Pricing policy of a U.S. telephone company

Journal of Public Economics 4 (1975) 35-56. 0 North-Holland

PRICING

POLICY

Publishing Company

OF A U.S. TELEPHONE

S.C. LITTLECHILD University

and

COMPANY*

J.J. ROUSSEAU

of Aston, Birmingham,

England

Received September 1973, revised version received July 1974 This paper analyses the pricing policy of a major U.S. telephone company in 1967. A mathematical programming model was used to calculate the prices per telephone call on each of three representative routes in each of four periods of the day which would be implied by a variety of alternative maximands (consumers’ plus producers’ surplus, profit, sales units, sales revenue), under a variety of alternative profit constraints and assuming capacity to be either fixed (at 1967 levels) or variable. Cost and demand data were supplied by several telephone company officials, and supplemented by published material. Sensitivity analysis was carried out on the demand elasticities. A total of one hundred versions of the model are reported on. Our major conclusions include: (i) Maximising consumers’ plus producers’ surplus subject to a pair of minimum profit constraints provided a good approximation to 1967 policy. (ii) There is perfect discrimination between large and small users for interstate toll calls. (iii) The effect of the state regulatory commission was to keep down the price of intrastate toll calls at the expense of interstate toll calls. (iv) As alternatives to regulation, perfect competition, if attainable, would increase benefits by about $100 million whereas perfect monopoly would redtice ihem by $300 million per Aurn, within the area of the company’s operations.

1. Introduction Telephone systems present formidable analytic challenges. The pricing problem, in particular, involves millions of interdependent demands for calls each requiring a vast network cf heterogeneous equipment. Perhaps for this reason there have until recently been relatively few economic analyses of telephone pricing policies. ’ And yet modern telecommunications systems *Acknowledgements: Bell System officials, particularly R.R. Auray, G.W. Groepper, G. Haefelein and J.J. Oddy, have been most helpful in supplying data, and C.E. Horn kindly organised a seminar at Illinois Bell to discuss the research. However, none of these officials are responsible for the use we have made of the data. Comments and suggestions have been too numerous to acknowledge individually, but we should like to mention W.M. Gorman, M. McManus, T. de Montbrial, S. Prais, R. Turvey and J. Wiseman, as well as the editor and a referee. A much fuller version of this paper, containing complete tables of results, is available as Working Paper no. 1, University of Aston Management Centre, September 1973, referred to in the text as Littlechild and Rousseau (1973). ‘Previous studies include those of Hazlewood (1951), Shepherd (1966), Marchand (1967, 1972), National Board for Prices and Incomes (1968), Kay (1968), de Montbrial and Muller (1969) and Pyatt (1972), but none of these, with the exception of Shepherd and the NBPI report, refer to actual data. Deschamps (1974) is currently working on the Belgian system. An excellent discussion of current issues in U.S. telecommunications regulation can be found in Kahn (1970, vol. II, ch. 4) and references therein. The basic model used in the present paper was developed by Littlechild (1970), where references are given to the extensive peakload pricing literature.

36

S.C. Littlechild nrrdJ.J. Rorrssean, U.S. telephone pricing policy

involve enormous revenues and investments. The Bell System alone accounts for approximately one quarter of all corporate capita1 raised annually in the USA. Some further analysis of operating policy seems to be justified. The present paper attempts to analyse the pricing policy of a major U.S. telephone company in 1967. We wish to answer three questions. (1)

What structure of telephone call prices, by route would most closely reflect marginal costs?

(2)

What pricing philosophy

(3)

What were the effects of regulation, both state and federal; the potential benefits from a revised regulatory emphasis?

best explains

the actual

and by time of day,

1967 structure

of prices?

and what are

A mathematical programming mode1 was used to calculate those prices per telephone call on each of three representative routes in each of four periods of the day which would be implied by a variety of alternative maximands (consumer plus producer surplus, profit, sales units, sales revenue) under a variety of profit constraints and assuming capacity to be either variable or fixed at 1967 levels. Cost and demand data were supplied by telephone company officials and supplemented by published material. Sensitivity analysis was carried out on the demand elasticities. This paper is based upon results from a total of one hundred versions of the model. We begin by developing the basic theoretical mode1 (section 2) and discussing its application to an actual network (section 3). The subsequent three sections answer the three questions posed earlier. Section 7 is devoted to sensitivity analysis while Section 8 discusses some qualifications and extensions. A final section summarises the results.

2. The basic model Samuelson (1952) pointed out that competitive equilibrium (in spatial markets) could be characterised by the conditions for the maximisation of a ‘net social payoff function’ defined by the sum of the areas under the demand functions less costs. Our procedure here is rather similar. The model developed by Littlechild (1970) maximises value of calls made (as given by the integral of the demand curves) less operating and capacity costs, subject to capacity constraints for each item of equipment at each time of day. The primal solution yields competitive volumes of calls and levels of investment in equipment, while competitive prices of calls emerge as appropriate sums of dual variables, which in turn represent opportunity costs of using corresponding items of equipment. One difficulty of nomenclature arises in the present context. We do not wish the term ‘competitive prices’ to imply that these prices would ensue if regulation (and in particular restrictions on entry) were abolished. We shall therefore say that the resulting prices are equal to marginal (social) costs, though this

37

S.C. Littlechild and J.J. Rousseau, US. telephone pricing policy

term is itself not without various connotations. When a long planning horizon is envisaged, so that capacities are variable, we shall use the term long-run; for a short planning horizon when capacities are fixed we use the term short-run. Because cost functions are assumed linear we have essentially that long-run marginal cost equals long-run average cost. The following formal exposition of the model is self-contained but brief. The reader should refer to Littlechild (1970) for a discussion of relevant telephone technology. There are three major simplifications: we take the number of customers as given, and we ignore consumption externalities and congestion costs. These assumptions are discussed in section 8. Let there be calls over IZ different routes (subscripted i) during q different periods of the day (superscripted k) requiring capacity on m items of eqt ipment (subscripted i). We shall assume a fixed routing pattern, so for each route j the set A, of items of equipment used by every call on that route can be identified. Similarly, for each item i of equipment, the set B, of routes using that equipment can also be identified. There are two types of variables, both required to be non-negative, xkJ = the mean volume of (three-minute) calls per hour on route i during period k; yi = effective capacity (in number of calls per hour at a specified quality of service) provided on equipment i. (In the short-run model the variables yi are fixed at prescribed levels.) Since mean hourly demand varies within each period, we define the intra-period peak factors, hy = ratio of maximum demand (in any hour) for calls on route j in period k to mean demand (per hour) on that route in that period. The capacity are written

constraints

for each item of equipment

in each period

of the day

Let hourly mean demand functions be denoted $(p,!, . . .. pz), with inverses p$(xf . . . . xg), where prices p! are measured in cents per call. Let )

tk = duration (in hours) of period k, where ‘&tk = 24; cf = constant marginal traffic cost (in cents per call) on route j in period k; gi = constant marginal cost of equipment i (in cents per day per three-minute call capacity). Note that we assume constant unit costs for each item of equipment. Economies of scale are reflected in the use of cheaper capital equipment on higher-volume routes. The capital costs include the allowed rate of return.

38

XC. LittIechild and J.J. Rousseau, U.S. telephone pricing policy

The maximand is consumers’ evaluation of usage less traffic and capacity costs, or tkp#

, *. ., ~$1d+C

t’c;xjL

(2)

k

where r$ is a variable of integration for x,.6 The line integrals are taken from the origin to the points of optimal usage (of , . . ., ~7) and are well-defined providing the integrability conditions, k

# I, j = 1, . , ., n,

(3)

are satisfied. This is a reasonable approximation where only a small proportion of income is spent on the good, as with telephones. [Cf. Hotelling (1938) or, for a recent discussion, Burns (1973) and references therein.] Let U: be the dual variable corresponding to the typical constraint (1). It may be interpreted as the marginal opportunity cost (in cents per call) of using capacity i in period k. By complementary slackness, if an item of capacity is not fully utilised at any time, then the marginal opportunity cost of using it is zero. From the Kuhn-Tucker optimality conditions we derive the following characterisations of competitive or marginal cost pricing and investment policy, p:’ = p;(xf,

= cj+h;

. ..) 4)

C

uf,

j=

l,...,

n,

k=l,...,

q.

kAJ T

t54: = gi,

i=

1 ) . ..) ml.

(5)

The price of a call in any period is set equal to its marginal traffic cost plus the sum of the marginal opportunity costs at that time of using the capacities it requires (allowing for the spare capacity necessitated by the intra-period peak factor). Each item of equipment is purchased to the point where the marginal value of the capacity it provides, summed over all periods, equals its marginal cost. 3. Application of the model The model was applied to a simple three-route network comprising a local call within Chicago, Ill. (route j = I), an intrastate toll call from Chicago to Peoria, Ill. (j = 2), and an interstate toll call from Chicago to New York, N.Y. (j = 3).

S.C. Littlechild and J. J. Rousseau, U.S. telephone pricing policy

39

The day was divided into four periods, corresponding to those obtaining for pricing purposes in Illinois in 1967 (to which year all data refer), namely Day Evening Night After Midnight

(k = 1) 6 am to 6 pm, (k = 2) 6 pm to 8 pm, (k = 3) 8 pm to 12 pm, (k = 4) 12 pm to 6 am.

Six types of equipment were identified, then aggregated into five ‘items’. The first three items contained transmission and receiving equipment particular to the three routes, the fourth was toll office equipment used by both toll routes and the fifth contained outgoing exchange and local conduit equipment common to all routes. Current Bell System qualities of service were adopted. We refer the reader to Littlechild (1970) and to Littlechild and Rousseau (1973) for further details of the network, but several aspects are worth discussing in further detail here. (a)

costs

Traffic costs comprise wages of operators and relevant commercial and accounting staff plus an allowance for uncollectibles. Equipment costs consist of capital or installation costs of the equipment, multiplied by an annualization factor incorporating maintenance costs, property taxes, physical depreciation and obsolescence, and cost of capital (including interest, income tax, dividends and retained earnings). Equipment costs in the previous paper led to prices for interstate calls of the order of one tenth of present levels. In view of this we have attempted to compare the costs used in our model with the prices which the telephone company charges to businesses for usage on a bulk basis (i.e., per channel rather than per call). Using our costs, we calculate that it would be possible to provide a connection between a Chicago user and a New York user at a cost of $597 per channel per month. Nearly two-thirds of this figure is accounted for by coaxial cable, costs of which were based upon jhe testimony of Froggatt (1966) before the FCC. Radio relay costs would have been somewhat lower. The rates which obtained in 1967 for the Bell System TELPAK service are shown below, cf. Woods (1970). (Terminal costs are excluded in both cajculations.) Evidently, the costs we have used would imply a price per channel somewhere between TELPAK schedules B and C on a full utilisation basis, or a price approximately equal to the cost per channel of TELPAK schedule’ C operated at two-thirds of base capacity. In short, the level of interstate prices in our model is not incommensurate with those charged by the Bell System on a bulk basis to large industrial and commercial users. The order-of-magnitude difference between these rates and private line service rates is a classic example of price discrimination. [Cf. also Kahn (1970, vol. II, ch. 4) and Coase (1970).]

40

S.C. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

TELPAK schedule

Base capacity (channels)

Monthly cost per system per mile

Monthly cost per channel x 900 miles at maximum base capacity utilisation

A

12

$15

31125

: D

24 60 240

$20 325 $45

$750 5375 $169

(b) Demand functions

In contrast to the assumption used in the previous paper, demand functions were taken to be interdependent between different times of day (but not between routes). Omitting the route subscript j for simplicity, they were approximated by linear functions k = 1, . . ..q.

xk = ak+ 2 a”p’, I=1

The coefficients may be written ak =

$ el”

P

and

ak = Ek( l-i1

ek’),

where p and X denote initial (1967) prices and call-volumes, and ek denotes the elasticity of demand in period k with respect to price in period I, defined in the usual way. Hence the demand curves may be fitted once the elasticity matrices are specified. We then work with the inverse demand curves pk=bk+k

I=1

bk’xz,

(8)

which yield the following quadratic expressions for value of calls in the objective function (2) bkxk++C

bk’xkx’ I

.

(9)

>

These expressions are concave providing the matrices [bk’] are negative-definite, which in turn requires the elasticity matrices [ek’] to be negative-definite. This will be the case providing own-elasticities are sufficiently large compared to cross-elasticities. 1967 revenues from the three routes were in the proportions: local calls 86 %, intrastate toll calls 0.2%, interstate toll calls 14%, whereas in Illinois Bell as a

XC. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

41

whole the proportions were 66x, 11% and 23 ‘A, respectively. The initial volumes of toll calls were therefore adjusted upwards to achieve the overall Illinois Bell ratio. Assuming 330 equivalent working days per year, the traffic on these three routes, thus adjusted, yields an annual revenue at 1967 prices equal to $lSlm. This is between 35 y0 and 40% of Illinois Bell’s annual revenue from telephone calls which in turn accounts for about 60% of the company’s total operating revenues of $819m. Dobell et al. (1972) and Davis et al. (1973) have published econometric estimates of price and income elasticities in Canada and the U.S.A. respectively, but their work is based on aggregate revenue data which do not yield estimates of cross-elasticities by time of day. Auray (1969) presents data on the effect of certain ‘after 9 pm’ rate reductions. From these data the present authors have calculated a Night own-elasticity of about -0.55 and a Day-Night crosselasticity of about 0.12 for calls in the range 507-925 miles. For calls in the range 9263000 miles the corresponding estimates are - 1.0 and 0.37. Nonetheless, these data are insufficient to give estimates for the four periods of day required by our study. We therefore obtained from Illinois Bell estimates of traffic changes in each of the four periods generated by Night and After-Midnight rate reductions in 1962 and 1963 for interstate and intrastate calls, respectively. The change in Day traffic was small but had the ‘wrong’ sign, probably because of error in making certain corrections, and was ignored. The remaining three estimates provided three restrictions on the sixteen parameters of the elasticity matrix for each toll route. The integrability conditions provided six further restrictions. In the absence of further information we assumed cross-elasticities were equal between ‘adjacent’ periods and were zero between ‘non-adjacent’ periods of the day. Evening own-elasticity was assumed equal to the simple average of Night and After-Midnight own-elasticities. Day own-elasticity was arbitrarily assumed equal to half this average (to reflect a higher proportion of business calls then). These assumptions provided the seven final restrictions on the parameters. The resulting matrices are set out below where the successive rows and columns refer to Day, Evening, Night and After-Midnight periods.

Demand elasticities by time of day Intra-Chicago (local call)

_

0.68 -1.04 0.12 0 0 0.14 -0.91 0.12 0 0 -0.52 0.12 01.82 -1.17 0

Chicago-Peoria (intrastate call)

Chicago-New York (interstate call)

I[-0.64 I[ 0.22 0 1.61 -1.28 0.22 0 0.40 -0.79 0 0 01.17 -1.76 0 0.22

1.04 -2.11 0.19 0 0.27 -2.17 0.19 0 0 -1.06 0.19 01.63 -2.05 : I

42

S.C. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

These matrices imply elasticities of overall demand with respect to constant percentage change in price at all periods of the day of -0.99 for interstate and -0.43 for intrastate toll calls. Prices for local calls have always been constant by time of day, so crosselasticity estimates are not available. The upper triangle of the local elasticity matrix was assumed equal to 0.6134 times the simple average of the interstate and intrastate upper triangles while the lower triangle was completed using the integrability conditions. The figure of 0.6134 was chosen to give an overall elasticity of -0.4 for local calls, to correspond with the data given in Auray (1969, exhibits 1 and 2, pp. 6a, b). (c) Computation’ The model as described consists of a quadratic and concave objective function in 17 variables (12 in the short-run with capacities fixed) with 20 linear constraints. It was solved using a modified version of the van de Panne and Whinston quadratic programming algorithm. Subsequent variants of the model (described in section 5) involved quadratic and concave objective functions but also one or two quadratic constraints defining a convex feasible region. We experimented with piecewise linearisation but this would have necessitated considerable programming and use of computer time to do a satisfactory job. We therefore used a nonlinear programming code, the Sequential Unconstrained Minimisation Technique (SUMT) developed by Fiacco and McCormick (1968). The size of our programme lay well within the limit of their code, but for larger and more realistic applications it would probably be preferable to take advantage of modern linear programming codes by means of linearisation. A drawback to the SUMT algorithm is that dual variables are unreliable so we determined prices in our solutions by evaluating the inverse demand curve (8) rather than by summing dual variables as in (4). 4. Marginal cost pricing structures The long-run and short-run marginal cost pricing structures are set out in table 1, together with present prices. In order to fully utilise existing 1967 capacity, the average level of prices on local, intrastate and interstate routes would need to have been reduced by 38 ‘A, 30 % and 11x, respectively. In the long-run, with capacity variable, average price levels would fall to less than half 1967 levels for local calls and to about one sixth 1967 levels for toll calls. The short-run price reductions would generate traffic increases of about 10 %, 2 % and 10 % for the three routes; the long-run price reductions would generate traffic increases of 21x, 21% and 82%. 2We have been aided by the generousadviceand assistanceof A.D. Chesher, A.C. McKay, C. Mylander and F.Y. Phillips.

43

XC. Littlechild and J.J. Rousseau, U.S. telephone pricing policy Table 1 Marginal cost pricing structure.’

Route

IntraChicago

Period

Short-run marginal costs (fixed capacity)

Long-run marginal costs (variable capacity)

Day

5

5

Evening Night After Midn.

5 5 5

3 1 1

3 1 1 1

Averageb

5

3

2

Daily volume of calls

Day Chicage Peoria

Initial (1967) situation

7,208,200

7,914,692

8,744,828

Evening Night After Midn.

65 50 40 40

65 34 5 5

13 5 5 5

Average

54

38

9

Daily volume of calls

Day ChicagoNew York

100,932

120,146

Evening Night After Midn.

140 100 70 70

129 95 60 5

9 16 29 5

Average

105

93

17

Daily volume of calls Revenue’ Traffic cost Operating profit Capacity cost Net profit Consumer surplus Total surplusd

99,142

106,904 549 52 497 141 356 674 1030

117,508 466 58 408 141 267 788 1055

194,320 235 68 167 I67 0 1107 1107

“All prices are in cents per (three-minute) call. “Average price is calculated as the sum of prices in each period of the day weighted by usage in each period. Weighting by duration of period gives essentially the same result in most cases. ‘These figures are in thousands of dollars per day. Subtractions may not exactly agree because of rounding error. “Total surplus is the sum of consumer surplus and net profit (producer surplus).

44

S.C. Littlechild

and J.J. Rousseau,

U.S. telephone pricing poliry

In the short-run profits would fall by one quarter; in the long-run they would vanish. (Recall these are ‘excess profits’, over and above the allowed rate of return which is embodied in the capital costs.) The time-of-day structure of prices is about what one would expect for the short-run. It involves prices gradually declining from morning till night, at a rather more rapid rate than in 1967, and after midnight down to the level of traffic cost of a few cents. In the long-run capacity would be expanded on local and intrastate routes to such an extent that there would be spare capacity after 6 pm, and therefore evening prices also would be reduced to the level of traffic costs. Capacity costs would be borne by daytime callers alone. However, on the long distance route a strange situation appears, for the competitive price rises towards midnight. Actually this is easily explicable, but it highlights a difficulty with the model. At the initial level of capacity daytime callers have the highest marginal valuation of output, but their demand is least elastic because they are predominantly business users. As output increases the daytime demand curve falls fastest and in fact falls below the night demand curve at outputs in the vicinity of optimal long-run capacity. At the same time, because of the linear approximation to the demand curves, elasticities fall to implausibly low levels. Linear approximations are probably inadequate when prices are cut by five-sixths and outputs are nearly doubled. If we had assumed constant elasticity (log-linear) demand curves a more plausible price structure would probably have emerged, but because the demand curves would fall less slowly they would generate output increases perhaps up to tenfold. The basic difficulty is that we have no experience of price cuts of the magnitude envisioned. On the interstate route at least, our estimates of long-run time-of-day price structure and resulting call volumes are not reliable. (The average Zetlel of prices, however, depends upon cost and is essentially independent of demand elasticities.)

5. Alternative pricing philosophies In this section we wish to ascertain which pricing philosophy best explains the 1967 structure of prices on the routes in question. Bonbright (1961, p. 23) believes that ‘public utility services are designed to be sold at cost, or at cost plus a fair profit’ which would be consistent with the marginal cost pricing structure designed by maximising surplus, possibly subject to a minimum profit constraint. By contrast Stigler (1971, p. 3) has argued that ‘regulation is acquired by the industry and is designed and operated primarily for its benefit’, so that one might expect a profit-maximising price structure. Finally, Baumol (1959) and Williamson (1964) have suggested various sales maximisation hypotheses; in particular, Peltzmann (1971) has suggested that a regulated firm will be induced to act as a vote maximiser, and hence to increase output. It is fairly obvious how the objective function (2) of the surplus-maximising

S.C. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

45

model developed in section 2 would be modified to maximise profits, sales revenue or sales volume. The overall minimum profit constraint takes the form x~~)-c~]-C

1

giyi

~

356,000,

(10)

where the right-hand side is profit per day actually obtained in 1967 on this network. 3 Because the company is regulated by both state and federal agencies, we have also explored the effect of replacing this overall profit constraint by a pair of profit constraints on intrastate and interstate calls in amounts of $242,000 and $114,000 respectively, with capacity costs allocated in proportion to actual 1967 usage in the spirit of the ‘separations procedures’ used by the regulatory agencies. In all cases models have been run with capacity fixed (short-run) and variable (long-run). Consider first the three philosophies of maximising surplus, maximising profits and maximising surplus subject to the pair of profit constraints. The implied pricing structures are shown in table 2. The unconstrained surplus-maximising philosophy, which leads to marginal cost prices, has already been discussed. If the company were maximising profit, prices of local calls would be doubled, prices of intrastate toll calls would be trebled, but prices of interstate toll calls would hardly be increased at all, compared to 1967 levels. In other words, the prices of telephone calls between Chicago and New York were effectively set at profit-maximising levels in 1967. Since long-run optimal capacity is less than 1967 capacity, there is little difference between short- and long-run prices. In the short-run maximum profit would be about 40% higher than in 1967; in the long-run about 55 % higher with the reduction of surplus capacity. An extremely close approximation to 1967 pricing practices, both by average level per route and by time of day, is obtained by maximising surplus subject to the pair of intrastate and interstate profit constraints, especially when capacity is variable. The major change from 1967 practice would be a slight reduction in intrastate toll capacity, and consequently, an average increase of under 15 % in intrastate toll prices. It may be thought that this pricing policy is essentially determined by the pair of profit constraints, but the maximisation of profits, sales revenues or sales volume subject to these two constraints leads to quite different pricing structures. For reasons of space we shall not give the detailed implications of the sales maximisation philosophies, but we may summarise the results. Maximising sales revenue leads to a pricing policy almost identical to that obtained by profit maximising regardless of whether or not a profit constraint is imposed and whether or not capacity is fixed at 1967 levels. In fact, total revenue is only 1 “//, 3This profit was calculated by substituting 1967 prices j, call volumes 2, and capacities 7 in the left-hand side of eq. (10). In the company as a whole this ‘excess’ profit was compensated by ‘losses’ on subscriber equipment and other services, as discussed in Littlechild (1970).

ChicagoPeoria

IntraChicago

Route

40 54 99,142

Average

Daily volume of calls

65 2

Day Evening Night After Midn.

Daily volume of calls 7,208,200

5

Average

Day 5 5 5

5

Period

Evening Night After Midn.

Initial (1967) situation

SlUpluS maximisation (marginal costs)

100,932

38

65 34 5 5

7,914,692

3

3 1 1

5

of different pricing philosophies.’

61,708

163

161 194 141 112

4,856,852

9

9 10 8 13

Profit maximisation

93,336

78

49

81 :;

7.410.624

5

6

5 :

Surplus maximisation s.t. pair of minimum profit constraints

Short-run (fixed capacity)

Comparison

Table 2

120,146

9

13 5 ;

8,744,828

2

3 1 :

surplus maximisation (marginal costs)

60,078

168

165 194 141 112

4,372,418

10

10 10 1;

Profit maximisation

100,110

62

6”: 50 40

7,301,086

4

5 4 3 5

Surplus maximisation s.t. pair of minimum profit constraints

Long-run (variable capacity)

Day

106,904

Daily volume of calls

?Gee footnote to table 1

549 52 497 141 356 674 1030

105

140 100 $

Average

Evening Night After Midn.

Revenue Traffic cost Operating profit Capacity cost Net profit Consumers’ surplus Total Surplus

ChicagoNew York

466 58 408 141 267 788 1055

117,508

93

129 95 60 5

681 37 644 141 503 321 824

101,598

110

153 108 67 74

550 54 496 141 355 680 1035

109.744

102

138 99 66 66

235 68 167 167 0 1107 1107

194,320

17

9 16 29 5

671 34 637 83 554 277 831

97,162

116

155 113 73 74

544 54 490 135 355 684 1039

109,396

103

136 100 68 65

48

XC. Littlechild and J. J. Rousseau, U.S. telephone pricing policy

higher and profit only 2% lower than under profit maximisation. The reason for this is that marginal costs are very low compared to optimal prices. Maximising sales volume (i.e., total number of calls) subject only to breaking even leads in the short-run to opportunity cost prices. The long-run policy is remarkably different. Instead of all prices being lowered, prices of toll calls are raised to profit-maximising levels while local calls are given away for free. This policy remains basically the same when either form of profit constraint is imposed, regardless of whether capacity is assumed fixed, except that average price of local calls is raised to about 4 cents. Thus it does not seem that either form of the sales maximisation hypothesis provides a complete explanation of actual prices on this network. Note, however, that in many areas within Illinois, but outside of Chicago, local calls are unmetered and hence free, although the reason given is the resulting saving in metering costs. To summarise, the best explanation of 1967 pricing policy is the maximisation of surplus subject to a pair of intrastate and interstate minimum profit constraints. But this policy essentially involved the maximisation of profit on the interstate route with prices for intrastate calls midway between average cost and profit-maximising levels. Furthermore, there was price discrimination in that long distance telephone lines were available to large users on a bulk basis at prices approximately equal to long-run average costs.

6. The effects of regulation In this section we shall attempt to identify and evaluate the effects of regulation of the telephone network. We examine three issues: peak-load pricing, regulation as a whole, and state regulation in particular. It will be convenient to use consumer and producer surplus as a measure of benefits. There is no point in reviewing here the extensive discussion concerning this technique; for recent analyses see Harberger (1971), Burns (1973) and Bergson (1973). From the recent economic literature [e.g., Littlechild (1970) and references therein] one has the impression that increased attention by regulators to peakload pricing would yield substantial benefits. We have shown in section 4 that rates set equal to marginal costs would have a much steeper time-of-day structure. But this is not the case once minimum profit constraints are imposed. Indeed maximum surplus subject to these two constraints is less than 1% above the 1967 level. Alternatively, the increased benefit is less than 2% of 1967 revenue. If our small network were representative, these savings would amount to about $8m per annum in Illinois as a whole, but surely would require such fine tuning as to be unattainable in practice. Moreover the cost of installing a two-period (peak/off-peak) metering system for local calls in Chicago has been estimated at $15m-$2Om. In Illinois the benefits from more enlightened regulation will not come from improved peak-load pricing structures alone, and in

S.C. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

49

particular, it does not seem worthwhile to differentiate local call prices as long as the existing profit constraints are operative. What would happen if regulation of telephone companies were abolished? If new competition or the threat of it could drive down call prices to the level of long-run average costs, then one would expect prices of local calls to be cut by about 60 ‘A and of toll calls by 80-90 %. The net benefits from the new telephone calls thus generated would amount to about one eighth of 1967 revenue in our network, or about $60m per annum if valid for Illinois Bell as a whole. But if, alternatively, one or more telephone companies were able to establish (joint) profit maximising rates for calls, then one would expect prices of local calls to double and prices of intrastate toll calls to almost treble. The resulting reduction in telephone calls would represent a net loss equal to somewhat over one third of 1967 revenues, or about $185m per annum for Illinois Bell as a whole. Thus, the effects of regulation depend crucially upon what one anticipates the alternative would be. Since the FCC decision (in the MCI case) to allow limited entry in telecommunications systems, there have been over 2000 applicants for licenses. This suggests that long-run marginal cost pricing would obtain on highervolume interstate routes. Perhaps regulation could keep down prices of intrastate calls if prices of other services, especially rentals, were allowed to rise to cover costs of those sources. Revised regulation coupled with free entry might therefore generate net benefits of up to $60m annually in Illinois. It is interesting to speculate on the national implications of this figure. In 1967 Illinois Bell accounted for about 5% of operating revenues from all US telephone companies. To the extent that our network and Illinois Bell are representative of the national scene, it seems that net benefits from revised regulatory emphasis might amount to about one billion dollars annually. This is in excess of Harberger’s (1954) estimate of welfare loss from monopoly in manufacturing industry as a whole, namely one tenth of one percent of national income, which would amount to about $8OOm for 1967. [Bergson (1973) has recently argued that Harberger’s calculatron is open to question, and might well be an underestimate.] These calculations refer to net changes in benefit, i.e., to so-called ‘allocative efficiency’, but this aspect is dramatically outweighed by distributional considerations. Assume again the network is representative of Illinois as a whole. Under an opportunity cost pricing policy consumers would not only obtain the net increase in benefits of $6Om, but would also receive a transfer of the telephone company’s total ‘excess’ profits of $316m per year. Conversely, a profit-maximising policy would yield a net loss of $185m but this conceals a loss by consumers of $362m offset by a gain in company profits of $177m. In order to evaluate the effect of the Illinois state regulatory commission, let us compare the pricing policy when the pair of minimum profit constraints is replaced by a single overall profit constraint. With fixed capacity there is

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S.C. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

little difference in the price structure. Brief details of the variable capacity case are given in table 3. In the long-run prices of intrastate calls (both local and toll) increase by about 20% while prices of interstate calls fall by about 45 %. In other words the effect of state regulation is to reduce prices of intrastate calls and to keep the price of interstate calls nearly twice what they would otherwise be (given the total profits to be earned by the company). The net cost of this state influence in terms of lost consumer surplus amounts to nearly 43% of 1967 revenue. For Illinois as a whole this would amount to about $21m per year. The company’s annual loss of $35m profit on intrastate business is exactly compensated by increased profit on interstate business. However, allocating the equipment costs to routes on the basis of 1967 usage reveals that the net loss of $21m on consumer surplus is actually a gain of $46m to intrastate callers offset by a loss of $67m to interstate callers. This redistribution of benefits to the state commission’s ‘constituents’ presumably justifies its existence. Stigler and Friedland (1962) have presented evidence that regulation of U.S. electricity utilities is ineffective. They gave two reasons: electricity utilities have little long-run monopoly power anyway, because of substitute fuels, and effective regulation of a complex industry is difficult to enforce. By contrast, our data suggest that demand for telecommunications is inelastic so that monopoly prices are significantly above costs; our results indicate that regulation was effective at the intrastate level but not at the interstate level. It is easier to explain these results in terms of Stigler’s (1971) theory of economic regulation. The telephone industry, dominated by a single large firm and faced by millions of mostly small and geographically dispersed customers, has managed to ‘capture’ the FCC and maximise profits on interstate routes, making concessions to the largest customers where alternative technologies are available. (These ‘concessions’ have gone notably further since 1967, of course.) However, the industry has not had the same success at state level, where the regulatory commission has a better-defined and cohesive ‘constituency’ and opposing forces seem to be about evenly matched (in the sense that prices are roughly midway between cost and profit maximising levels). 7. Sensitivity analysis The limited data available on the effects of rate reductions at different times of day forced us to make quite crude assumptions about the pattern of demand elasticities. The resulting matrices of own- and cross-elasticities did not seem unreasonable. Nevertheless we carried out four systematic sensitivity analyses to determine the nature and extent of the dependence of our conclusions upon the particular values of elasticity chosen. The first two sensitivity analyses repeated the basic twenty sets of calculations (ten models, each for fixed and variable capacity) with elasticity matrices simply

‘See footnotes to table 1. “Without state regulation. cWith state regulation.

Average price Daily vol. of calls (‘000) Revenue Traffic cost Operating profit Capacity cost Net profit Consumer surplus Total surplus

Table 3

40 337 115 222 443 665

698; 317 70 5 6.5 6 59 116 175

57 155 95 8 87 12 75 148 223 543 54 489 133 356 707 1063

7239

Total

730: 353 42 310 119 191 483 674

Chicage New York 103 109 129 6 123 9 114

ChicagoPeoria 62 100 62 5 57 6 51 127 178

IntraChicago

ChicagoNew York

IntraChicago ChicagoPeoria

Surplus maximisation with dual profit constraints (variable capacity)

Surplus maximisation with overall profit constraint (variable capacity)b

Effects of state regulatiun:

7510 544 54 490 135 355 684 1039

Total

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S.C. Littlechild and J.J. Rousseau, U.S. telephonepricing policy

increased and decreased, respectively, by 50%. In the third and fourth sensitivity analyses own-elasticities were increased relative to cross-elasticities, in the one case by increasing own-elasticities by 50% and in the other case by decreasing cross-elasticities by 50%. The third and fourth cases gave very similar results, and will not be distinguished here. We examine in turn the three questions dealt with in sections 4, 5, 6 respectively. In order to save space the tables of prices themselves are not reproduced here. (a) Marginal cost pricing structure Our previous characterisations of marginal cost pricing structures are essentially independent of the general level of elasticities, for both fixed and variable capacity. Thus, a 50% change in the level of all elasticities, whether increase or decrease, produces at most a 5% change in average price on any route. Increasing own-elasticities relative to cross-elasticities essentially reduces the ability to shift from peak to off-peak periods, with the result that peak-load pricing structures are slightly steeper. The long-run average price of the interstate call is also slightly higher, at one fifth rather than one sixth of the 1967 level, but this amounts to an absolute difference of only 4 cents. (b) Alternatice pricing philosophies For all sets of elasticities, the price structure which most closely resembles that of 1967 is obtained by maximising surplus subject to a pair of inter- and intrastate minimum profit constraints. The similarity is closest with the original set of elasticities, although halving all elasticities also produces a close result. For intrastate toll calls the correspondence is closest in the long-run when elasticities are highest. 1967 interstate prices are consistently close to profitmaximising ones, especially for the lowest elasticities. Under all of the elasticity transformations, maximising sales revenue is essentially equivalent to maximising profits while maximising sales volume produces profit-maximising prices for toll calls with free local calls. (c) The effects of regulation For all the sensitivity analyses, abolishing the Illinois profit constraint leads to price increases within Illinois and price decreases for interstate calls. However, for most sets of elasticities the price changes are lower: from 8 % to 22 % increases for Illinois calls, compared to 20 % originally, and from 20 % to 50 % decreases for interstate calls, compared to 45% originally. The net effect is an increase in surplus ranging from 1.5% to 4% of 1967 revenue, compared to 4-)x originally. If the network is representative of Illinois as a whole, it would

SC. Littlechild and J.J. Rousseau, U.S. telephone pricing policy

53

seem that the net costs of state regulation might be as low as one third of the $21 m per annum originally estimated. Our evaluation of regulation as a whole is even more dependent upon elasticity. Generally speaking, the more elastic is demand the less scope there is for monopolistic price increases, but the greater is the loss from a given monopolistic price increase. Suppose first that all elasticities are doubled, or that ownelasticities are doubled relative to cross-elasticities. The benefits of a competitive fee structure would be about 25 % higher than originally estimated. On the other hand a profit maximising price structure would involve much lower price increases for intrastate calls, with resulting net loss in surplus of the order of one quarter of 1967 revenue, rather than one third as before. Originally, for Illinois as a whole we were balancing a potential competitive gain of $60m against a potential monopoly loss of $185m; with higher elasticities we are balanci.ig a potential gain of $75m against a potential loss of S140m. The risk of modifying regulation is rather less. But now suppose that all elasticities are halved. The competitive price structure is not much changed but the output is lower and benefits are worth only 6% of 1967 revenue. On the other hand profit-maximising prices are increased five- or six-fold within Illinois and the loss of surplus is over half as much again as 1967 revenue. We are now balancing a potential gain of $30m against a potential loss of over $750m. Is the risk worth taking? 8. Qualifications and extensions We shall examine in turn in what way our conclusions depend upon certain simplifications in the model, namely, fixed number of subscribers, no consumption externalities and no congestion costs. It seems to be the case that in Illinois in 1967 (and indeed in telephone systems throughout the world) basic equipment rentals were cross-subsidised at the expense of calls. As both rentals and call prices are adjusted towards costs we would expect most subscribers to remain in the system, some new subscribers to join for whom consumer surplus now exceeds rental, and some previous subscribers to leave for whom the converse is the case. For the first group the increased rental is simply a transfer of income to the company, with no net social loss. The second group represents an additional consumer surplus from calls not included in the previous calculation. The third group represents a loss in previously calculated consumer surplus but a loss which is more than offset by reduction in consumer costs of membership in the system. Consequently, our calculations of potential benefits from marginal cost pricing are unambiguously underestimates when number of subscribers is allowed to vary. It is sometimes suggested that there are external economies of consumption associated with telephone calls because people like receiving calls. It seems probable that most of these benefits can be internalised by reverse charge calls

54

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and J.J. Rousseau,

U.S. telephone pricing poIicy

and other means. More often, it is suggested that there are significant external economies associated with membership in a telephone system, which justifies the practice of cross-subsidising rentals at the expense of call prices. There seems to be no empirical evidence on the extent of such externalities, and indeed the policy of cross-subsidisation would probably be consistent with profit maximisation, c.f. Littlechild (forthcoming). We suspect that, in the present U.S. telephone system, the external economies sacrificed by setting rentals equal to consumer costs would be minimal, and in any case offset by non-external economies, but at present there is no way of proving or disproving this conjecture. Marchand (1967, 1972), Kay (1968) and Pyatt (1972) have embodied congestion costs in their theoretical models and it should be possible to do the same for the present models, rather than specify a fixed quality of service. The difficulty once more is that no empirical information seems to be available on consumer evaluations of time lost. The numerical examples calculated by Deschamps (1974) suggest that congestion costs will make less steep the optimal time-of-day pricing structures because peak demand is partly accommodated by deteriorating quality of service. Elasticities of demand, consumer costs, external economies and congestion costs are clearly important topics for further empirical research in telecommunications systems.

9. Conclusions We have developed a mathematical programming model of a small telephone network centred on Chicago, in order to analyse the pricing policy of the Illinois Bell Telephone Company in 1967. With reference to the questions posed in the introduction, our results may be summarised as follows: (1) (2)

(3)

With capacity allowed to vary, marginal cost prices would be about one half 1967 levels for local calls and one sixth 1967 levels for toll calls. 1967 pricing policy is well explained by the maximisation of consumer plus producer surplus subject to a pair of interstate and intrastate minimum profit constraints but this policy actually involved profit maximisation on the interstate route; sales maximisation is not a complete explanation. (i) There is no further scope for peak-load pricing as long as interstate and intrastate profit constraints remain. (ii) If regulation were to be modified marginal cost pricing might yield net benefits of the order of $60m annually in Illinois, whereas profit maximisation might involve a net loss of $185m. In either case these resource allocation elements would be overshadowed by redistribution between consumers and the telephone company. (iii) Illinois state regulation keeps the price of interstate calls nearly twice what they would otherwise be (for a given company profit). This

S.C. Littlechild

and J.J. Rousseau,

U.S. telephone pricing policy

involves an annual gain of about $46m to Illinois by a loss of $21m to interstate callers.

intrastate

55

callers offset

Extensive sensitivity analysis revealed that results (1) and (2) and (3i) were robust with respect to changes in price-elasticities of demand but that the costs and benefits of regulation are quite sensitive to elasticities. The model might usefully be extended to analyse the number of subscribers in the system and the effects of congestion costs and consumption externalities.

References Auray, R.R., 1969, Discussion of‘Margina1 cost pricing of telephone calls’ by SC. Littlechild (Long Lines Department, American Telephone and Telegraph Company) paper presented at Public Utilities Seminar, Dartmouth College. Baumol, W.J., 1959, Business behaviour, value and growth (MacMillan, New York). Bergson, A., 1973, On monopoly welfare losses, American Economic Review LXIII, no. 5, 853-870. Burns, M.E., 1973, A note on the concept and measure of consumers’ surplus, American Economic Review LXIII, no. 3, 335-344. Coase, R.H., 1970, The theory of public utility pricing and its application, Bell Journal of Economics and Management Science 1, no. 1, 113-128. Davis, B.E., G.J. Caccappolo and M.A. Chaudry, 1973, An econometric planning model for American Telephone and Telegraph Company, Bell Journal of Economics and Management Science 4, no. 1, 29-56. Deschamps, P.J., 1974, The computation of optimal telephone rates, mimeo. (Center for Operations Research and Econometrics, Heverlee, Belgium). Dobell, A.R., L.D. Taylor, L. Waverman, T.H. Liv and M.D.G. Copeland, 1972, Telephone communications in Canada: Demand, production and investment decision, Bell Journal of Economics and Management Science 3, no. 1, 175-219. Fiacco, A.V. and G.P. McCormick, 1968, Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York). Froggatt, A.M., 1966, Testimony to FCC, Docket no. 16258, Bell Exhibit 24. Harberger, AC., 1954, Monopoly and resource allocation, American Economic Review (Proceedings) 44, 77-87. Harberger, A.C., 1971, Three basic postulates for applied welfare economics: An interpretive essay, Journal of Economic Literature IX, no. 3, 785-797. Hazlewood, A., 1950-1951, Optimum pricing as applied to telephone service, Review of Economic Studies 18, 67-78. Hotelling, H., 1938, The general welfare in relation to problems of taxation and of railway and utility rates, Econometrica 6, 242-269. Kahn, A.E., 1970, The economics of regulation: Principles and institutions, 2 vols. (Wiley, New York). Kay, J.A., 1968, Pricing and investment criteria in public utilities: The case of telephone service, unpublished M.A. dissertation (University of Edinburgh). Littlechild, S.C., 1970, Peak-load pricing of telephone calls, Bell Journal of Economics and Management Science 1, no. 2, 191-210. Littlechild, S.C., forthcoming, Two-part tariffs with consumption externalities, Bell Journal of Economics and Management Science. Marchand, M.G., 1967, Welfare pricing of a randomly rationed commodity under a budget constraint: The case of telephone services, CORE Discussion Paper no. 6711 (Center for Operations Research and Econometrics, Heverlee, Belgium). Marchand, M.G., 1973, The economic principles of telephone rates under a budgetary constraint, Review of Economic Studies XL (4), 124, 507-515.

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de Montbrial, T. and J.C. Muller, 1969, Tarification du telephone, Mimeo. (no source given). National Board for Prices and Incomes, 1968, Post office charges, Report no. 58, Cmnd 3574 (HMSO, London). Pyatt, G., 1972, So.me economics of a public utility, Discussion Paper no. 28 (Center for Industrial, Economic and Business Research, University of Warwick). Samuelson, P.A., 1952, Spatial price equilibrium and linear programming, American Economic Review 42, 283-303. Shepherd, W.G., 1966, Residence expansion in the British telephone system, Journal of Industrial Economics 14, 263-274. Stiglcr, G.J., 1971, The theory of economic regulation, Bell Journal of Economics and Managcment Scicucc 2, no. 1, 3-21. Stigler, G.J. and C. Friedland, 1962, What can regulators regulate? The case of electricity, Journal of Law and Economics V, l-16. Williamson, O.E., 1964, The economics of discretionary behaviour: Managerial objectives in a theory of the firm (Prentice-Hall, Englewood Cliffs). Woods, F.J., 1970, Testimony to FCC, Docket no. 18128, Bell Exhibit 2.