A Practical Approach to Quality-Adjusted Price Cap Regulation

By Kevin M. Currier*

Abstract

Price cap regulation is often combined with service quality regulation since price caps may create incentives for quality degradation. A service quality adjustment factor (the Q-Factor) in the price cap formula insures that allowed prices fall as quality declines. In this paper, we discuss some considerations in determining the appropriate form of the Q-Factor. We first examine the difficulties involved in exploiting the price/quality tradeoff. We then present a quality-corrected price cap procedure –– possessing desirable properties –– that can be implemented with reasonable informational requirements.

Key Words: Telecommunications Regulation, Price Caps, Service Quality Adjustment Factor

*Department of Economics and Legal Studies in Business, Spears School of Business, Oklahoma State University, Stillwater, Oklahoma, 74078, e-mail .

1. Introduction

Price cap regulation represents the principal innovation in regulatory policy in the last 20 years. In the U.S., price cap regulation has been applied to AT&T, the dominant long distance carrier. In the U.K., price caps have been applied to British Telecom since privatization. Unlike traditional rate-of-return regulation, price caps have been shown to provide strong incentives for cost reduction and price rebalancing (Brennan, 1989; Cabral & Riordan, 1989; Vogelsang, 2002; Cowan, 2002; Vogelsang & Finsinger, 1979).

A potential drawback to price cap regulation, however, derives from the fact that incentives for cost reduction may lead to degradation of service quality (Sheshinski, 1976; Sappington, 2003, 2005; Weisman, 2005). Indeed, under a price cap, the firm may be able to increase profit by reducing costs without regard to service quality, particularly if it is difficult for consumers to directly discern delivered service quality levels.

The empirical evidence regarding service quality degradation under price cap regulation is mixed. Armstrong, Cowan, and Vickers (1994) find evidence of reduced service quality for British Telecom in the mid- to late-1980s. Tardiff and Taylor (1993), however, find no evidence of degraded service quality for the former Bell companies. Alexander (2001) cites evidence of reduced service quality for Ameritech, and OFTA (2004) notes evidence of telecommunications service quality problems in Hong Kong. It is interesting that Sappington (2003) finds evidence that under price cap regulation, some aspects of telecommunications service quality have improved while others have apparently degraded.

Despite this mixed evidence, regulators do appear to be increasingly concerned with the need for (additional) service quality regulations. However,the approach to service quality regulation to date has been largely ad hoc. The regulator first identifies a group of monitorable performance indicators known to be of concern to consumers. In telecommunications in the U.S., this group consists of installation of service, operator-handled calls, transmission and noise requirements, network call completion, customer trouble reports, major service outages, service disconnection, billing and collection, customer satisfaction surveys, public payphones, and 911 databases (Perez-Chavolla, 2003). The regulator may then require that the firms pay consumers rebates for substandard delivered service quality. Alternatively, service quality targets may be specified with bonuses paid for exceeding targets and penalties imposed for failure to meet targets. In addition, regulators often require publication of performance pledges and performance statistics. For example, telecommunications firms are regularly required to submit performance statistics to regulators in Australia, the U.S., the U.K., and Canada, among others. Finally, price cap plans may utilize a service quality adjustment factor (a “Q-Factor”) whereby the level of the cap is reduced if quality degradation is determined to have occurred. Thus, when a Q-Factor is employed, penalties for service quality degradation take the form of mandated price reductions. In the U.S., Q-Factor regulation has been employed in Rhode Island (Intven, 2000), Utah (PSCUT, 2001), New Mexico (NMPRC, 2002), and Massachusetts (Vasington, 2003). Q-Factor regulation has also been employed in Italy (toll motorway franchises and natural gas) as well as the U.K. (water supply).

Ideally, a service quality adjustment factor should reflect consumers’ price-quality tradeoff. The regulated firm should thus be “selling” higher quality to consumers through higher prices or, alternatively, be “bribing” consumers via lower prices to accept lower quality levels. However, little theoretically rigorous guidance has been offered to regulators as to how best to exploit this tradeoff. In this paper, we examine this complex issue and provide a practical suggestion for incorporation of service quality adjustments into the price cap formula.

2. Difficulties Associated with the Q-Factor

A number of practical difficulties arise when attempting to apply a service quality adjustment to a price cap. These difficulties can be illustrated by considering a regulated firm that produces a single output x, which is sold at price p. Furthermore, assume that the firm’s output is characterized by a scalar index of quality q.

Consumer surplus is V(p, q). We assume that V is twice continuously differentiable and satisfies Roy’s Identity where x(p, q) denotes market demand. We define , the marginal social valuation of a change in quality at price p. Note that υ is the change in the area below the demand curve and above the price, resulting from a small change in q. In addition, it is reasonable to assume that consumer “willingness to pay” for an increase in quality is highest when quality is low (DeFraja & Iozzi, 2004). The isosurplus curves are therefore convex with d2q/dp2 ≥ 0 for any fixed surplus level. This property is formalized by assuming that V is quasiconcave. Note that this assumption implies that is convex, i.e., upper contour sets of V are convex. Figure 1 provides an illustration.

Under price cap regulation, the firm’s period t prices are required to satisfy

pt ≤ pt-1 (1 + RPI – X + Q)

where RPI is the percentage growth in retail prices, X is a general productivity factor reflecting productivity improvements derived from technological change and cost saving, and Q is a service quality adjustment factor (a Q-Factor) that insures that the required rate of decline in prices increases as the firm’s delivered service quality decreases. In this paper, our focus is on the appropriate form of Q; we thus assume for simplicity that RPI = X, implying that the price cap adjustment formula is

pt ≤ pt-1 (1 + Q).(1)

Figure 1. Isosurplus Curves

The value of the Q-Factor should accurately reflect the rate at which quality can be traded off against price. Suppose now that . Since Vp = –x < 0, it follows that along the isosurplus curve for . For non-infinitesimal changes in price and quality, there are two possible ways of evaluating this tradeoff: using lagged values where , and using current values where .

In view of this, two possible forms for the period t Q-Factor may be suggested:

(2)

and

(3)

where the subscripts L and C denote the terms “lagged” and “current,” respectively.

In either case, the firm is assumed to select to maximize period t profit πt subject to (1). It should be noted that if the firm selectsqt = qt-1, the price cap formula permits the firm to select pt = pt-1. Thus, under either QL or QC, application of (1) can never decrease profit. Hence, πt ≥ πt-1.

As is customary, we shall define social welfare to be the unweighted sum of consumer surplus and profit. Thus, period t welfare is Wt = Vt + πt. The following Proposition provides the main result of this section.

Proposition: Application of QL will not guarantee a welfare increase, but application of QC will.

Proof: See Appendix.

The Proposition demonstrates that contemporaneous values of the quality indicator, demand, and consumers’ quality valuation must be employed in the Q-Factor to guarantee a welfare increase. The following example provides a simple illustration.

Suppose that with and . Suppose further that , in which case Vt-1 = 10, , and . Using QC, the period t price constraint is . Since , the constraint may be rewritten as . Suppose now that the firm selects . This price-quality vector satisfies the constraint and yields . Since VtVt-1 and πt ≥ πt-1, welfare must increase.

Alternatively, if QL is applied, the period t constraint is or . If the firm again selects , now satisfies the constraint but with . Thus a welfare increase cannot be insured.

While QL has the desirable feature of employing lagged values of demands and quality valuations, it will not in general lead to a welfare increase. DeFraja and Iozzi (2004) have provided a generalization of the Vogelsang-Finsinger (1979) procedure, which leads to efficient pricing and quality provision (in the long run) using lagged values of demands and quality valuations. However, implementation of the procedure requires that the firm and the regulator perform complex calculations involving “distance” constraints, global properties of demand functions, and various “scaling factors.”

These calculations are needed to insure that the firm’s constraint sets are non-empty, the process doesn’t lead to regulatory “cycles,” and is monotonically increasing in welfare. These additional constraints, however, are likely to be an impediment to practical implementation. Thus, within this context, QCprovides the most direct approach to setting the Q-Factor.

Unfortunately, there are several reasons why the regulator is likely to find application of QC administratively impractical as well. First, the fact that contemporaneous values of demands and quality valuations are used necessitates forecasting. Period t demands, for example, are not realized until the period t price-quality vector is actually selected by the firm since . Thus, application of QC requires that the regulator be able to forecast xtbefore period t begins. The likelihood of forecasting error and expensive, time-consuming arbitration between the firm and the regulator regarding the demand estimates renders application of QCpotentially problematical (Brennan, 1989).

However, even if accurate demand estimates can be obtained by the regulator, determination ofthe period t quality valuation is likely to be a more severe impediment to application of QC. Structured survey techniques such as the Contingent Valuation Method and the Contingent Choice Method have been employed to (directly or indirectly) infer customers’ willingness to pay for such things as air quality improvements, food safety, and decreased risk of illness, etc. (Bjornstad and Kahn, 1996; Hanemann and Kanninen, 1998). Application of such techniques within the context of determining QCand consumers’ price/quality tradeoff will require that quality valuations be known at the beginning of the regulatory period, again involving forecasting of these values or a priori determination of consumers’ quality valuations over a broad range of price-quality combinations. Although such exercises have been attempted, the expense of implementing such a procedure at the beginning of every regulatory procedure is likely to render this approach prohibitively costly.[i]

Additional difficulties arise from the fact that in general, the regulated firm will typically produce several outputs, each with multiple service quality dimensions. In such a case, generalizations of the “willingness to pay” assumption and the result contained in the Proposition are not possible without imposing additional structure on consumer preferences. Moreover, if there are n-regulated outputs and m-quality dimensions, there arem × n price/quality tradeoffs to be determined and exploited.

The problems discussed above clearly reveal the need for a practical method for implementing quality-adjusted price cap regulation in a general (multiple output, multiple quality dimension) context. In the following section, we present such a procedure.[ii]

3. A Practical Approach to the Service Quality Adjustment Factor

In this section, we present an approach to quality-adjusted price cap regulation that can be applied in a straightforward manner with reasonable informational requirements. The process is based on the premise that a reduction in quality is a hidden form of a price increase and that consumers’ utility is a function of “quality-adjusted” consumption levels. Specifically, changes in quality levels are assumed to augment the “services” that the goods provide to consumers (Fisher and Shell, 1972, 1998).

Suppose, for example, that the “service” yielded by a telephone call is the “transmission of information.” Then for a phone call of a given duration, a higher value of voice transmission quality may imply that a greater amount of information is transmitted. Or consider the response time for operator services. A reduction in operator response time may increase the amount of information transmitted in any given amount of time (including the time spent with the operator).

Consider now a regulated firm producing output vector x = (x1, …, xn) with price vector p = (p1, …, pn). There are moverall quality of service measures for the firm: Q=(Q1,…,Qm). In addition, each output has a quality of service index qi = fi(Q1,…,Qm) where fi satisfies ,i = 1, …, n and 1, …, m. Thus the firm’s overall quality of service indicators imply a specific level of service quality for each regulated output. Furthermore, measures the effect of a small change in Qj on the service quality index for good i. If the overall service quality index Qj has no impact on the quality index for output i, then . For example, suppose that voice quality transmission statistics are compiled separately for local calls, domestic long distance, and international calls. Then the quality index of local calls is not likely to depend on voice quality transmission of international calls.

Consumer utility is , which is assumed strictly concave. Furthermore, , i = 1, …, n where and for each i. Thus, quality levels augment the “services” yi generated by output xi. Since , a ceteris paribus increase in the product-specific quality index qi increases “services” generated yi at a decreasing rate.

Consumers maximize consumer surplus or equivalently

(4)

where , i = 1, …, n. Maximization of (4) implies that for any (r,s) pair. Thus, consumers equate the marginal rate of substitution between any two “services” to the corresponding ratio of the quality-adjusted prices . Maximization of (4) yields demand functions , i=1,…,n. Substitution of these demands back into (4) yields the consumer surplus function . V is a convex function of quality-adjusted prices and satisfies Roy’s Identity , i = 1, …, n. Since V is convex, it is quasiconvex.[iii] Using an argument similar to the one used in the proof of the Proposition in Section 2, it is straightforward to show that

(5)

implies . Since , (5) may be expressed as

(6)

where and . Figure 2 provides an illustration for n = 2.

Figure 2. The Quality-Adjusted Pricing Constraint

In Figure 2, period t – 1 quality-adjusted prices are . By Roy’s Identity, the slope of the line tangent to the isosurplus curve passing through is . The set of points on or below this line is the set of all quality-adjusted prices that satisfy (5). With in this set, we are assured that .

To make themodel operational, assume that each output-specific quality indicator qi is selected to be a weighted average of the set of overall quality indicators (Q1, …, Qm). This may be express as q = AQ where:

with aij ≥ 0, i = 1, …, n and j = 1, …, m. In this formulation, aij is the marginal contribution of overall service quality index j to the quality index for output i. Furthermore, assume that hi(qi) = kiqi, ki ≥ 0, i = 1, …, n. Thus, for any fixed level of output i, the “level of services” generated yi is a linear function of qi. In this case (6) may be expressed as

.(7)

Suppose now that the regulator imposes (7) as the regulated firm’s period t constraint. If the firm selects prices and quality levels to maximize profit subject to (7) and qt=AQt, then we are assured that consumer surplus, profit, and hence welfare must increase.[iv] Indeed, (7) insures that consumer surplus increases as demonstrated above. Moreover, since (7) permits the firm to select and , profit cannot fall when (7) is applied.

We conclude by noting three important points. First, a vector of prices and qualities is efficient if consumer surplus is maximum, given the profit level of the firm. Suppose now that our procedure is iterated, thereby generating an infinite sequence of price/quality vectors. It is straightforward to show that long-run prices and quality levels are efficient (i.e., the steady state price/quality vector is efficient). This is a generalization of Brennan (1989), which demonstrates that when quality considerations are absent, Laspeyres-based price cap regulation leads to efficient Ramsey pricing.

Second, observe that if for all i, (7) reduces to

.

Thus, when quality is invariant, our procedure is equivalent to capping a Laspeyres index of the regulated firm’s prices.

Finally, consider the special case in which there is one overall service quality indicator for the firm where βj ≥ 0, j= 1, …, m. In this case, (7) may be expressed as

or, equivalently,

.

The term is the percentage change in the firm’s overall service quality index. If there is no degradation in overall service quality from period t – 1 to period t, the firm faces the conventional Laspeyres price cap. If QtQt-1, the level of the cap is increased, and if QtQt-1, the level of the cap is reduced. It is noteworthy that this is the approach to Q-Factor regulation adopted for telecommunications by public service commissions in Utah (PSCUT, 2001) and Rhode Island (Intven, 2000), among others. Our results then provide a sound theoretical justification for such an approach.

4. Conclusions

To prevent service quality degradation under price cap regulation, a service quality adjustment factor may be included in the price cap formula. Ideally, the regulator should attempt to exploit the price/quality tradeoff by insuring that firms “sell” higher quality to consumers via higher prices and “bribe” consumers to accept lower quality levels by lowering prices. We have illustrated that, in general, the practical difficulties associated with such an effort are likely to be formidable. Yet the need remains for a practical method of adjusting the price cap formula to allow for quality variations.

We have modeled telecommunications demands by assuming that consumers derive utility from the “services” generated by the consumption of the regulated outputs. Both the actual consumption levels and product quality are assumed to contribute to utility. In this way, quality reductions are essentially regarded as price increases and quality increases are viewed as price decreases. We proposed a modified Laspeyres price cap that utilizes “quality-corrected” prices, which are determined by actual prices as well as current and lagged quality levels. If the process is iterated, long-run prices and qualities are efficient. In reality, it is likely that the procedure would have to be terminated after a finite number of iterations. For this reason, it is significant that the procedure is monotonically increasing in consumer surplus, profit, and hence overall welfare. Finally, we have demonstrated that our procedure provides a sound theoretical foundation for some contemporary approaches to service quality regulation in telecommunications.