Multiproduct Pricing and Product Line Decisions with Status Externalities

By Frederick B. Zupanc
The Developing Economist
2015, Vol. 2 No. 1 | pg. 2/2 |

III. The Effect of Changes in Externalities on Pricing

This section examines how prices change due to changes in the magnitude of the spillover parameters. However, we first explore possible reasons for the existence of and changes in the externalities. We implicitly assume that the externalities exist due to a link between the low-end and the high-end products, as well as a link between the two groups of consumers. Due to the links consumers associate the low-end product with the high-end product. Therefore, a change in the sales for the one product will result in a change in the demand of the other product. An increase in the links is associated with an increase in the size of the externalities. The links are based on the interaction of the two consumer groups during which the product, which jointly branded with the product that can the purchased by the other consumer group, is displayed. Marketing can be used to alter the intensity of the link.

We assume implicitly that the link between the two groups of customers is affected by the extent to which the two groups of customers have information about each other's purchases. This depends on how frequently the two groups interact, since through interaction the purchase decisions are exhibited. The interaction is not limited to direct in-person interaction, but can occur indirectly via various media. The frequency of the interaction may be limited due to geographic or social barriers.

In addition to the frequency of the interactions between the two groups, we consider the extent to which the products are displayed throughout these interactions. Therefore, an additional factor that has an effect on the magnitude of the externalities is whether the products are consumed privately or publically. Products that are frequently displayed in public, such as accessories or smartphones, are associated with larger status externalities in absolute value than products that are usually consumed in private, such as furniture.

Furthermore, a link is established between the low-end and high-end products if the firm sells the two products under the same brand. If the products have recognizable similar features, such as name, logo, and design, the products will have a shared identity and therefore influence each other's reputation. In the case of status externalities, if the brand is associated with exclusiveness, a lower priced product may diminish the exclusivity and possibly decrease the value of the brand, since high-end exclusive customers want to dissociate themselves from the other group. If the firm brands the products separately, we assume that the link does not exist, β1 = β2 = 0, and neither the positive spillover β2 q1 nor the negative spillover β1 q2 would be experienced. The firm's decision to brand the products jointly or separately depends on the relative importance of the markets. The firm could also have sub-brands or luxury and regular product lines.

Furthermore, marketing can communicate to consumers the extent to which the products are similar or dissimilar, and therefore alter the link. The firm can, for example, advertise the exclusiveness of the high-end product. The firm can also advertise the products together and underline their similarities. In addition, high volumes of advertisement and prominent branding are associated with larger externalities because this results in the brand being more known and recognizable by the public. The firm may consider utilizing advertisement to minimize the magnitude of the negative externality β1 and maximize the magnitude of the positive externality β2.

We perform comparative statics using the implicit function theorem. The equilibrium prices p1 and p2 are implicitly defined as functions of β1 and β2 in the two equations that are yielded through the first order conditions.

We restrict F1 and F2 to the level set where F1,F2 = 0, values of p1, p2, β1, and β2 such that F1, F2 = 0, and denote the restriction Fr1 and Fr2. The partial derivatives of Fr1 and Fr2 with respect to p1, p2, β1, and β2, are equal to the partial derivatives of F1 and F2 with respect p1, p2, β1, and β2, however, the manipulation is simplified.

We want to determine the sign of each component of the matrix of partial derivatives of price with respect to β1, β2. To do so we calculate an expression for each component.

Based on our current assumptions, the signs of two of the below partial derivatives cannot be determined.

In each of the entries of the matrix below the sign of one of the partial derivatives cannot be determined. The two partial derivatives whose sign cannot the determined are equal, ∂Fr1/∂p2 = ∂Fr2/∂p1. Therefore, their product is either zero or positive. However, if their product is a nonzero positive we cannot sign the determinant.

To build intuition we will examine to the case where β1, β2 > 0, but the derivatives are evaluated at β1 = 0. Hence, we evaluate the impact of the externalities at the point where β1 starts with no impact. Given this assumption, the signs of the other partial derivatives remain unchanged and we sign:

However, under this assumption, we are still unable to sign the determinant.

We now examine the case where β12 > 0, but the derivatives are evaluated at β2 = 0. Hence, we evaluate the impact of the externalities at the point where β2 starts with no impact. Given this assumption the signs of the other partial derivatives remain unchanged and we sign: