Most of the Internet services are supplied through networks with traffic moving over leased telephone lines. However, there is a distinction in how the lines are used by the Internet and the phone companies. The Internet provides connectionless packet-switching service whereas telephone service is circuit-switched (MacKie-Mason and Varian, 1994).

Phone networks use circuit switching: an end-to-end (point-to-point connections between communication parties) circuit must be set up before the call can begin. A fixed share of network resources is reserved for the call and no other call can use those resources until the original connection is closed.

The Internet uses a technology called "packet-switching". The term "packets" (or frames, or cells) refers to the fact that data stream from a computer is broken up into packets of about 200 bytes (on average), which are then sent out onto the network. This technology is connectionless. This means that there is no end-to-end setup for a session; each packet is independently routed to its destination.

Having described the main technological and cost features of the Internet and highlighted the congestion problem likely to arise as the demand for Internet services grows, we address now the question of how to efficiently price those services. This has turned out to be an important issue given the dramatic increase in the demand for the services and the accompanying problems of congestion.

The price system has been suggested as a means of rationing the access to the services, much in the same way as it does for many other marketed goods and services. The thrust of such an approach is to use price discrimination to sort out the congestion problem by way of the establishment of a "priority service" scheme which relates the consumers' willingness to pay for different types of services to the actual price they pay to have their demand satisfied.

Among the various proposals found in the literature, the one set forth by Mackie-Mason and Varian (1994) has received a great deal of attention and is taken here as the basis of our discussion of pricing the Internet. In what follows, a partial equilibrium approach to a market for Internet services is set up and the scheme advanced by Mackie-Mason and Varian is presented and discussed.

Consider a market for Internet services composed by n identical individuals whose preferences are taken to be represented by the following utility function:

where q_i denotes the number of packets demanded by consumer i per unit of time (i = 1,...,n).

We thus can define aggregate demand, Q, as

To model the congestion problem one has to define the current total capacity of the network system and the current level of network utilization. Let K be the current total switching capacity of the Internet network. We then define the total utilization of the network, Y, as the following ratio:

The congestion problem arises when aggregate demand (Q) is above the current total capacity of the network (K). In this case, the demand of an additional consumer generates an external cost on the inframarginal consumers in the form of delays experienced in sending packets of information through the network. Consequently, although the service may be used privately, its quality is affected by the level of aggregate demand.

Let D represent this delay cost. As D imposes a disutility on consumers, we rewrite the utility function in the folowing way in order to incorporate that external cost:

The decision problem faced by consumer i is

The network utility is assumed to seeking to maximize total welfare as given by the sum of all consumers' utilities, that is,

Taking into account that D is a function of Y, the above problem of maximization yields the following first-order condition

The expression nD'(Y)/K gives the total delay cost imposed on all consumers due to congestion in the network pipes. An efficient way to deal with this problem is to impose a price (or equivalently, a Pigouvian tax) on consumers equal to the total delay cost so as to internalize the congestion externality. Letting p be such a price, with p = nD'(Y)/K, the maximization problem faced by the individual consumers may be rewritten as

The first-order condition for the above problem is

which guarantees that the individuals choose the optimal level of packet demand, that is, the level that takes into account the congestion cost imposed on third parties.

Suppose now there are m firms in the market offering connection access to the Internet network. As with consumers, it is assumed the existence of a representative firm with total capacity supply of K, the only possible difference between firms being with respect to the delay level offered to consumers. This typical firm carries along its physical connections a total of Q packets and charges a price p for each of them.

In the presence of congestion problems, the price the firm charges is a function of the delay level it contracts with the individual consumers. Therefore, firms may compete against each other in terms of delay levels, with difference across firms signalling product (quality) differentiation. Delay-based price discrimination is thus assumed, with prices being denoted by p(D).

The consumer maximization problem now is

and

The first condition says that each consumer will use the network facilities to send packets up tp the point where marginal benefit of sending an extra packet equals the price to be paid for that additional unit. The second condition sets the level of delay for which the consumer is indifferent between sticking to his current access provider and switching to another one.

From the firm's point of view, its maximization problem is

where c(K) is the cost of providing capacity K.

The first-order conditions for profit maximization are

and

The first condition shows that the price charged for packet sent should reflect the value of the additional delay associated with capacity utilization Y. The second condition affirms that the value of the additional delay should be equal to the marginal cost associated with capacity supply K.

Taking into account the fact that the expression -p'(D)q_i = 1 in aggregate terms becomes

and the dependence of Y on Q and K, we arrive at the following result:

This result means that the optimal price leads to an optimal mix of congestion and delay levels, and to an optimal capacity level. Moreover, as nD'(Q/K)K is equal to u'(q_i), marginal benefits to individual consumers are also optimal.

It is thus that the optimal price p is set taking into consideration two factors: the marginal cost of production and the marginal social cost of congestion. If the latter component were not accounted for, individuals would tend to demand a quantity qi above the social optimum.

The above analysis shows that some form of price discrimination in terms of capacity supply and delay cost is possible. Mackie-Mason and Varian (1994) have also developed a rationale for pricing consumers according to their specified needs. Such a schedule would define a "type-of-service" scheme based on different priorities and qualities of service as signalled by the individual consumers. Therefore, individual users may choose the class of service most adequate to their needs (applications).

As an example, those individuals demanding e-mail services could afford to experience some delay in sending their messages during peak periods (and would thus be given a low priority status), while those demanding real-time video services could not afford any delay (and would then be assigned a high priority status). This differentiation would be reflected in the pricing structure, with the first group of consumers paying a price less than that charged to the second group of consumers.

We would then have a set of consumers classified according to the priority/quality level required. An associated set of prices, p, is set in accordance with those levels. Suppose then there exist groups of consumers of type , , with f () being the frequency distribution function indicating the number of consumers of type . Each individual of type may choose from the set of services q and has the following utility function:

u(q, ) - D

with the maximization problem being

Max u(q, ) - D - pq

The solution to this problem gives the demand vector

q(p, )

In aggregate terms we have

Q(p) = q(p, ) f( ) d

The network utility faces the problem of maximizing total welfare:

Max W(p) = [u(q, ) - D - pq(p, )] f() d

Efficient prices for the maximization problem above should be set at

p = u'(q, ) - (D'/K)

In the last section we saw how the price system might be used to tackle the congestion problem in the Internet. Frequently, however, the government is concerned with the distributional impact of the pricing policy on the poor. This adds another dimension to the analysis of price determination in the Internet, since the price arrived at while dealing exclusively with the congestion problem might hurt poor consumers if set at too high a level.

In these circumstances, the pricing scheme has to balance conflicting objectives, a problem well known in the economics literature as the trade-off between equity and efficiency.

Some authors (e.g., Mackie-Mason and Varian, 1994) argue that distributional considerations in the Internet should be resolved outside the price system, through, for example, redistributive taxation/subsidization. We here ignore the possibility of resorting to explicit subsidies covered by taxation in order to deal with the equity problem, and instead assume that the trade-off between equity and efficiency is to be resolved by the pricing scheme.

In doing so, we do not mean that the last approach is superior to the first. In this paper we have chosen to explore the problem of distribution within the price system. In other words, we address the case where one is constrained to using prices to deal with the trade-off between equity and efficiency.

One way economists have addressed this question is by following Feldstein's (1972a, 1972b) method of introducing equity considerations in the pricing analysis through the specification of the "distributional characteristic" of a good or service, which is defined as

d_i= q_i(p,) ()f()d / q_i(p,)f()d

with being the marginal social utility of income of consumer group .

The expression for d_i gives the weighted average of each consumer group's marginal social utility of income, the weight being the participation of each group in the consumption of Internet service i.

An alternative way to deal with the equity problem in the Internet is the so-called "safety net" approach (Brown and Sibley, 1986). This approach is based on the idea of ensuring that each consumer can consume some minimal level of a given service. It comprises a two-step procedure, by which:

(i) the service(s), the desired level of contribution for consumers and the safety net are set on a social welfare basis;

(ii) the remaining services and consumers are priced according to the efficiency rule.

The Authors

Department of Economics
Universidade Federal de Pernambuco-UFPE
Cidade Universitária, 50670-901 Recife-Pe Brazil
Phone: (081)271-8381 Fax: (081)271-8378

The authors wish to thank the Administrative Committee of the Internet/Brazil for financial support which permitted their presentation of a previous paper (Cavalcanti and Nogueira, 1996) at the 4th International Conference in Telecommunication Systems, Modelling and Analysis, in Nashville, and at a seminar at the International Computer Science Institute-ICSI, University of California, Berkeley, USA, in March/1996.

S. Brown and D. Sibley, 1986. The Theory of Public Utility Pricing. Cambridge, Eng.: Cambridge University Press.

J. C. Cavalcanti and J. R. Nogueira, 1996. "The Internet, its Brazilian model and an approach to a pricing policy for its operation in Brazil," Annals of the 4th International Conference on Telecommunication Systems, Modeling, and Analysis, Nashville, Tennessee.

M. Feldstein, 1972a. "Distributional equity and the optimal structure of public prices," American Economic Review.

M. Feldstein, 1972b. "Equity and efficiency in public sector pricing: the optimal two-part tariff," Quarterly Journal of Economics.