high status.

The product line of the luxury vehicle manufacturerMercedesBenz offers a further example of a traditional high-end brand targeting lower markets. In 2012, Mercedes-Benz began marketing the CLA-Class, which has a starting price of $29,900 and is the brand's lowest priced model to have entered the United States automobile retail market. The CLA-Class is expected to be Mercedes' bestselling model and has been called the company's current "most important car". In addition to the expected increased revenue from the low-end market, this market's current clients will potentially become loyal to the brand and purchase higher priced models in the future. However, Mercedes-Benz must weigh the risks involved in targeting a more affordable market, since it may potentially deteriorate their high-end reputation (Stock, 2013).

Externalities associated with status products are not limited to the products of a single firm, but expand to the realm of two firms selling products that exhibit links to each other. In this case the status externalities could arise due to the product distribution's geographic proximity or close similarity in the product's design, which result in a strong association between the products. However, in these cases the status externalities are not internalized. An example is the market for counterfeits, where the two groups are the authentic producers and the counterfeiters.

Qian (2011) uses 1993-2004 product-line-level panel data on Chinese shoe companies to study the heterogeneous effects of counterfeit entry on sales of authentic products. The net effect of counterfeits on authentic product sales depends on the interplay of the negative substitution effects for authentic products and the positive advertising effects for a brand. The advertising effects arise when counterfeits enhance brand awareness and generate publicity for the brand, which signals brand popularity (Qian, 2011).

Qian (2011) finds that the advertising effect outweighs the substitution effect for the sales of high-end authentic products, which are less of a substitute for counterfeits. On the other hand, she finds that the substitution effect outweighs the advertising effect for low-end product sales. The net effect can vary even within the same brand. The net effect also differs between usage types. The positive advertising effect is most pronounced for high-fashion products, products tailored to a younger clientele, and products of younger brands that are less established at the time of the infringement (Qian 2011).

Qian (2011) gives recommendations for policy and business based on the heterogeneous impacts of counterfeiting. Counterfeiting incentivizes authentic brands to upgrade their quality and signal higher quality to ensure that consumers can differentiate the authentic product from the counterfeits. The focus of intellectual property rights enforcement should be directed toward counterfeits that are substitutes for authentic products. In addition, relatively fewer enforcement resources can be devoted to products that benefit from the positive advertising effect (Qian, 2011).

Qian (2011) states that her findings, that the entry of counterfeits has both a negative substitution effect and a positive advertising effect, can be applied beyond the realm of counterfeiting. Since in this paper we assume the markets are completely segmented, the substitution effect does not apply to our model. In addition, applying the positive advertising effect to product lines suggests that sales of a low-end product positively affect the demand for the high-end product. However, in this paper we assume a negative reputation effect on the status of the established brand and that sales of a low-end product negatively affect the demand for the high-end product. In addition, in our analysis the externalities are internalized.

In this paper we consider the product line and pricing decisions of a multiproduct monopolist under the assumption of status externalities. We compare the case in which the firm sells the two products with different brands to the case in which the firm sells the two products under the same brand. If the products do not share a common brand, then there are no status externalities. We perform comparative statics using the implicit function theorem to study the characteristics of the market. We examine how prices change due to changes in the externalities. We find that jointly branding products that were previously sold with different brands is associated with a decrease in the price for the high-end product and an increase in the price for the low-end product.

II. The Model

An additively separable model is used to explore a multiproduct monopolist's product line and pricing decisions of two differentiated status products, under the explicit assumption of two externalities. Specifically, whilst the sales of product 1 positively affect the demand for product 2, the sales of product 2 negatively affect the demand for product 1. The markets are completely segmented, due to which there is not spillage.

We implicitly assume product 1 is of higher quality and has higher status than product 2. We implicitly assume that the status externalities arise because the brand's status is associated with the average wealth of the brand's consumers. All consumers have preference to purchase from a brand whose clientele consists of wealthy consumers. The consumers of product 1 are wealthy, whereas the consumers of product 2 are not wealthy. Therefore, an increase in purchases by consumer 1 from the brand increases the average wealth of the brand's consumers and demand for product 2 increases. However, an increase in purchases by consumer 2 from the brand decreases the average wealth of the brand's consumers and demand for product 1 decreases.

We also implicitly assume that the two externalities are linked to network externalities. The bandwagon effect causes the demand of consumer 2 for product 2 to increase when consumer 1 purchases more of product 1, because it is desirable for consumer 2 to be fashionable and to purchase a product from the status brand from which wealthy consumers purchase products. However, due to the snob effect the demand of consumer 1 for product 1 is negatively related to sales of product 2, because consumer 1 values exclusivity.

The demand functions for product 1 q₁ and product 2 q₂ are linear combinations of the component of demand that is a function only of the own price of that product, respectively D*₁(p₁) and D*₂(p₂), and the component of demand given by the externality of the other good, respectively − Β₁q₂ and −Β₂q₁, a change in which implies a shift in respectively q₁ and q₂. By the law of demand in both cases there is a negative relationship between the own price and quantity demanded. We assume D*'₁(p₁), D*'₂(p₂) < 0

We also assume that D*'₁(p₁) and D*'₂(p₂) are twice continuously differentiable and that D*''₁(p₁), D*''₂(p₂) < 0. That is, we assume the demand functions for product 1 and product 2 to be strictly concave (Mas-Colell, Whinston, and Green, 1995).

A demand function being strictly decreasing and strictly concave implies that for a given price change in absolute terms, the price change is associated with a larger decrease in the quantity demanded if the price change occurs at a higher price than if it were to occur at a lower price.

We think this is a reasonable assumption in the market for luxury goods. Starting at a low price, a price increase may initially be associated with only a small decrease in the quantity demanded due to customer loyalty and because other luxury products may not be perfect substitutes. Starting at a low price, a price decrease may be associated with only a small increase in the quantity demanded since consumers' demand may already be saturated (Scott, 1997).

However, starting at a high price a price increase may be associated with a large decrease in the quantity demanded, since consumers are increasingly deterred from purchasing the good. Consumers may choose to purchase a similar luxury good from a substitute luxury brand or choose not to purchase a luxury good at all since it is not considered a necessity. We rewrite the demand as functions of p₁ and p₂.

The magnitudes of the externalities are measured by Β₁, Β₂. To assure that q₁,q₂ ≥ 0, we restrict 0 ≤ Β₁ ≤ D*₁(p₁)/D*₂(p₂). Note that if Β₁ = 0, then q₁ = D₁(p₁, q₂) = D*₁(p₁). Similarly, if Β₂ = 0, then q₂ = D₂(p₂, q₁) = D*₂(p₂). We implicitly assume that not branding the products together implies that Β₁ = Β₂ = 0.

implies that (1=(2=0. Given the above assumptions the price effects are:

The relationship between p₂ and q₁ is that which we would expect in the case of substitutes, whereas the relationship between p₁ and q₂ is that which we would expect in the case of complements.

Let R₁ and R₂ be the respective revenues generated through sales of products 1 and 2.

Let the total revenue be R = R₁ + R₂

Let the total cost be given by C(q₁, q₂) = F + c₁q₁ + c₂q₂, where F is a constant shared fixed cost, and c₁, c₂ are constant per unit costs, such that c₁ > c₂, since product 1 is the status good, which is of a higher quality that product 2. We rewrite the total cost C as a function of p₁, p₂.

Let profit π be a real-valued function of p₁, p₂. Let π : A ⊂ R² → R, where A = {(p₁, p₂) ∈ R² | 0 < p₁, p₂ < ∞}.

We want to determine the maxima of π. A point p₀ ∈ A is a critical point if π is differentiable at p₀ and if D_π(p₀) = 0 (Marsden and Hoffman, 1993). We take the partial derivatives of π with respect to of p₁ and p₂ and set the partial derivatives equal to zero.

If p₀ is an extreme point, either a local minimum or a local maximum for π, then p₀ is a critical point. However, if p₀ is a critical point, it does not necessarily imply that p₀ is an extreme point (Marsden and Hoffman, 1993). Furthermore, even if p₀ is an extreme point, we want to test that at this point π is maximized. We check whether the second order condition is satisfied, that is the Hessian matrix of second derivatives is negative definite. The Hessian matrix is:

We evaluate the partial derivatives at p₀ = (p^m₁ , p^m₂ ):

First we note that both diagonal elements are negative. This is assured through our assumption that

Second, we want to check that the determinant of the matrix is positive. The determinant is:

We cannot sign the determinant in general. However, evaluated at Β₁ = Β₂ = 0, the determinant is positive:

We assume that at p₀ π is maximized in general. We denote the multiproduct optimum. The multiproduct monopolist chooses the multiproduct monopoly prices p^m₁ and p^m₂ which determine the multiproduct monopoly outputs q^m₁ and q^m₂. The two equations below implicitly define the multiproduct monopoly prices p^m₁ and p^m₂ as functions of β₁ and β₂

We will now calculate the single product monopoly optimum. If the firm operates only in the high-end market q₂ = 0 and q₁ = D*₁(p₁). The revenue generated through sales of product 1 is R₁ = p₁q₁ = p₁D*₁(p₁). Given that F₁ is the constant fixed cost, and c₁ is the constant per unit, the total cost in terms of p₁ is C = F + c₁D*₁(p₁).

Let profit π be a real-valued function of p₁. Let π : A ⊂ R →, where A = {p₁} ∈ R | 0 < p₁ < ∞}, π(p₁) = (p₁ - c₁)D*₁(p₁) - F. We want to determine the maxima of π. A point p₀ ∈ A is a critical point if π is differentiable at p₀ and if D_π(p₀) = 0 (Marsden and Hoffman, 1993). We take the partial derivative of π with respect to p₁ and set it equal to zero.

The second order condition is satisfied, because the second derivative is negative.

Therefore, the single product monopolist chooses the single product monopoly price p^S₁, which determines the single product monopoly output q^S₁.

Similarly, if the firm operates only in the low-end market, then q₁ = 0 and q₂ = D*₂(p₂). In this case, the single product monopolist chooses the single product monopoly price p^S₂ which determine the single product monopoly output q^S₂.

The single product monopoly pricing for a firm which operates either only in the high-end market or only in the low-end market, which results in zero sales of the other product, is equivalent to the multiproduct monopolist optimum when the demands are independent, β₁ = β₂ = 0. There are no externalities if the products do not share a common brand. If the multiproduct monopolist separately brands the two products, the respective demands are:

The first order conditions are:

We define ε^S₁₁ = ∂q₁/∂p₁ p₁/q₁ and ε^S₂₂ = ∂q₂/∂p₂ p₂/q₂ to be the respective price elasticity of demand for the case where the products are branded separately. We rewrite the first order conditions:

In the case where externalities exist, the two equations below implicitly define the multiproduct monopoly prices p^m₁ and p^m₂ as functions of β₁ and β₂.

The price elasticity of demand is:

The cross-price elasticity of demand is:

As for substitutes ε^m₁₂ is positive and as for complements ε^m₂₁ is negative. The cross-price elasticity of demand is zero if the demands are independent, which is the case if β₁ = β₂ = 0.

We rewrite the first order conditions for the case where the products are jointly branded and solve for price:

Since a monopolist does not produce on the inelastic portion of the demand curve, ε^m₁₁, ε^m₂₂ < −1 (Pindyck and Rubinfeld, 2009). Therefore, all else equal an increase in β₂ is associated with a decrease in p^m₁, whereas all else equal an increase in β₁ is associated with an increase in p^m₂. This analysis is possible since ε^m₁₁ is independent of β₂ and ε^m₂₂ is independent of β₁.Continued on Next Page »