Positive and Negative Externality Effects on Product Pricing and Capacity Planning

A Dissertation Abstract
Postscript Version -- 141 pages

Susan Y. Chao
Department of Engineering-Economic Systems
Stanford University
chao@bishop.berkeley.edu
http://best.me.berkeley.edu/~chao

Subscription-based services which are bound by physical constraints can experience opposing market forces which affect product adoption. In such networks, a positive externality due to increases in subscribership encourages more consumers to sign up. As a result, the addition of users to the system then leads to an increase in network load (measured in call minutes for the entire system). At some point, call demand exceeds network capacity and subscribers are forced to wait for call completion This translates to a negative externality in the form of congestion and not only reduces the consumption by current customers but also discourages some future subscribers from signing up. These concurrent positive and negative externalities ultimately determine demand dynamics, given subscriber attitudes and pricing changes. This research models markets with positive and negative externalities to enable the decision-maker to determine an optimal dynamic pricing strategy, while taking into consideration a variety of environmental factors as well as overall objectives.
Consumer Characteristics

The customers modeled in this research are assumed to have an observable maximum amount each is willing to pay for services, depending on various factors. For instance, the customer has a higher willingness-to-pay the higher his income. Similarly, an increase in total system congestion would lead to a lower willingness-to-pay. Other influences with less defined effects on willingness-to-pay include the total number of customers and consumption quantity. In order to decide whether to purchase the product and how much to purchase, each consumer maximizes his/her consumer surplus, which is defined as the difference between willingness-to-pay and product cost.

Provider Characteristics

The service provider charges each customer a quantity-sensitive price, which is typical of the current revenue schemes for several telecommunications services. Subscribers periodically pay a fixed subscription fee to be able to consume the product; their consumption quantity then determines an additional variable cost. The provider maximizes producer surplus, or profit, which is defined as the difference between total revenues and total costs.
System Dynamics

The dynamics of service/product adoption by consumers are as follows. Consider a typical prospective consumer A. This consumer evaluates the current pricing plan, number of subscribers, her income, the quantity she would consume if she signed up, and the resulting total congestion of all consumers. If her willingness-to-pay exceeds the price she would pay for her anticipated consumption, she will subscribe.

This evaluation is carried on by all prospective consumers. In particular, a certain subscriber B, who has a lower income than A, will also consider the prevailing prices, number of customers, etc. leading to his specific willingness-to-pay. In contrast to A, however, B will have a willingness-to-pay that does not exceed his anticipated consumption cost; rather it equals it. Since, it is assumed that consumers subscribe in reverse order of income, all prospective consumers with income levels lower than B's will not subscribe, at least for the current pricing scheme and number of subscribers. B thus becomes the "marginal consumer".

Once the marginal consumer is determined, the subscriber set has been determined and consists of all consumers with income at least as great as that of B. The remaining prospective consumers reevaluate their willingnesses-to-pay using the new total number of consumers and the subscription process reiterates.

Regulator Objectives

Whereas the producer and consumers optimize their own surpluses, the job of the regulator is to maximize a weighted sum of total consumer and producer surpluses. In doing so, the regulator must consider some external factors. These include:

Improvements in technology : may lessen congestion and/or increase system costs.

Regulatory changes : a change in electromagnetic spectrum allocations could lead to an alleviation of congestion problems.

Method of Solution

The model is formulated as a bivariate optimal control problem which maximizes the regulator's total weighted surplus. A solution of the optimal control problem includes the necessary conditions satisfied by any optimal set of system variable values. In addition, Mathematica is used to solve specific examples numerically.

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