modelling the telecommunication pricing decision

Modelling the Telecommunication Pricing Decision Kate Brown Department of Accounting and Finance, University of Otago, Dunedin, New Zealond

Richard Norgaard School of Business, Universify of Connecticut, Storrs, CT 06269

ABSTRACT The local telecommunication pricing decision on residential, business, and private lines is modeled.

This study demonstrates that when regulators use a weighted sum linear goal programming model to determine prices, adjustments can be ma& to Ramsey pKices that nflcct the regulators' concerns about the trade-off of fairness with efficiency. An actual example shows that when regulators' preferences were taken into account, residential prices were 14 percent lower than efficient optimal Ramsey prices.

Subject Areas: Decision Analysis, Coal Programming, and Regulation.

INTRODUCTION

The purpose of this article is to demonstrate the use of weighted sum linear goal programming (WSLGP) to improve decision making in telecommunications pricing. Specifically, we deal with the vexing problem of determining local telephone rates. The problem with determining local telephone rates is that the best solution is competitive pricing which is unavailable in the current regulated industry. Economists have demonstrated that Ramsey pricing is the second best solution within the Pareto efficiency framework [2] [6]. The Ramsey solution does not address equity and fairness issues, however, and has been rejected as a pricing method for regulated industries. WSLGP is a third-best economic solution that offers regulators the opportunity to adjust Ramsey prices to reflect an appropriate faimes criterion. Given that regulators have multiple criteria in making pricing decisions, WSLGP is a more accurate model of their decisions than the economically efficient Ramsey price solution.

Currently, local residential telephone rates are priced below cost, reflecting a past cross-subsidy instituted by AT&T in the name of universal service. The cross- subsidy involved higher than cost long-distance rates subsidizing local residential rates. With the breakup of AT&T and the creation of a competitive long-distance market, the problem for regulators is how to establish fair and efficient local rates for all customers, given the inherited cross-subsidies. This article provides a tool for establishing fair and efficient rates in light of perceived conflicts between efficiency and fairness.

In the next section there is a discussion of Ramsey pricing and the regulatory problem. Following that is a development of the weighted sum linear goal programming model applied to telecommunications. An application and a conclusion are then presented.

RAMSEY PRICING AND THE R:EGULATORY PROBLEM

Historically, governments have assumed that local telephone service, with its high fixed costs and twisted-pair wire distribution system, is most efficiently provided

673

674 Decision Sciences [Vol. 23

by a monopoly. As a result, government gave local exchange carriers (LECs) a monopoly in their service area in exchange for regulation of prices-the regulatory compact.

For regulators, the problem is to maximize total welfare, W, which is defined as

W = a$,+ apSp

where S,=consumer surplus-the gain from buying at a price less than the price one is willing to pay; Sp=producer surplus-the gain from selling a unit of a commodity at a price greater than the maximum price at which the producer would be willing to sell; and a, and ap--the assigned relative weights.

producers surplus equals economic profit, or

where Il is economic profit, p is product price, x is the output of the product or service, and C(X) is the total cost of production, including the cost of capital. The regulatory compact effectively sets Il=O, although Baumol [l] and Kahn [I41 recommended that Il=k>O to encourage efficiency. As long as producer surplus is a constant, the problem for regulators is to maximize consumer surplus constrained by producer surplus = k 2 0.

A solution to the problem was provided by Ramsey [I61 which subsequently was called Ramsey pricing or the inverse elasticity

where * i t pit

dpit xit t = - - -

and pit is the price of product i to customer type

rule:

(3)

t , Mi, is the marginal cost of product i to customer type t , k is the Ramsey constant, eit is the elasticity of demand, and xir is the output of product or service. Cross elasticities and income effects are assumed to be zero in (3).

The Ramsey solution implies that the greatest deviation from marginal cost should apply to the product or service that has the least elastic demand. The rule guarantees that the amount of consumer surplus lost when compared to the surplus at competitive prices is equalized across all consumer groups over the total output of the fm. Total consumer surplus is maximized when those customers least willing or able to do without the service are charged the largest positive deviation from marginal cost. Economists agree [2] [6] [7] that Ramsey pricing is the most efficient way to maximize constrained consumer surplus under regulation.

Equation (3) has been proposed by economists in the areas of telecommunications, postal services, transportation, and others. Yet regulators have consistently rejected the Ramsey solution [20]. The regulators’ mandate is to establish prices that are both “just and reasonable,” or “fair and equitable,” and regulators tend to view Ramsey prices as neither just nor fair. This is because Ramsey prices in

19921 Brown and Ncvgaard 675

vital utility services may charge the most to those least able to do without the service (e.g., the elderly, p r , and start-up businesses). Zajac [21] called this a regulatory dilemma where fairness and efficiency are not compatible. While the Ramsey solution guarantees efficient resource employment, it treats all stakeholder groups with equal consideration based on their need to use the service.

In telecommunication pricing, the use of the Ramsey solution is particularly difficult because of past pricing behavior. F'rior to 1984, AT&T cross-subsidized local telephone rates with long-distance rates. After 1984, seven regional holding companies were formed from the former .AT&T system and the long-distance portion of the system was allowed to gradually become fully competitive. This eliminated the long-distance subsidy. Powerful consumer groups made it difficult for regulators to allow local rates to reflect the loss of the subsidy, so the LECs raised business rates relative to what they would be in competition and continued to hold intra-local access and transportation, area (LATA) calls at the old AT&T rates. IntraLATA calls are those made within an area code which continued to be in the regulated market in most jurisdictions'.

Unfortunately for regulators and LECs, businesses have alternatives to the local telephone exchange. Large telephone users, who represent up to 80 percent of telephone traffic, can connect directly to carriers in the competitive market such as AT&T, Sprint, MCI, and Comsat, and thus bypass the local carrier. This meant that to hold local rates down, it was considered necessary to raise business rates and intraLATA rates even more, increasing the threat of bypass. Thus, regulators face a nearly insolvable dilemma from residential phone consumers demanding subsidized rates while businesses consider bypassing the local loop to avoid the subsidy.

This is the setting for our problem in which regulators, through the use of a mathematical programming model, are allowed to adjust Ramsey prices to reflect concerns about fairness while preserving the viability of the LECs and, ultimately, residential telephone service.

WEIGHTED SUM LINEAR G.OAL PROGRAMMING

Weighted sum linear goal programming (WSLGP) was developed from multiple objective linear programming which has been used extensively in areas such as agriculture, power supplies, economics, oil and steel production, production planning and control, and transportation [8]. WSLGP is applied here to telecommunication pricing because the principals (regulators) are both economic and political agents who must balance social welfare and fairness through their preferences [ 131.

In WSLGP, the objective function represents a minimization of a penalty function comprising a vector of goals and clonstraints. This approach results from the desire to maximize a vector of objectives that is not a well-defined problem. Consequently, the problem is defined in terms of non-dominated solutions [Ill. Specifically, non-dominated solutions are those that have first degree stochastic dominance over other solutions. From the set of non-dominated solutions, the decision maker must choose one for the final value. In the chosen solution, some

'Pressure from consumer and business groups to make the intraLATA market competitive is causing many jurisdictions to end the LEC monopoly. The irony is that some of the same groups wanting competition in the intraLATA market want to maintain the residential subsidy.


goals may be exceeded while others are not reached. The introduction of potentially two-sided deviations from each goal and constraint in the problem allows the entire situation to be expressed as one penalty function that can be minimized with respect to the weights assigned to each component.

In WSLGP the objective function is in the form:

Min Z = C cX,y,,, N M

(4)

where X are the penalty weights assigned by regulators to N component with ZA= 1. These components are defined in terms of an auxiliary variable, yJ, which specifies the possible direction of the allowed deviations from the goals and the flexibility of the constraints. Thus, y r y J - y j with yJ20, yj20. The positive deviation of yJ is represented by y; and the negative deviation by y j (see [lo, p. 2391 for details). Auxiliary variables are added to each goal and constraint equation to transform inequalities to equalities. If a particular goal or constraint is allowed to vary in both directions, both the positive and negative components of the auxiliary variable enter the penalty function; if the allowed deviations are direction specific, only one component will be included, and the other component will be set equal to zero. The weights assigned to the auxiliary variables allow a proportional degree of deviation, which may be different for each goal or for each directional deviation for each goal. The product of the weight and the auxiliary variable component is the penalty assigned to the failure to reach the particular goal in the specified direction.

A multiple objective linear goal program was constructed for the local telecommunications pricing problem from the following:

The Ramsey equation, the optimal efficiency goal: is

The company profit equation is

The individual product or service goal that each service should cover its own variable costs is

W i t 2 Cif i i t . (7)

The positive variable constraint is

p, c, x 2 0. (8)

In (7), c is a variable cost for the period of one month. The difference between C(x> and EiZfci,xif represents total firm fixed costs. Auxiliary variables were added

'The model is designed for multiple product/service and customer combinations. The numerical example has only seven combinations, and the subscript notation has been simplified in the actual model accordingly. The actual subscripts are listed in Appendix C.

19921 Brown and Norgaard 677

to (5), (6), and (7), to convert them to constraints with allowed external deviations. The penalty function (4) was then derived with weightings assigned to all relevant auxiliary components.

Data Sources

To demonstrate that WSLGP can be used in the pricing decision for monthly telephone service provided by an LEC, we use two classes of customers: residential and business. A flat rate, per-line, per-month charge is the standardized form of reference chosen for all but interstate carrier access charges for which the rate is per minute of use. Although business usage and intraLATA toll charges are also on a per-minute basis, these have been averaged. The averaging process would lead to an individual customer bias but would not affect the overall distribution of costs within a class of customer.

Five services are modeled: access, usage, private line, intraLATA toll usage, and inte~~tatc canier access. Access refers to the system costs of ondemand service. Usage refers to the cost of the individual call. Private lines are business phones controlled through a PBX which in turn is connected to the local loop. The values for the variables were obtained from actual rate hearing dockets. Elasticity, demand, and cost estimates came from New England Telephone as part of a rate request case in Massachusetts.

The initial set of equity weights were determined from a nationwide survey that quantified regulator preferences pertaining to the various concerns inherent in the local telecommunications pricing decision. The survey used a Likert-type sum- mative scale and had a response from 68 percent of 192 regulators surveyed. The results of that survey support the conclusion that the regulators believe they are trying to achieve a balance among the conflicting desires of producers, business customers, and residential customers. Using the infomation from the survey, average regulator preferences were determined to be 36 percent, 28 percent, and 36 percent for residential, business customers, and producers, respectively. A minimum value of .01 was assigned to private, intraLATA (business) and interstate access service which was deducted'from the business preference. htraL,ATA (resident) was deducted from the resident preference. The minimum weights reflected the lack of equity concern for the affected service^.^

It was also assumed that regulators preferred under-achievement of major equity related objectives so penalties were asymmetric with a penalty weight of .65 for over-achievement and .35 for under-achievement. A test of results based on symmetric performance indicated little sensitivity to asymmetric penalties. For weights used in test of model see Appendix B.

The set of weights established by the survey is an average response, primarily because responses were kept anonymous to encourage participation in the study. A consensus of opinion by regulators is neither expected nor considered desirable. In an actual application of the model, the regulators for the particular jurisdiction would be interactively involved with the model, and each set of weights would be

%kcawe of the timing, private line and interstate carrier access were not part of the questionnaire and thus no specific value could be determined for the regulators' preference function. The results are biased accordingly but sensitivity tests did not suggest the bias was significant. (For details of the survey and justification of the values, see [3].)


expected to be at least marginally different. The averages from the survey were used only as a starting point, and the iterations with different weights were intended to demonstrate that boundaries exist for the range of feasible solutions, and the model provides a mechanism for decision makers to articulate their preferences and see the pricing consequences of those choices.

SOLUTION TO MODEL

The model was solved in two steps. The Ramsey prices and corresponding constant were solved iteratively by the GIN0 programming algorithm (see Appendix A). The actual model, shown in Appendix B, the Ramsey constant, and the data shown in Appendix C were then combined using the LINDO programming algorithm. The Ramsey prices were then used for comparison to actual prices and the model results. In solving the model, as in solving the Ramsey equations, certain assumptions are necessary. In this application elasticities and marginal costs were assumed to be constant in the region of concern. This assumption is particularly troublesome. The Ramsey solution to a specific problem generally produces a set of prices that differ substantially from those in actual use, most notably in the least elastic product. The intuitive response to this is that demand would take on very different elasticities at the Ramsey price levels, rather than continue to respond with the assumed constant elasticities. In spite of this problem, most estimates of Ramsey prices make the assumption of constant elasticities [2O].' The Federal Communications Commission (FCC) [7] and Mitchell 1151 reported that the elasticity for telephone service is stable within a narrow range. Furthermore, because some of the more elastic services would be priced well below current actual prices, any gain in demand in those products would offset any losses caused by mis-specification of the residential elasticity, if the regulators were convinced that the price vector best reflected their preference function.

The specific difficulty arising from the constant elasticity assumption relates to the recovery of fixed costs. In both the Ramsey solution and the model developed here, the burden of fixed costs is distributed among the various products. In the case of the Ramsey prices, the recovery of fixed costs is determined by the inverse elasticity rule. Each product is responsible for some contribution to fixed costs. Part of the flexibility of the model developed here compared to the Ramsey solution is in the assumption that the goal of having a service recover variable costs and then contribute to fixed costs, may or may not be met. In each of the tests reported here, only some of the services are expected to contribute to fixed costs. In general, these are the least elastic. In the base model, the contributing services are residential, business access, and business usage. Since residential is the only service of the three being priced by the model above actual cost, its elasticity is the only one of concern in the problem. It is, however, less of a problem in the model results than in the Ramsey solution because the regulatory preferences, A, can dampen the effect. Repeated trials with elasticities over a reasonable range of values demonstrate that the model is less sensitive than the Ramsey solution to variations in elasticities.

'In 1986 approximately 13 percent of residential telephones and 37 percenf of all business telephones (prunarily in New York City, Chicago and La Angels) were priced on a per-call basis (also called local measured service (LMS) [4]). In [7], Per1 showed that LMS increases the elasticity, thus giving the user more control over cost.


There have been attempts to avoid constant elasticities. Tye [19] reported that Wecker used the mean and standard deviation of the elasticities to maximize expected consumer surplus. This technique can be shown to be equivalent to the standard approach using a truncated distribution for point estimates, but has not been accepted as a solution to the problems associated with point estimates [17]. Necessary data to try this method were not available. Ijiri [ 121 developed a method of solving piecewise linear functions using goal programming. His solution could be incorporated into this model if sufficient cost and demand data were available. His technique determines quasi-elasticities which change at each cusp of the piecewise linear demand function.

The problem with determining elasticities affects any model for pricing. Changing competitive conditions complicates estimation techniques further. The benefit of the kind of model presented here is that any values of elasticities that decision makers believe possible can be put into the model to test for the impact of these values. The solutions will all be feasible, non-dominated sets of prices. The decision maker can then monitor and adjust their values as better information becomes available in real situations.

In the actual solution the values for marginal costs and demand elasticities were determined as point estimates [9]. From these, the values for Ramsey prices and the Ramsey constant were derived simultaneously using the non-linear algorithm GINO. The Ramsey constant, k, is a number formed by the ratio of the Lagrangian constants in the derivation of the Ramsey equations. At the optimum, this ratio will be the same for all services provided by the multiproduct firm. When k=O, price equals marginal cost, and consumers' surplus is maximized. This is the first best solution of a competitive market. When k=l , the revenues of the producer are maximized, with economic profit still constrained to be zero [5]. For a given problem, k is derived simultaneously with the Ramsey prices. The derived value for k was .032334. This number then was imputed to the model in Appendix A.

RESULTS

Table 1 gives a comparison of prices for seven services based on the costs and weights shown in Appendix B. Prices and costs are from 1987 Massachusetts docket information on a New England Telephone (NYNEX) filing. LATA costs and all elasticities are from internal data from NYNEX and GTE. In Table 1 the difference between marginal cost and prices is fixed cost including the cost of capital. Note that residential service is charged less than its marginal cost with the fixed costs plus the additional marginal cost of $15.23-14.78=$.35 being made up with higher prices in other services. The difference between the three prices, (actual Ramsey, and model) is a function of cost allocation. In the Ramsey solution, fixed costs are allocated through the inverse elasticity rule (i.e., the least elastic contributes the most toward fixed cost). Thus, residential contributes the most although business makes a significant contribution as well. The issue of the allocation of fixed costs, also called non-traffic sensitive (NTS) costs, is hotly debated at rate hearings, since many fixed costs are joint costs that defy easy allocation. With the Ramsey solution, fixed costs are efficiently allocated but resulting prices raise the issue of fairness. In effect the model used here allows some changes in the fixed charge allocations, specifically addressing the regulator's perceptions of equity conflicts.


Table 1: Marginal costs, actual, Ramsey, and model prices.

Marginal Actual Fbmsey Model Customer Type Costs ($) Prices ($) Prices ($) Prices ($)

Residential service 15.23 14.78 43.10 37.34 Business access 10.80 33.22 15.96 15.96 Private line service 7.38 41.72 8.80 41.13 Business usage 3.56 18.17 5.97 5.97 IntraLATA toll residential 3.52 7.84 3.63 3.53 IntraLATA toll business 6.49 32.44 6.7 1 3.59 Interstate carrier access* .004 . a 9 5 .0042 .0206

*Per minutes of use. All other prices are per line per month.

Using the weights previously discussed, five of the seven possible prices vary from Ramsey and all vary from actual. Three services would be priced by the model below Ramsey prices: residential service by $5.76, residential intraLATA toll by $.lo, and business intraLATA toll by $3.12. Two services would be priced above Ramsey: private line service by $32.33, and interstate carrier access service by $.0164 per minute (all other dollar amounts are per line per month). Two services, business access and business usage, would be priced at the Ramsey values. The company achieves the defined break-even profit levels in this application. Three product lines exceed their variable costs: residential service, business access, and business usage.

These results are not obvious from the initial formulation of the model. For example, the product/customer groups with low weights (i.e., categories other than residential service, business access and business usage, and company break-even) do not automatically get priced higher than the Ramsey prices. The model simultaneously takes into account the preference weights, demand quantities, variable and marginal costs, and elasticities.

The effect of regulator preferences is seen in the difference in actual, Ramsey, and model prices. Private line service and interstate cattier access both deviate significantly from the Ramsey prices and are much closer to actual prices. In the critical area of residential and business, the model results show the classic regulator dilemma of business versus residential prices. Residential prices are only 14 percent lower than Ramsey after regulator preferences; whereas, business access and usage are at Ramsey. This suggests that regulators understand the long-run impossibility of pricing residential below cost while making up the difference from business.

In the actual case, residential telephones are priced 66 percent less than Ramsey and business telephones are priced 48 percent greater than Ramsey. The model solution based on average regulator opinion suggests that regulators want to significantly increase residential telephone rates while lowering business telephone rates, but not to the full extent of Ramsey pricing. This seems reasonable and in line with the use of goal programming. Nevertheless, model prices for residential telephone rates are much greater than actual prices. The disparity between actual and model prices suggests that an interactive goal program can play a significant role in bringing regulator actions in line with their beliefs.

The value of the technique used here is both the incorporation of more information than the Ramsey solution, and the identification of a particular weighting

19921 Brown and Norgaard 68 1

assignment for a particular outcome. Thus, regulators can approach the problem both from the perspective of assigning the weights they think should apply, and from looking at a set of results and discovering what sort of weight assignments lead to an acceptable solution. Steuer [18] and Zionts and Wallenius [23] showed this technique can involve a group interactively applying the model. This type of immediate feedback system should prove invaluable.

SENSITIVITY OF WEIGHTS

The essence of the problem in telecommunications pricing is to allow regulators to adjust Ramsey prices for equity considerations. Thus it is important to know how sensitive non-dominated solutions are to the set of weighting preferences. The standard procedure is parametric programiing, and this was performed. There were only small variations around variables which is consistent with large numbers of constraints.

Table 2 shows sensitivity of variables to extreme weights. In the base model the weights were 36 percent for residential, 28 percent for business, and 36 percent for producers. When weights were equal for all categories, residential prices deviated modestly from Ramsey and interstate prices significantly. Columns 3 and 4 of Table 2 show that heavy weighting of residential service does not guarantee maximum negative deviations from Ramsey. This is caused by the barriers in the model, and the way fixed costs are allocated. Since actual residential service deviates 66 percent from Ramsey, Table 2 suggests that it would be impossible to reach such a level and still retain efficiency. In summary, the results indicate:

1. As decision makers become less -willing to differentiate between the achievement of goals, the value of the multicriteria methodology diminishes, but is not completely eliminated. The basic economic foundation of the model, the Ramsey solution, becomes a more likely result for individual components of the model as the decision maker reduces the distinctions incorporated into the multiple objective framework. Further, as the number of products or services increases, the difficulty in assigning reasonable discriminatory values increases. More products mean more constraints and associated parameter variability decreases. This suggests that regulators should deal with the three or four services they feel are most at issue, assigning minimal values to the rest,, as done in the model.

2. The constraints of the model define the feasible region. The linear nature of the model guarantees that for any weighted combination of the penalty function, the solution is a global maximum. The linear functions define a closed convex set, which is a necessary and sufficient condition for a global optimum [22]. Each solution, which is a nondominated optimum, is the best feasible solution for the given weight assignment, all other variables held constant. Since the procedure is only recombining the same basic elements of the problem within a fairly small range of changes, it is not surprising that the same solution is the optimum for several weight combinations.

3. Loading residential service with more weight does not automatically lead to greater differences from Ramsey pricing. The constraints of the model form a feasible region barrier that defines some limits to the regulatory options. For residential, the maximum variation within the model was 15 percent around the base solution. Thus there are no weights that regulators


Table 2: Sensitivity analysis of penalty weights (in percent deviations from Ramsey).

P e d t y f a Penaltyfa Equal Heavy Over- Chehqug ' Penalty

Weightto Heavy Weightto charging RBidertisl for Base All Weight to Business Private Inba- ovacharging

Service Model Services Resickdial Usage Lames LATA Interstate -13.4 -10.3 -10.3 -15.4 -10.0 - 15.4 -5.1

Business 0 0 -32.1 0 0 0 0 access Private 367.4 0 367.4 367.4 0 367.4 367.4 line Business 0 0 -4.4 0 0 0 0

IntraLATA -2.75 0 -2.8 0 0 0 0 residential IntraLATA -46.5 0 -46.5 0 0 0 0 business hterstate 390.5 390.5 390.5 390.5 390.5 390.5 0

US?

can use in the model to bring about current pricing. This is not a condem- nation of the model, but rather support for the impossibility of maintaining heavily subsidized residential telephone rates.

4. Allowing a positive level of profit to encourage the telephone company to improve its efficiency does not affect the allocation of prices between residential and business. A positive level of profit is effectively a fixed cost to be allocated to services.

CONCLUSION

The breakup of AT&T in 1984 not only made telephone prices more competitive, it also resulted in the loss of a well-established cross-subsidy of local residential phone prices by long-distance calls. Since AT&T no longer dictated local phone rates, the maintenance of the local telephone subsidy fell on regulators. Regulators have kept business telephones and intraLATA calls above cost in order to maintain the subsidy. Unfortunately, businesses have alternatives to the local loop which they can and do utilize when prices do not reflect cost. The problem for regulators is how to adjust prices to reflect equity without losing business customers to alternative communication systems.

The answer suggested in this article is to use weighted sum linear goal programming. This allows regulators to adjust Ramsey prices by injecting their equity concerns into the equations. As a demonstration of the technique, prices, costs, and elasticities were developed from Massachusetts docket information as well as internal data from New England Telephone (NYNEX) and GTE. Regulator equity concerns were determined by a national survey. These were inputs into the goal program.

In the long run the viability of the local telephone companies depends on retaining business customers. In a market that contains unregulated companies in


competition, efficiency requires that controlled prices must approach Ramsey values. Goal programming offers regulators a way of bringing this about because it addresses equity issues not included in the Ramsey solution. To the extent that goal programming encompasses the influences on the regulatory decision process, the set of prices closest to being simultaneously the most efficient, feasible, and equitable is both limited and solvable. This is a “third” best kind of solution to the multicriteria problems of local telecommunication pricing in the current regulatory climate in the United States. [Received: February 27, 1991. Accepted: September 25, 1991.1

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517-537.


APPENDIX A Determining Ramsey Prices and Ramsey Constant

The following equations were used to solve the Ramsey prices and Ramsey constant:

M i n - k

cppi - C(X) = 0 i = 1, ..., 7,

pi 2 0 i = 1, ..., 7,

1 2 k 2 0 .

To maximize consumer surplus, k is minimized. Producer surplus is set at zero but could be positive by adding a constant to the right-hand side of (a). Mi, xi, C(X) are given in Appendix C.

Given the conditions associated with the parabola in (Al) and the negative sign of elasticities, it is highly likely that a set of feasible solutions exists in this type of problem.

APPENDIX B Model of the Pricing Decision for Local Telecommunications

p2[ 1 - -1 k - y; + Y;= M29

Ez

p3[ 1 - -1 k - y; + Y;’ 4 9

€3


Xil 2 0, y; 2 0, y , 2 0, EL, = 1,

where el = price elasticity for local residential service, E;! = price elasticity for local business access, e3 = price elasticity for local private line service, e4 = price elasticity for local business usage, e5 = price elasticity for intraLATA toll (resident), &6 - price elasticity for intraLATA toll (business), E, = price elasticity for interstate carrier switching, xl = total demand for local residential service (lines), ~ 2 = ~ 4 = total demand for local business service (lines), x3 - total demand for local private 'dine service (lines), x5%6 = total demand for intrastate senrice (lines), x7 = total demand for interstate carrier switching, C(X) = total cost for producing the setvices listed above, M, = marginal (incremental) cost of residential service, per line per month, M2 = marginal (incremental) cost of business access, per line per month, M3 = marginal (incremental) cost of private service, per line per month, M4 marginal (incremental) cost of business usage, per line per month, Ms = marginal (incremental) cost of intraLATA toll, per line per month

(residents),


M,

M7

k - Ramsey constant, cI (x , ) = variable cost of producing residential service, c2(x2) - variable cost of producing business access, c3{x3) = variable cost of producing private line service, c4(x4) = variable cost of producing business usage, cs(x5) = variable cost of producing intraLATA toll (residents), c&S) = variable cost of producing intraLATA toll (business), c7(x7) = variable cost of producing interstate carrier switching, n,, An

= marginal (incremental) cost of intraLATA toll, per line per month

= marginal (incremental) cost of interstate carrier switching, per line (business),

per month,

= zero economic profit level, $0, = weight assigned by the regulator to the over or under achievement of

goal m.

APPENDIX C Values for Variables

Model M X

(line per cx (Million Subscript Service month) (Millions) E lines)

1 Residential access $15.23 $224 -.05 27.179

2 Businessaccess 10.80 72.5 -.lo 6.686 3 Private line 7.38 76.5 -.20 1.86 4 Businessusage 3.56 24.0 -.08 6.686 5 IntraLATA residential 3.52 96.0 -1.00 35.725 6 IntraLATA business 6.49 24.0 -1.00 35.725 7 InterLATA .m* 15 1 .o -.75 7.348*

and usage

Notes: *minutes of use, Total Cost=$1,509 million per month, k=.032334.

Penalty Weights

Kale Brown is Senior Lecturer in Finance at the University of Otago, Dunedin, New Zealand. She received her Ph.D. in finance from the University of Connecticut. Her research interests are in telecommunications regulation, cost of capital, and dividend policy.

Richard Norgaard is Professor of Finance, University of Connecticut. He received his Ph.D. in finance from the University of Minnesota. His areas of interest are utility regulation, capital budgeting, and working capital management. He recently published in Decision Sciences. He is a member of the Decision Sciences Institute and TIMS.

modelling the telecommunication pricing decision

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