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Aur"‘bf’ . “V. a. . » 3.3.2.... .9 :72 . ...w:fl.v.v; {11.1.5.3}; .. rt '7 7-1 .vnyIJ I I) 'lle)” :rfiifiiifin: v-1...fiyi. :5... 2.3..- .1 . figufii cavoc~t ‘ . . .\ veil/l .120); fig . . 4.}. run»; . ..:.g .0061". graph“ ,linv) "u’l’f r . «4.0%. dunno. .1, I .. a e: ¢...)Lup..0o. 4.3,... at 12.3.19 32:7 2?...“ rurxl x... 27‘ . . .. a ._.....r .J : 1.......... .3. o. 19.. v.5 «In... . u Ir‘vnr .W‘u\fiUl.‘.od 3. u... . .. . ....»m.... 5 4. n 3.00.... er.»!f../:tt. - . 99.9»: 7. a!» #1.»). 9 . if.) .7... 5.. n .tr.v!l:rfnlru¢ ’1‘}: 3......» 1.... . .y. . . y .. L’y .. 7. a. . a.....w....1.ox:l\v\ l.)- xt..3v<..m.flx. fiflmamarJi-Z .. : .\ 2...: 5.. . 5.101%: sad.” , 3W5: «. , 139%! ABSTRACT POSTAL PRICING PROBLEMS AND PRODUCTION FUNCTIONS by Rodney E. Stevenson The reorganization of the U.S. Post Office Depart- ment in 1971 established a new and quasi-private United States Postal Service (USPS) and transferred the authority to establish rates, fees, and classifications from the Congress to the Postal Rate Commission (PRC) and the USPS. A basic question facing the newly formed PRC is the extent to which price discrimination is desirable and allowable in the USPS rate structure. To analyze the question, two pricing models which predicate price discriminatory pric- ing rules are considered. One, the Boiteux-Baumol con- sumer surplus maximization model, is shown to require prodigious quantities of information for proper and justi- fiable implementation. The other, the classic economy of scale model, rests on an assumption of increasing returns in the postal production function. The technical relation- ships of the postal production processes are investigated to test for the existence of economies of scale. The study employs input, output, and cost data for the years Rodney E. Stevenson 1961—1971. Through the estimation of production functions, cost functions, and factor demand functions and the con- sideration of Kendrick-type productivity measures, it is found that the USPS did not operate under conditions of economies of scale. Rather, it appears that the postal process operates under conditions of decreasing returns to scale. Thus, price discriminatory rate structures appear to be neither beneficial nor justifiable. In addition, the need for maintenance of a legal monopoly over letter mail is strongly questioned. POSTAL PRICING PROBLEMS AND PRODUCTION FUNCTIONS BY {3 . a) Rodney ET7Stevenson A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1973 Copyright by RODNEY EUGENE STEVENSON 1973 To Marguerite B. Stevenson ii ACKNOWLEDGMENTS The successful completion of a Ph.D. dissertation is a rather common feat which requires an uncommon amount of guidance, encouragement, tolerance, constructive ex- tortion, forbearance, patience, and goodwill from people who have little to gain from the venture. The author of this work is particularly fortunate to have had the as- sistance of several exceptionally generous individuals. Professor Harry M. Trebing fully deserves the author's deepest and warmest appreciation. Dr. Trebing has continued to provide intellectual stimulation, rational advice, and moral encouragement far beyond that offered by the average dissertation committee chairman. Indeed, not only this thesis, but the author's basic framework of economic analysis and perception as well, owe a debt to Professor Trebing. The other members of the thesis committee, Pro- fessors Lawrence Officer and Paul Strassman, have made a significant contribution to the work. Their prompt at- tention and helpful suggestions are strongly appreciated. Jan Kmenta has read and criticized parts of the disserta- tion and in doing so has greatly improved the logical iii iv tightness and justification of the entire study. Arthur Havener and Jeffrey Roth have provided several helpful suggestions. A special word of appreciation is due to Professor Warren Samuels for having conveyed to the author a feeling for the basic power struggles which un- derlie the deceptively dry and value judgment free pre- tense of the economic field. Special thanks are due to Delbert M. Steiner. This study literally could not have been completed without his exceptional understanding and encouragement. Dr. Beatrice Aitchison and Norman Schwartz, as well as Mr. Steiner, have provided the author with a wealth of information, a ready sounding board, a measure of candor, and a refreshing spirit. Linda D. Stanley, who typed the drafts of this manuscript, is greatly appreciated for her excellent typing, her good humor, her tolerance of the author's abominable verbal skills, and her wise advice and understanding which came from having just helped her husband successfully complete his dissertation. Finally, any married Ph.D. candidate who did not acknowledge his enormous debt to his spouse would be guilty of a venial sin, if not a mortal one. The author hopes to keep his sins to a permissible minimum. TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . LIST OF FIGURES . . . .I. . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . . . . USPS - THE INSTITUTION . . . . . . . . . . . Services . . . . . . . . . . . . . . . . Size . . . . . . . . . . . . . . . . . . Production Process . . . . . . . . . . . Structural Organization . . . . . . . . . Competitive Environment . . . . . . . . . THE PRICING PROBLEM OF THE POSTAL RATE COMMISSION . . . . . . . . . . . . . . . . The Boiteux-Baumol Model and the Inverse Elasticity Rule . . . . . . . . . . . . Pricing Under Conditions of Economies of Scale . . . . . . . . . . . . . . . . . PRODUCTION FUNCTIONS, COST FUNCTIONS, AND PRODUCTIVITY . . . . . . . . . . . . . Postal Production Functions . . . . . . . Postal Cost Functions and Factor Demand Equations . . . . . . . . . . . . . . An Alternative Approach to Cost and Factor Demand Equation Estimation . . . Productivity Measures . . . . . . . . . . Qualifying Remarks . . . . . . . . . . . CONCLUSIONS AND POLICY IMPLICATIONS . . . . The Pricing Question . . . . . . . . . . Results from the Investigation of the Postal Production Process . . . . . . . Implications for Pricing Policy . . . . . Implications for Broader Public Policy . vii ix ll 15 18 21 25 30 41 46 46 56 67 73 75 85 87 91 92 95 vi BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . 97 APPENDIX A: REVIEW OF RELEVANT LITERATURE . . . . 106 APPENDIX B: DATA, DATA SOURCES, AND METHODS OF COMPILATION . . . . . . . . . . 115 10. 11. 12. l3. 14. 15. 16. LIST OF TABLES Page RELATIVE IMPORTANCE OF VARIOUS MAIL CLASSES AND SERVICES . . . . . . . . . . . . 10 COMPARISON OF THE UNITED STATES POSTAL SERVICE TO THE LARGEST INDUSTRIAL, RETAIL, AND UTILITY COMPANIES . . . . . . . 12 BUDGET AUTHORITY AND EMPLOYMENT OF MAJOR FEDERAL AGENCIES . . . . . . . . . . . 14 RETURN TO SCALE PARAMETERS OF THE COBB- DOUGLAS, CONSTANT ELASTICITY OF SUBSTITUTION, AND GENERALIZED PRODUCTION FUNCTION . . . . . . . . . . . . 55 COST FUNCTION PARAMETERS . . . . . . . . . . . 64 LABOR DEMAND EQUATION . . . . . . . . . . . . 64 SPACE DEMAND EQUATION . . . . . . . . . . . . 64 TRANSPORTATION DEMAND EQUATION . . . . . . . . 65 CAPITAL DEMAND EQUATION . . . . . . . . . . . 65 RETURN TO SCALE ESTIMATES . . . . . . . . . . 66 COST FUNCTION . . . . . . . . . . . . . . . . 71 LABOR DEMAND . . . . . . . . . . . . . . . . . 72 CAPITAL DEMAND . . . . . . . . . . . . . . . . 72 SPACE DEMAND . . . . . . . . . . . . . . . . . 72 TRANSPORTATION DEMAND . . . . . . . . . . . . 73 SCALE PARAMETERS . . . . . . . . . . . . . . . 73 Vii Table 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. viii Page PRODUCTIVITY MEASURE . . . . . . . . . . . . 75 RATIO OF POSTAL WAGE TO WAGE OF ALL PRIVATE INDUSTRY . . . . . . . . . . . . . 81 QUALITY OF POSTAL SERVICE FOR SELECTED CLASSES OF MAIL . . . . . . . . . . . . . 83 OUTPUT WEIGHTS FOR MAIL CLASSES AND SPECIAL SERVICES . . . . . . . . . . . . . ll9 POSTAL DATA . . . . . . . . . . . . . . . . 129 COST FUNCTION . . . . . . . . . . . . . . . 132 LABOR DEMAND . . . . . . . . . . . . . . . . 132 SPACE DEMAND . . . . . . . . . . . . . . . . 132 TRANSPORTATION DEMAND . . . . . . . . . . . 133 CAPITAL DEMAND . . . . . . . . . . . . . . . 133 SCALE PARAMETERS . . . . . . . . . . . . . . 134 Figure 1. LIST OF FIGURES Page REDUCTION IN UNIT COST DUE TO A DEMAND SHIFT . . . . . . . . . . . . . . . 42 PRODUCTIVITY CHANGE OVER TIME . . . . . . . 76 GRAPH OF AGGREGATED OUTPUTS BASED ON VARIOUS WEIGHTING SYSTEMS . . . . . . . . 120 INTRODUCTION Over the last few years, the behavior and perform- ance of the United States Postal Service, and its prede- cessor, the U.S. Post Office Department, have come under severe and rising criticism. Complaints, generated by the rising postal costs and the falling quality of service, have given rise to several Congressional hearings, a major Presidential Commission investigation, and a sweeping Congressional reorganization of the Post Office Department. AS part of the reorganization plan, which severed the POD from the President's Cabinet and reinstituted it as a "public corporation", a regulatory commission, the Postal Rate Commission, was established to consider rate and classification matters. Previously rate and classifica- tion issues had been decided in the political environment of Congress. The reorganization attempted to replace political considerations with rational and economic ones. This study is concerned with economic issues which bear greatly on the rate and classification problems facing the Commission, and the task of regulation in general. The study investigates two major, related issues. The first, and of primary importance, pertains to the nature of the Postal Service's underlying production process. An inquiry is made to determine the degree of returns to scale (a production function concept) or scale economies (a cost function concept) in the relevant region of production. The investigation of the technical relationship among outputs, inputs, and costs is conducted through several different approaches. Three types of production functions (Cobb-Douglas, Constant Elasticity of Substitution, and the Zellner—Revankar Generalized) are estimated directly. In recognition of the possible existence of simultaneous equation bias, the technical model is reformulated using the approach of cost minimi- zation to a production function constraint. The result- ant derived input factor demand equations and cost func- tions are estimated in order to obtain the production function coefficients. Such an approach is feasible because of the Shepherd duality between cost and produc- tion functions. The cost function and derived factor input demand equations are formulated in the usual manner, i.e. in terms of factor prices and output. An analysis of the first order conditions of the cost minimization lagrangian equation indicates that the cost equation can be recast in terms of the ratio of factor inputs, the index of price of one factor, and the level of output. Likewise, the factor demand equations can be recast solely in terms of factor input ratios and the level of output. This approach, which to the knowledge of the researcher has not been previously employed, avoids several data and data manipulation problems. The recast equations are also estimated. A final alternative approach to the investigation of returns to scale is made through the consideration of the Kendrick type total factor producti- vity measure. Though previous researchers have considered the technical production relationships of the postal system (5, 6, 12, 24, 29, 34, 49, 59, 87, 101), this study constitutes the first thorough empirical investi- gation of the scale economies of the total postal system. A second issue considered in this study centers upon the desirability, or applicability, of discriminatory pricing practices for postal services. Two major models, the classic economies of scale model and the Boiteux- Baumol consumer surplus maximization model, have been suggested as either a rational for price discrimination or an appropriate approach for determining quasi optimal prices which may be price discriminatory. These are considered in light of the statutory constraints of the Postal Reorganization Act which prohibit the existence of undue discrimination. The two approaches are investi— gated to determine their informational requirements and their applicability to the postal problem. The Postal Service is a unique governmental and business organization. The combination of its institu- tional characteristics, production procedures, market environment, and operational problems sets it apart from other ventures. As such, the USPS is fully deserving of careful and thorough analysis in its own right. However, an investigation of the Postal Service will yield infor- mation which is also applicable to several problems which lie in the general economic domain and which face other enterprises. Generally, this study contributes to the growing analysis and re-evaluation of the regulatory process. Over the last few years there has developed an expanding body of literature on regulatory problems. This revived concern with regulation has been stimulated by major theoretical developments (e.g. those dealing with the behavior of the regulated firm (4), peak load pricing (78), quasi-optimal pricing under regulatory constraint (8), etc.), fostered by the analysis of performance under regulation and of the regulatory framework itself (e.g. MacAvoy (50), Trebing (79), Noll (66), et al.), and has brought forth new text books (38, 69), a new regulatory journal (The Bell Journal of Economics and Management Science), and major studies in government (3) and presti- gious foundations (e.g. The Brookings Institution). Many of the problems incurred in regulating the Postal Service are parallel to regulatory problems in the traditional commissions. Thus, this study contributes to the study of economic problems common to several institutions. Speci- fically, this study adds to the economic literature through its analysis of the Boiteux-Baumol pricing model and the development of appropriate techniques for estimation the scale economies of an industry whose output is solely demand determined. The format of the study is as follows: The in- stitutional background and setting of the Postal Service is considered in Chapter 2. Chapter 3 specifies the pricing problem facing the Commission and considers two pricing models: the Boiteux-Baumol model, and the classic economy of scale model. An investigation into the tech- nical relationships among the postal products, factor inputs and factor prices which might indicate the existence of economies or diseconomies of scale is reported in Chapter 4. Also, Kendrick type productivity measures are deveIOped and considered. In the fifth chapter, findings are summarized and potential policy conclusions are set forth. A review of the literature pertinent to production function and productivity studies of the Postal Service, production functions, and productivity problems, is out- lined in Appendix A. The sources of data, methods of aggregation and data problems are specified in Appendix B. An alternative cost function is reported in Appendix C. USPS - THE INSTITUTION The institution chosen for this study is a unique economic organization in certain respects, yet is quite common in others. Under the authority of Article I Sec- tion 8 of the Constitution, the Service has grown to be a large economic enterprise by any standard. Like the Tennessee Valley Authority and the National Railroad Passenger Corporation, it is a government corporation engaged in a market type activity. Unlike other govern- ment operations, however, the USPS is the only major socialist enterprise actively regulated on economic matters by another body within the government.1 Like other large business corporations, the Ser— vice is a multi-product enterprise which operates in markets with varying degrees of monopolistic control. Indeed, certain similarities can be drawn between the USPS pricing philosophy and that of other large firms-- particularly those in the regulated sphere. Unlike other organizations however, the Service is forbidden to operate at a profit. Five aspects of the Service—-its service 1Technically the Federal Power Commission has an oversight authority with the Tennessee Valley Authority, but this authority has never been actively or meaningfully asserted. offerings, size, internal operations, competitive environ- ment, and organizational structure--bear strongly upon the institutional constraints of this study and thus deserve attention. A. Services The USPS is a communications firm involved in the delivery of letters, printed matter, and small shipments. Factors which bear upon the dimensions of its product are distance, size, shape, weight, speed of handling, special service attention, and the nature of pickup and delivery. For some classes, though not for all, prices are con— structed on the basis of the various output dimension lines appropriate to them. The major mail class service offerings are: (1) Air Mail (6) Third Class Mail (2) First Class Mail (including (7) Fourth Class Mail Post Cards and Postal Cards) (8) Official Mail (3) Priority Mail (including Free (4) Second Class Mail for the Blind) (5) Controlled Circulation In addition, the USPS provides the following special services: (1) Registry (4) Collect on Delivery (2) Certification (5) Special Delivery (3) Insurance (6) Money Orders Air Mail and First Class Mail consist primarily of personal correspondence, bills, and business 2A full description of the Service's offerings, as well as all relevant rules and regulations pertaining to them, are contained in (96). communications. Approximately 70 percent of Air Mail and First Class volume is generated by business, with the remaining 30 percent eminating from households.3 Priority mail provides a "First Class" type service for letters, flats or parcels weighing more than twelve ounces. Second Class and Controlled Circulation mail are primarily magazines and newspapers. Third Class mail primarily encompasses direct mail circulars, catalogs, and small parcels of merchandise weighing less than one pound. Approximately 95 percent of the volume comes from business. Fourth Class includes parcels, books, records, and other small shipments. The volume of this Class is approximately 10 percent household and 90 percent business. Official Mail encompasses franked mail and penalty mail (i.e., government mail), and free mail matter for the blind. International mail includes both surface and air letters and parcels mailed to or from foreign destinations. The relative importance of the various classes in terms of mail volume and revenue is shown in Table l. 3Information on the customer components of the various mail classes was derived from the Arthur D. Little marketing study (1) and from discussions with postal experts. lO .mmmD m£# MO unommu mamaamcd umOO paw mscm>mm Hema OED Eonm Um>flnop mmz coaumEHOMCH one "mousom .mmuspflpcwmxm Hmuou mo unmouwm on maco OOHO>OO mmscm>wm I muozRR .mCHCGDOH OD USO ppm Mom was momMDCOOHOmR RRooo.oon.mmn.mw .um.so ooo.noo.mam .mna ooo.mmo.mnm.ma ooo.ooo.mmm.mm AHMSUOOV Hapoe OOH ooa ooa ooa Rxpamoumdv Hmuoe m.v II I: II mmOH>me Hafiommm H.e h.H n.a o.a HA6: HMCOHPMQMOMCH o.m m.m v.e m.m Ham: HMHOHmmo H.NH h.mv N.om H.H mmmau Cpusom w.ma m.mH H.ma w.mm mmmau CHASE m. w. m.H m. OOAMMHDOHHU OOHHOHMCOO m.m N.na m.em o.HH mmwao paoomm v.v m.m m.m m. Ham: thHOflHm m.am m.HH H.NH m.nm mmmau umnflm wa.m we. we. wn.a aflmz Mfld mmscm>mm Doom OHQDO pgmfioz mmomflm Aauma Ammo mMUH>mmm 92¢ mmmm¢do HHdS mDOHm<> m0 MUZ¢BmOmZH M>HB4Hmm H mqmflB ll B-§i_z_e The USPS is both a Brobdingnagian "corporation" and government organization. In 1971, on the basis of sales, the USPS would have ranked fifth among the U.S. industrials, second among the retailers, and second among the utilities. Only General Motors and American Telephone and Telegraph employed more personnel. In terms of assets the USPS would rank twenty-first among the industrials, ninth among the utilities and second among the retailers. In 1971 only the military, the Department of Health, Education, and Welfare, and the Treasury had a larger budget authority in the federal government. And only the military employed more full—time permanent civil- ian personnel. During FY 1972, the Service's accrued cost ex— penditures were $9,576,168,000.4 During that year it employed a total of 706,433 personnel, maintained 31,661 post offices, and operated 91,434 vehicles.4 This massive plant was used to process and deliver over 86.3 billion pieces of mail,4 or approximately 413 pieces per capita. The average per capita payment (direct or indirect) for the Service was $45.82. 4See the USPS report (98). 12 ooo.mna mOHCOHuOOHm w OGOEQHOB Hmumcmw AHHm.mmnv Ammmov www.mnn nmmummame w mcoamoame CMOHHmad mOHMflHHDD mnm.m~m Buuozaooz .3 .m eeo.mme ache: euom ooo.mem Rosamom .mummm Adam.mmev Imamav Aaam.wmnv Ammmpv mmm.mnn mHODoz Hmumcmo Heapmm mHMHMUmSOCH momhoHQEm mm>.omw.m woesouuomam w OCOCOOHOB Hmumcmo Loom.nmm.mv Ammmpv mmhtoam.mam mehmmame w mconmmame CDOHHOEfl mmflpfiaflpp moe.mnm.m EMH Aoom.nmm.mv Ammmbv oom.mme.m awe oeuflomm oom.mme.m 6AAD66HM Hmumcmo w Oflpcmapm pmmuw ooo.mmv.wa “Opoz Ouom Room.nmm.mv Ammmsv Hme.ooe.ma A.e.zv HAO eumenmpm wvH.moo.oam IIIIWWDQOOM .mummm wam.mmm.mmm mHOpoz Hmumcmo Hflmuom mHmHMUmDOCH Aooov mmamm mMHZ¢m200 MBHQHBD 02¢ .AHfiBmm .QflHmBmDQZH Emmwm¢q mmB OB MUH>mmm HfiEmOm mmeflfim QMBHZD mmB m0 ZOmHmdeOU N mqmdB l3 mnma we: .Ocspuom "monsom hmm.mao.m mom a OHHDOOHM OOH>MOm Oflaasm Ammm.mvm.mv Ammmbv mmm.mmv.m COMHUm MACHOMHHOO CHOCDDOm nem.mam.m mOflcOHuome a omosmmawe Hmuwcoo mmm.hvm.vmw Cmmnmmame w OGOCQOHOB COUHHOE< mmflaflawub mmo.mmm.m Ramos qmaummm Ammm.wvm.mv Ammmbv nmm.mmv.m Hompm Emcmaspom mow.owm.m HOOHOE Hmm.nmm.m OHHDOOHM mmsonoaflpmmz 16mm.mem.mv Ammmov oom.aem.ma muouoz Hmumqmo mmm.mam.mmlllwmmboom .mummm oom.aem.omw A.e.zv Hflo enmesmpm Heapmm meHHMmDUCH Aooov mpwmmm UODCHDCOUIIN mqmflfi l4 .mnma .MGOECHO>OO MODMDm UUPHGD OED mo ummpsm one "monsom mma.om wusmmmue mmm.eoa 3mm mme.mma coflumupmflcfisem mcmumpm> www.mow OOH>Hmm Hapmom mD Hee.meo.a macapoqsm mnmuflaflznmmnmmmo “COSMOHmEm GOHHH>HU pawcmfiuwm OEHBIHHDM Hhma mam.oa COHDMHDMHCHE©¢ mcmnmpo> mmN.HH soapmpuommcmue Rem.ma mofl>umm Hmpmom m: noo.am MHSMMOHB www.me 3mm mmm.ae SHEDAHAEImmcmMmo 1000.0002 SDAHOEUBE Dmmesm Heed mMHUZmU¢ Q¢mmomm MOb¢S mo Bzmzwoqmzm 02¢ wfiHmOZED¢ BMUQDm m mam¢B 15 The number of plants and the number of employees could affect the Postal Service by increasing the com- plexity of the task of management. Conversely, increased size could afford the USPS an opportunity to organize and specialize its system better and to utilize technologies not practical for smaller operations, thereby enabling the Service to take advantage of economies of scale. C. Production Process The Postal Service production process is a massive distribution system geared to collecting, sorting, and delivering mail. The system can be segregated into the following functional activities:5 (1) Collection (6) Processing - (2) Acceptance incoming mail (3) Processing — outgoing mail (7) Delivery (4) Processing - transit mail (8) Window Service (5) Transportation Collection includes both the pickup of mail from collection boxes and other mail receptacles available to the public and the transport of that mail to post offices or other mail handling facilities. Acceptance constitutes the physical receipt of mail at the postal facility and the validation of postage. Processing for outgoing, transit and incoming mail consists of preparation (cull— ing, facing, cancelling), distribution (sortation), and mail handling (sack and parcel processing). Transportation 5A discussion of the mail flow process can be found in part in (62). 16 encompasses all mail movements between post Offices. De- livery covers the dispatch of mail by carriers or by window employees. Window service includes customer and adminis- trative functions such as selling stamps, setting postage meters, answering inquiries, etc. The manner in which the USPS carries out these functions would seem to rely on three criteria: speed, damage rate, and cost. The speed of delivery (including frequency of deliveries and loss rate) and the damage rate levels which the Service seeks to attain affects its cost level. (By seeking to process mail within ninety minutes after acceptance rather than holding mail for processing at off-peak times, for instance, the service increases its labor costs.)6 Unfortunately, the Service has not consistently maintained indices of the quality of service factors.7 The Service may affect its costs, or be affected by them, through its relative use of input factors (labor, capital, space) and the internal structure of its system (centralized local processing, nature of transportation 6GAO Report: (8). 7 . . . Various measures of particular quality aspects for certain classes have been made by the Postal Service. Of these, the National Service Index, which has been maintained on a quarterly basis since 1967, provides the most comprehensive measure of speed of processing. The index reports the time elapsed for mail moving between the point of cancellation and the point of destination is limited, however, to Air Mail, First Class, and Fourth Class Mail. l7 and distribution centers, etc.). The Service has been, and continues to be, extremely labor intensive. Over eighty percent of the accrued costs go for labor related expenses. Though the capital base has been growing, the capital labor ratio continues to be very low. In PFY 1971 the ratio of capital to labor was $1,499. For the same year AT&T's capital labor ratio was $70,223, U.S. Steel's was $34,841 and GM had $23,588 per employee.8 The Service's low capital labor ratio, though, does not necessarily mean that it is producing in a less than optimal region of its production map. Given the state of technology, capital substitution may be more costly than desired. The internal structure of the Postal Service pertains to the ordering, tracking, and location of its various processing units. Various processing procedures, e.g. transportation routes, are altered to improve the speed of delivery and not necessarily to reduce costs. Other changes, such as the transportation of unprocessed mail from small centers to large ones for processing, are intended to reduce costs through centralization as well as to increase the speed of processing. As such, these internal structural changes could affect the costs of the Postal Service. 8This information was derived from the Fortune 500 data reported in Fortune, May 1972. 18 D. Structural Organization Many of the attempts at improving the Postal Service have centered on reorganizing its managerial structure.9 Indeed, its structure has been shaped by shared authorities, political patronage and influence, union activity, and Civil service policies. For many years, the Post Office was under a cabi- net level official. Its authority was shared with other agencies. In addition the internal chain of command was highly concentrated in its Washington office.10 Under this arrangement, susceptibility to political interference was great. Congress and the Office of Management and Budget (formerly the Bureau of the Budget) controlled the budget and/or established services and set rates. The Government Accounting Office maintained many of the books of accounts. Because many offices were staffed by politi- cal appointment, Changes in Presidential administrations brought changes in the upper and middle management. Con- sequently, the Post Office lumbered under a system which prevented the development of a strong middle and upper level management and lacked incentives for efficient or entrepreneurial behavior. 9Of major importance is (39). 10Note the discussion in (24 Chapt. 3) as well as (39). 19 The President's Commission on Postal Reorganization found the Post Office's managerial structure to be one of the greatest barriers to improved postal performance. Not only did shared authority limit the organizations ability to independently establish specific methods of production, but the internal concentration also prevented local postal officials from running their own offices efficiently. (During Commission hearings several postmasters indicated that they were not told, nor could they readily ascertain, the cost of running their own facilities.) Consequently the Commission recommended a reorganization of the Post Office Department. As a result of these recommendations, legislation was proposed in Congress and in 1970 the Postal Reorganization Act11 was enacted. The major purpose of the Act was to improve the performance of the Post Office by limiting political interference, internalizing previously dispersed authority and improving managerial behavior. The Post Office was thus transformed into an independent public corporation. An eleven member Board of Governors, appointed by the President and confirmed by the Senate, acts as a board of directors. It is its function to approve the budget and rates and generally to oversee the functioning of the Service. Operating author- ity is vested in the Postmaster General, who is the chief llPublic Law 91 - 375, enacted August 12, 1970. 20 executive of the headquarters staff. Reporting to head- quarters are five regional offices, each of which has authority over the postal processing facilities in its respective area. As a result of reorganization, there has been a decentralization of authority. Local post- masters now have much more authority over their own faci- lities and operations.12 The new organization also includes a new regula- tory body — the Postal Rate Commission. Established by the Act, the Commission is charged with the responsibility of recommending rates and classification schedules to the Board of Governors. The Service cannot increase permanent rates or alter classifications without a hearing before the Commission.13 The PRC represents a novel approach to government enterprise, i.e., as a governmental body, it seeks to regulate the economic aspects of another govern- mental body. The merit and success of this approach, however, remains to be established.14 Further, the full extent of the Commission's authority remains to be determined. 12The increased authority of local postmasters over their own facilities was repeatedly stressed by USPS management at the sixth Postal Forum (95). 13The exact scope of this jurisdictional authority is under dispute. See (92). 14For an evaluation of the Act and its success thus far see (17). 21 The managerial structure of the Service is impor— tant, for it affects the ability of management to organize the means of production efficiently. Thus, changes in the structure of management, and changes in the quality of management itself, could substantially affect the pro- ductivity of the organization. Unfortunately there are no indices readily available to measure postal managerial ability. (It has been suggested that one potential in- dicator of the quality of management could be the size of the postal deficit. For a firm not under outside controls and facing stable factor prices and demand patterns, such a measure might be reasonable. However, since postal rates had been out of direct managerial control, and Since the major investment programs had to be approved by Congress, the total blame for the postal deficit cannot fall on postal managers alone. Hence, the deficit would not be an adequate measure of the quality of management) E. Competitive Environment The USPS mail and service offerings traverse market structures ranging from monOpolistic to highly competitive. Though it has been suggested that the Ser- vice maintains a "natural monopoly" in certain aspects of its Operations,15 the market structure the USPS faces did not arise from a free market natural competitive 15See (29 pg. 3:9—14). 22 selection process. Rather, the market structures are, at least in part, maintained by artificial supports. The two major supports are the restrictive Private Express Statutes and (at least historically) the maintained rate structure. The "Private Express Statutes" are laws enacted under the authority of Article, Section 8, of the Constitution. The statutes prohibit the private carriage of letters, thus creating a legal monopoly over this type of mail. Further, the acts prohibit the use of private mail boxes by any carrier except the Postal Service, thus creating a barrier to entry for even non—letter material. The major purpose of these acts, as stated[l967] by the then General Counsel of the Post Office Department, is to ". . . safeguard the revenues of the Government derived from the transportation and delivery of letters for others by prohibiting competition with the Post Office Department in the carriage of letters by persons seeking to engage in the delivery of letters for compensation." (89). The Service's rate structure has also acted as a barrier to competition. Based on a full allocation of costs, no class for which rates are established, other than First Class, Air Mail, and Priority Mail, has gener- ated revenues equal to or in excess of costs since 1945. (85 (1970) pg. 144). For classes of mail such as Second Class, this has resulted in the maintenance by the Service 23 of a 'de facto' monopoly. And certainly the competitive— ness of the other classes of mail is tempered by the price structure of the Postal Service. Yet the Service does face direct competition and is not immune from indirect competition. (105). Compe- tition exists for several reasons: a high sensitivity to quality of service parameters, efficiency gained through small scale or specialized operations, the development of technological alternatives for transmitting messages which would otherwise have gone as "letter mail", etc. The delivery of letter mail, which has tradition- ally been monopolized by the Postal Service, faces a growing amount of competition. Local delivery of bills, statements of account, checks, etc., have eroded the volume of first class mail. (36). Electronic voice communications and telegraph systems have provided al- ternatives for certain types of messages. (22). Elec- tronic computer systems allow transmittal of information outside of the mail system. (15, 60). The development of satellite and cable television systems and facsimile systems will provide further sources of competition. (70). Magazine publishers (second class mailers) are experimenting with specialized private delivery systems and with "piggy backing" delivery on other routes (e.g. milk delivery routes, etc.). (37, 53). Direct mail 24 advertisers (third class mail) may purchase the services of the Independent Postal Service Association (IPSA) for mass deliveries in urban areas. (10, 33). Fourth class mailers (books, parcels, etc.) may choose to do business with the United Parcel ServiCe, American Delivery System, bus lines (e.g., Greyhound), REA Express, and a multitude of small shipment motor carriers. (72, 73). Competition may act as a chastising force on the Postal Service. Where the potential for monopoly profits exists, and where there is no controlling force such as a strong manager-owner interested in net income, the firm might well turn "excess profits" into institutionalized inefficiencies, larger wage agreements with strong unions, managerial emoluments, expanded public relations and ad- vertising, and excessive research and development.16 In— creased competition which threatens revenue stability, volume expansion, etc., could result in more efficient and productive performance, depending on the true objectiVe function of the firm. 16There is an expanding body of literature on managerial and firm behavior patterns which are alterna- tives to the strict profit maximization approach. Notable in this area are Galbraith's investigation of the new in- dustrial community (30), Cyert and March's development of a behavioral theory of the firm (l9), Williamson's analy- sis of managerial behavior (104), Baumol's writings on sales maximization (7), Leibenstein's work on x-efficiency (48), Averch and Johnson's analysis of the regulated firm (4), and Marris' writings on managerial capitalism (54). Also of interest is Machlup's comments on competiting theories of the firm (51). THE PRICING PROBLEM OF THE POSTAL RATE COMMISSION As stated above, one of the major functions of the Postal Rate Commission is to recommend a schedule of rates for the various mail classes to the Board of Governors of the USPS. Statutory guidance for this pric- ing function is spelled out in Section 3622 of the Postal Reorganization Act.17 The Act requires the Commission to give consideration to the following criteria: (1) the establishment and maintenance of a fair and equitable schedule; (2) the value of the mail service actaully pro- vided each class or type of mail service to both the sender and the recipient, including but not limited to the collection, mode of transportation, and prior- ity of delivery; (3) the requirement that each class of mail or type of mail service bear the direct and indirect postal costs attributable to that class or type plus that portion of all other costs of the Postal Service reasonably assignable to such class of type; (4) the effect of rate increases upon the general public, business mail users, and enterprises in the private sector of the economy engaged in the delivery of mail matter other than letters; (5) the available alternative means of sending and receiving letters and other mail matter at rea- sonable costs; 17For a good review of postal pricing policies prior to the Postal Reorganization Act see D. M. Steiner (77). Also see M. Baratz (5, 6) and J. Kennedy (43). 25 26 (6) the degree of preparation of mail for de- livery into the postal system performed by the mailer and its effect upon reducing costs to the Postal Service; (7) simplicity of structure for the entire sched- ule and simple, identifiable relationships between the rates or fees charged the various classes of mail for postal services; and (8) such other factors as the Commission deems appropriate. (82 pg. 42, 43). Further, in section 403, paragraph c, the Act specifies that: In providing services and in establishing classifi- cations, rates, and fees under this title, the Postal Service shall not, except as specifically authorized in this title, make any undue or unreasonable dis- crimination among users of the mails, nor shall it grant any undue or unreasonable preferences to any such user. (82 pg. 5) Also, prices are constrained to a set which will produce revenues sufficient to cover the costs of postal operation but not exceed it. Of these criteria, major consideration is given to the questions of discrimination, cost recovery by class of service, and the constraint that total revenues must equal total costs. One difficult problem for the Commission is the determination of the weight to be given to the "value of service" criteria. Since value—of—service based rate structures are price discriminatory, or, at least, lead to cross-subsidization among the various classes of mail, it is necessary to investigate the extent to which price discrimination could be beneficial and thus not be 27 "unduly" discriminatory. As a broad guideline, it could be said that price discrimination is admissible to the extent that it promotes economic efficiency and/or reduces the postage costs to be borne by the individual mailer, or at least does not increase those costs. Further, if a price discriminatory rate structure is to be employed, it should be operationally demonstrable that the supposed benefits can indeed be realized. While pricing schemes which are theoretically plausible might be devised, it might not be possible to implement them in such a manner as to demonstrate that they are not "unduly" discrimina- tory. This is particularly the case if the pricing rules rely upon what Edward S. Mason has called ". . . the theoretical techniques of price analysis (which) have been constructed without regard to their empirical applica- bility . . . ." (56 pg. 66). Price discrimination refers generally to the es- tablishment of product price differentials, either among products and classes or within the same product or cus- tomer class group, which do not directly correspond to 18 This definition is "broad" differences in supply costs. in the sense that, as Officer (67) has noted, "If the conventional wisdom is that non—discriminatory rates must be based on costs, then all pricing systems are 18For a discussion of price discrimination, see (25). (52), (68), (74). 28 discriminatory." Such a cost based definition was employ- ed by critics of the transport rate differences between U.S. imports and exports to claim that maritime freight rates are discriminatory. However, as Officer pointed out, when non-discriminatory pricing practices are defined with attention given to capacity utilization, the freight rate differences do not necessarily imply price discrimination. Similar problems arise in the utility area (see especially P. O. Steiner (70). In analyzing rate structures to de- termine the existence of, or extent of, price discrimina- tion, one must be careful. For that which is discrimina- tory in one industry might well be rational, fair, and nondiscriminatory in another. For the purposes of the PRC, it can be said that a nondiscriminatory pricing structure is one which is based on (a) the costs which can be associated with a particular class of service (including peak related costs) and (b) any "non allocable", "non-associable", or "in- stitutional" costs which are distributed among the classes of service on some basis other than market position or relative strength of demand. The present rate structure is price discriminatory--both in an intra- and inter- class sense. The most obvious example of intra-class discrimination is in the regular rate second class cate- gory. Second-class mailers (newspapers, magazines, etc.) 29 are charged one rate for the advertising portion of their publication and another rate for the editorial content. Since it does not cost any more to deliver an all commen- tary publication than an all advertising one, it is ob- vious that discrimination exists. Inter-class discrimina- tion arises from the Postal Service's cost allocation and rate setting procedures. As explained in the first rate case (Docket No. R7l-l) the Service allocated half of its costs to the classes of mail and of service on a cost causality basis. The other half, or approximately five billion dollars, was distributed on the basis of "market factors" (i.e., relative elasticities of demand, competi- tive position, etc.). Such a strong reliance on market factors implies that the rates are indeed price discriminatory. The existence of price discrimination is not in itself necessarily undesirable. Under certain conditions, price discrimination is both desirable and beneficial to all parties. However, when these conditions are absent, price discrimination can lead to anticompetitive activity, allocative inefficiency, and income redistribution. Fur- ther, under the Postal Reorganization Act, unjustified price discrimination is illegal. Two models of price analysis have been put forward alternatively as either a justification for the existing 30 rate structure or as an appropriate framework for estab- lishing a new rate structure. The models are the Boiteux-Baumol model, and the classic economies of scale model.19 Each model predicates a pricing rule which is price discriminatory. And, under certain assumptions, the pricing rules are straightforward and implementable. In this section, each model is analyzed to determine its applicability to the postal pricing problem. A. The Boiteux-Baumol Model and the Inverse Elasticity Rule In his original article M. Boiteux (11) suggested a pricing rule applicable to the task of determining a set of prices for a public enterprise monopoly. In his restatement of the rule, Baumol (8) has suggested that similar criteria could be applied to regulated enterprises operating under a profit constraint. In its simplest form, and assuming no cross elasticities of demand, the rule states that prices for any two goods should be set such that the ratio of percentage deviation of any two prices from the good's respective marginal cost would be inversely related to the ratio of the price elasticity of demand for the two goods. The model, which seeks to 19These models have been used to justify rate structures in other regulated industries. Note espec- ially (9), (38 Chapt. 5), (31 Chapt. 10), and (69 Chapt. 10). The shortcoming of these pricing rules have been aptly noted by W. H. Melody (58), among others. 31 maximize consumer surplus within a profit constraint, is as follows: Let: The and 0) :> I O) "O I-'- 0) > I O) "O N ll TR 2(pl, lagrangian is then: A: ) be the unspecified consumer surplus function where (pl, . . . . , pn) is a vector of prices for the respective vector of goods (x1, . . . , Xn) be the total revenue function be the total cost function be the profit constraint such that TR - C = M (M can be zero) Z + A (Z pixi - C - M) l the derivatives of the lagrangian with respect to and . p) are: WM Xk i . ——l + Z ——— pk - c.-——— 3x. 3 8pi k pi 1 3pi axk k Bpi 8x 2 axk Bxi ——1 + ——— p - c ——— Bpj k Bpj k 1 Bpj 3xk> k 8 . p3 where k # i,j and Ci = g: , the marginal costs with respect to good i x. 1 8x. . Denoting price elasticity as eij = Ffii‘il , noting the j i p. x. 20 Slutsky relationship that 8.. = 8.. —J——l- , taking the 13 31 Pi Xi derivative %E_ to be the compensating variation corre- i 82 21 sponding to a price change, or 55— = -xi , and setting i the derivative of the lagrangian equal to zero, we see that -§—— and 8%- can be restated as: p.-c. p ”C- P ‘C _ pi pi J pj k pk p.-c. p.-c. p -c _ -———:A ( l)+a--(—l—l)+zek-(k )—-—-= Pj 3 Pi 33 Pj k 3 Pk Assuming that Eij = O for all i and j where i # j, 20 It is assumed that the income effect will be of no practical significance. 21See Baumol (8), Hicks (35), Feldstein (28). 33 the equations reduce to: E (pi-Ci) = 1-A 11 pi A p -c. _ e,_._'J___1 = 1_A JJ( pj ) A Equating the two equations, we have the pricing rule p.—c. p.-c. 8.. l l _J__l. = _11 [pi] [pi] €11 Thus, within the set of prices allowing a profit level M, the greater a class's inelasticity of demand, the greater should be the percentage deviation from its respective marginal cost. Setting aside the practicality of marginal cost measurement problems, all that is necessary for es- tablishing a set of "quasi-optional" prices is knowledge of a set of prices which meet the profit constraint, the class's elasticity of demand, and the respective marginal costs. The straightforward nature of the pricing rule is lost when the assumption of zero cross elasticities is relaxed. In this case, the ratio of percentage price 34 deviations from marginal costs becomes: I- - 1 n .- pi Ci pk Ck W 8..-'€.. E .‘8 . Pi 33 13 + 2 Pk k1 k3 p.-C. — 8 -€ . k p.-C. 8 '8 —1——1 ii j1 —l——l ii ji _ pj - - 9:3 A Thus, there is no longer a direct and straight- forward relationship between the percentage price devia- tions from marginal cost and the respective elasticities of demand. Whereas in the previous case, it was clear that classes with a greater inelasticity of demand should have a greater disparity between price and marginal cost, with cross elasticities not equal to zero this relation- ship need not hold. Indeed, depending upon the magnitude of the various cross elasticities, it is wholly conceiv- able that a class with a greater inelasticity of demand might be priced such that the percentage deviation of its price from its marginal cost is less than that for other classes, including classes with a more elastic demand. Feldstein (28) expanded the model by considering the concept of "distributional equity". Feldstein assumes that each consuming unit has a marginal social utility of income, U'(y), which is invariant with respect to price but Which varies among households with different income levels. His maximand is the weighted sum of consuming 35 unit consumer surpluses where each consumer surplus has been weighted by the consuming unit's respective marginal social utility of income. Maximizing his objective func- tion subject to a profit constraint, M, he derives pricing rules which are, in the terms of Baumol, "quasi- optional". The derived pricing rule depends in part upon the "distributional characteristics" of the various goods. The distributional characteristic for a single good is the weighted sum of the consuming unit's marginal social utility which has been weighted by the amount of the good consumed. In the special case of zero cross elasticity of demand, the pricing rule is: [p.-C.] 8.. R.-A i 1 J] 1 P~ P-‘C- = “‘ 1 [4L—;% 8.. R.-A Pj 11 3 where A is the lagrangian multiplier and Ri is the "distributional characteristic" of the ith good. This would reduce to the Ofiginal formulation of the Baumol pricing rule only if'Kl) the marginal social utility of income is the same for all households, or (2) the rela- tive quantities purchased of the two goods is the same for all households, or (3) some extremely improbable balancing of differences in quantities and social utilities occurs." (28, pg. 34) 36 Thus, in the more general case,22 establishing prices so as to achieve a maximum of consumer welfare would require knowledge of marginal costs, own-price elasticities of demand, cross-price elasticities of de- mand, the marginal social utility of income for the var- ious consuming units, and the consumption patterns of goods for the various consuming units. The models discussed so far have not explicitly considered the effects of pricing on other firms which might compete directly, or indirectly, with the public enterprise or the regulated firm. If the public enter- prise or regulated firm were a true monopoly in the sense that it did not face other firms which produced substitut- able products, then "competitive effects" would not need to be considered. However, if at least some of the firm's products faced competition, consideration should be given to the competitive impact of the pricing rules discussed. If the multi—product public enterprise produces a product or service in a market which is perfectly competi- tive, then there will probably be little or no competitive 2ZIn a two good model with non zero cross elasti- cities, the pricing rule is: Pi'ci pi E22 (Ri'A) ‘ E12 (Rz’i) P -C _ _ _ - 2 2 611 (R2 A) 821 (R1 A) pz (28 pg. 34) 37 impact upon competitors resulting from the firm's pricing policy. If, on the other hand, the markets in which the public enterprise's products face competition are olig- opolistic, then competitors could be seriously affected by alternative pricing policies pursued by the firm. Given the ability to cross-subsidize competitive services with excess revenues from the noncompetitive services, the public enterprise or regulated firm could either limit the profitability of the competitors to the extent that they would find strenuous competition nonremunerative, or it could forestall competition through limit entry pricing. While a reduction in the number of competitors might be of no immediate consequence, a reduction in the level of competition might have an adverse effect upon the perfor— mance of the public enterprise or regulated firm. As competition lessens, the market position of the public enterprise is enhanced. Since the enterprise is fore- closed from realizing its market gain in the form of in- creased profits for its total operations, due to the profit constraint, it might capitalize upon its position in other ways. Managers could capitalize upon these gains in the form of Williamsonian managerial emoluments. Also, the reduction of competition could reduce the need for productive efficiency; thus, the market gains could result in overstaffing, reduced quality control, excessive 38 capitalization and staff expansions, or a reduction in work standards. All of these results would have the effect of increasing the inefficiency of the product line or of the firm. In addition, a reduction in competition might slow the rate of technological innovation and adoption. By reducing the competitive pressure of the market, the incentive to disturb the production line's status quo with the adoption of a new and possibly risky technology would also be reduced. The results would be felt in a real growth in factor productivity below that which might have been achieved under a more rigorous program of technological advancement. Thus, in determin- ing the desirability of a set of product or service prices, the potential increase in consumer surplus should be weighted against the present and discounted future cost increases resulting from a price structure which improves the firm's market structure by reducing the level of competition. While the inverse elasticity rule is intuitively appealing, it does not appear that its direct application to the postal pricing problem will result in the desired results of maximized consumer surplus. First, items which move through the mail can often be mailed under several mail categories. Thus, it cannot be assumed that the cross elasticities of the various services are in fact 39 zero. Indeed, the Postal Service recognized the existence of non-zero cross elasticities of demand when it argued in Docket R7l-l for a rate spread of a specified amount between two services to avoid a revenue loss through inter-class diversion. (91 pg. 3:77). Second, given the plausibility of a varying marginal social utility of in- come for the various consuming units, the distributional characteristics of the various products cannot be ignored. As noted earlier, the financial characteristics of the customer groups which use the mail services vary from class to class. Thus, knowledge of the marginal social utility of income and the consumption patterns of the respective consuming units is necessary to determine an "optimal" set of prices within the profit constrained area. Third, there is a distinct possibility that the inverse elasticity rule would have an anticompetitive impact. The elasticity of demand for a particular firm's product is in large part determined by the existence of viable alternatives or substitutes. As one has more and more suppliers among whom to choose, his elasticity of demand for any one firm's product will become more and more elastic. Thus, differences among the elasticities of demand of the various classes of service could well represent the fact that certain classes are protected from competition while other classes of service are not. 40 If the inverse elasticity rule were applied, then prices for the competitive service would be relatively lower with respect to its marginal costs than the prices charged the monopolized services. In addition, if the firm and the product lines operated in a region of constant returns or decreasing returns to scale, the prices for many of the competitive services would be set significantly below their marginal costs. This would have a definite anti- competitive impact. Therefore, if the Commission were to seek to set prices to maximize consumer surplus, it would have to know the marginal costs of the respective classes of mail and service, the respective own—price elasticities of demand, the cross elasticities of demand, the marginal social utility of income of the consuming units, the con— sumption patterns of the respective consuming units, and the cost consequences of a reduction in the level of competition. Further, it would be necessary to derive the exact set of prices which would achieve a consumer surplus maximum. Because of the theory of the second best, it cannot be shown that prices which merely "tend" toward the optimal price structure would result in a higher level of welfare satisfaction than an alternative price strUc- ture. Thus, the task of demonstrating that a price dis- criminatory rate structure, predicated under the objective 41 of maximizing consumer surplus when profits are constrain— ed, is not unduly discriminatory is at best a prodigious effort. B. Pricing Under Conditions of Economies of Scale The previous model, predicated on the maximization of consumer surplus within a Set of prices which meet the profit constraint, was equally applicable under the exist- ence of economies of scale, diseconomies of scale, or constant returns to scale. The present model considers only the possibility of the existence of economies of scale. The pricing objective under this model is to re- duce the unit costs of operation through an expansion in volume. Price discrimination could be argued as justi— fiable if it led to a reduction in the price charged for all services, or at least to a reduction of price for some services without necessitating an increase in the price of other services. The argument is predicated on the assumption that changes in the relative structure of rates can lead to a shift of the aggregate demand curve for the firm's various products. In other words, a shift in the structure of rates would cause the demand curve D - D (see Figure—l) to shift to D - D thus reducing l l 2 2 the unit cost of production from C1 to C2 as the aggregate quantity demanded expands from Xl to X2 . Dollars 42 LRAC Xl X Volume FIGURE 1 REDUCTION IN UNIT COSTS DUE TO A DEMAND SHIFT 43 The rationale for this model depends upon the assertion that the aggregate demand curve can be shifted through a change in the structure of prices or in the relative prices of the various services. This assertion should be demonstrated. Consider a firm with three products lines. The demand for each product is >< M II A 'OlI—J [\J v N X = (1.)3 3 p3 Further assume that prices are established such that the ratio of the price of one product to its average cost is equal to a constant times the ratio of the price of another product to its average cost. In other words: P p P P 1 2 1 3 or p-232. p.._p_1_i§. 2 k cl 3 1 cl Thus a X=1_l 1 pl d _d2 x — —— d = 2 pl d . 3 x = 2— f = 3 (pl) Total volume equals the sum of x d a 1 l d 2 b 3 V = —— + —— + —— p1 pl pl Total revenue is: d -l 1 1 dz-l TR = ( > + (d/pl) + (f/Pl) p1 And the "price" for the firm is: and x . i.e., d3-1 Holding the price of the firm constant, TR _ — —v—— X, we can solve for d in terms of f, x and p1 . This implies 45 a whole set of (d,f), and hence a set of (k,l), for which the "price" of the firm would be constant. Yet, given the volume function and given d2 # d3 , differing d and f would result in different levels of output. Thus, the "demand curve" for the firm's aggregate product can be shifted by varying the rate structure. The existence of economies of scale is an empiri- cal question. Thus, the applicability of this rationale for price discrimination can be determined by looking at the technical relationships of the postal outputs and factor inputs. And it is to this empirical question that we now turn our attention. PRODUCTION FUNCTIONS, COST FUNCTIONS, AND PRODUCTIVITY To discern the technical relationships of the postal process, we must turn to models which relate factor inputs with postal outputs.23 Four such correspondences are the production function, the cost function, factor demand equations, and productivity measures. Information obtainable from each of these approaches will be consider- ed in this section. A. Postal Production Functions The "production function" is a correspondence which directly relates the physical output of a firm to its factor inputs. For the postal service, the nature of its output is not obvious. Unlike manufacturing firms, it does not produce a physical product which may be ob- served or counted. It does not produce letters or maga- zines or circulars or parcels. Rather it provides a delivery service for transporting these items from a 23A review of previous studies of the production function and productivity of the postal operation, as well as a review of the literature on production func- tions, cost functions, and productivity is given in Appendix A. Items reviewed include (2, 5, 6, 12-14, 16, 21, 23, 24, 27, 32, 40-42, 46, 47, 49, 55, 57, 59, 61, 63-65, 71, 76, 87, 99, 100, 106, 107). 46 47 point of origin to their indicated destination. In pro- viding this service, the USPS must produce a given level of delivery capability which embodies a given standard or quality of service. The existent level of delivery capability is determined by the use of appropriate factor inputs. The appropriate and desired level of delivery capability is determined both by the total mail volume moving through the system and the cyclical variation of the mail flow within the time frame of measurement (e.g., monthly variations within the Postal Fiscal Year). Thus we have two output relationships. The first is a prof duction relationship, i.e. the relationship which relates the output or delivery capability to the factors of pro- duction. The second is an exogenous demand requirement relationship, i.e. a relationship which states the re- quired level of delivery capability necessary to handle the exogenous mail flow. The Specification of an de- livery capability relationship and a required exogenous demand is not a standard approach. Most production func- tions are directly specified in terms of the physical outputs and inputs. And indeed, the measure of physical output is the relevant concept for the production func- tion. The approach used in this study was necessary, however, because of the stochastic nature of the pro- duction process and the nature of the output itself. One 48 can correctly Specify a stochastic production function relating the output of a furniture company, say chairs, to the relevant inputs. By its stochastic nature, the production function implies that upon any two given days, or in any two given plants, the exact same quantities of inputs will not result in the exact same level of pro- duction. The random and noncontrollable stochastic error of the production process affects directly that which is produced. For the Postal Service, however, the relevant measure of output, or at least the one used in this study, is the physical volume of mail passing through the postal process and the monthly volume (or accounting period) flow pattern. Both of these factors are exogenous to the postal system. Neither random errors in the production process nor varying levels of inputs will affect the amount of mail tendered for delivery. Thus, to specify a pro- duction function which directly relates this measure of output to the postal inputs would be incorrect. The product produced by the combination of postal inputs is the transportation delivery of the exogenously determined mail flow. The process is stochastic in the sense that random error results in either a little excess system capacity (i.e., the Postal Service has the ability to deliver a few more letters than are actually tendered for delivery) or minor aberrations in the quality of service 49 (e.g., the mail is handled slightly slower than normal). By specifying an exogenous demand and a delivery capabi- lity relationship, and by assuming that postal managers marshall their inputs so that the available capacity is always just enough to meet the required level, it is possible to develOp sensible and reasonable estimatable relationships which are correctly identified. Succinctly, the specification of the two capacity relationships allows the identification of a stochastic production and cost relationship which can be estimated by employing an output measure which is determined by exogenous forces and not by the production process itself. For purposes of this study, four factors of pro- duction are identified: labor, capital equipment, space, and purchased transportation.24 Labor includes the ser— vices of postmasters, supervisors, Clerks, mailhandlers, letter carriers, etc. Capital equipment encompasses letter sorting machines, conveyor belts, postal vehicles, office equipment, etc. Space includes interior, platform and outside areas. Purchased transportation covers air, truck, railroad, and water transport. It is assumed that other factors (e.g., utility services, paper and supplies, purchased legal services, etc.) are either fixed 24The identification of these variables, the sources of information, and the methods and assumptions employed in aggregation are discussed in Appendix B. 50 coefficient factors or factors which do not vary with capacity. We can state, then, the following two relation- ships: DC = F(L,K,S,T) ED = G(Q,R) where: DC = Delivery capability S = Space ED = Exogenous Demand T = Purchased Transportation L = Labor Q = Yearly Mail Volume K = Capital Equipment R = Volumatic Load Factor25 It is assumed that the USPS attempts to maintain a specified quality standard delivery capability which is great enough to meet the volume requirements and that factors are adjusted yearly so that excess capacity (i.e. (DC-ED) > 0) does not exist. This being the case, one can directly relate factor inputs to mail volume and load factor. To estimate the production relationships among inputs and outputs, the following alternative functional relationships are employed: 8 B (1) DC =AL1KZS3T e 25Volumatic Load Factor is defined as the average "monthly" volume of mail moving through the system in the peak "month". A fuller explanation is contained in Appendix B. 51 é o (2) DC a [Ble + BzKp + BBSp + B4Tp + U] B B B B (3) DC eeDC _ 1 2 3 4 eU l 35 t-1 2*. m t—l (where U is a stochastic error term) The first relationship is the venerable Cobb- Douglas production function. The function is economically meaningful for all L,K,S,T Z 0, for all Bi such that 0 : Bi 3 1 (i = 1,2,3,4) and for A > O. The function is homogeneous and has returns to scale of degree 81 + 82 + 83 + 84 . And the elasticity of substitution between any two factors is constrained to a value of one.26 The second relationship is the Arrow, Chenery, Minhas, and Solow CES production function. It is econo— mically meaningful for all K,L,S,T Z 0, for all Bi such that 0 : 8i i l, for 6, d > O and for D such that -w < p < I . The function is homogeneous and has returns to scale of degree 6. And the elasticity of substitution among any of the factors is constrained to 26Note, the explanation of these functions follows closely those given by Ramsey and Zarembka (71). 52 the value of p .27 The third relationship is Zellner and Revankar's generalized production function. It is a generalization of the Cobb-Douglas function. It is economically mean- ingful for all L,K,S,T : 0, for all Bi such that 0 i 8. 1 , for A > 0 , and for 8 such that I A i 6 C . . (DC e ) Z 0 . The function has a varying returns to U scale Y (DC) such that 81 + 82 + 83 + e 1 + 8 DC Y(DC) = The elasticity of substitution among the factors is fixed and of value one. The functional form of the required capacity 27The specification of this production function is subject to the valid criticism that it holds the partial elasticities of substitution (capital for labor, capital for space, etc.) to be the same. While it would be far preferable to estimate a function which was not subject to this limiting constraint, the lack of a sufficient number of observations prevented a more general model. (It should be noted also that the constraining assumption of equal partial elasticities could be leveled against the Cobb-Douglas formulation.) 53 relationship used is: Assuming managers adjust inputs so that total available delivery capability just meets the requirements placed on the system by the exogenous demand, the rela- tionships to be estimated are of the form: (1) QRw = AL K S T eU 6 w _ o o o o 5 (2) QR — alel L + 82 K + 83 S + 84 T + u] W B B B B (3) QRw eeQR = AL 1 K 2 S 3 T 4 eU The relationships were estimated in the follow- ing manner. OLS was applied to the logged Cobb-Douglas 281t is assumed that mail volume and the monthly load factor are multiplicative separable elements which together determine the overall delivery capability re- quirements of the Postal Service. It is further assumed that the elasticity of required capability with respect to mail volume is one, and the elasticity with respect to the load factor is w . This means that a one percent increase in mail volume results in a one percent increase in the delivery capability of the system. On the other hand, when the load factor varies by one percent, the variation in required delivery capability will be only T percent. This is because some factors are relatively fixed on a month-to-month basis while others can be varied more readily. 54 function.29 Iterative least squares with a course net — fine net search over the nonlinear parameters 6 and p was applied to the transformed CES relationship: 0 O 11’) (QR = aBle + QBZKD + @8350 + QB4TQ + U An iterative least squares with a course net - fine net search over the nonlinear parameter was applied to the logged generalized production function. The parameter 30 was estimated from a cost function relationship. The 29It is assumed that U is distributed normally with zero mean, homoskedastic variance, and non auto— regressive disturbances, and that the independent varia- bles are distributed independently of the production function error term. Thus OLS is unbiased and efficient, and has all desirable large sample properties. 30See section B below. The parameter U was estimated from a cost function based on a C-D production function. Misspecification of the functional form could, of course, bias the estimate of w . It is assumed, how- ever, that any such bias is deminimous. An alternative approach would be to search over w for each equation. This was not done, however, due to limitations in time and resources. 55 returns to scale parameters are listed in Table 4.31 TABLE 4 RETURN TO SCALE PARAMETERS OF THE COBB-DOUGLAS, CONSTANT ELASTICITY OF SUBSTITUTION, AND GENERALIZED PRODUCTION FUNCTION Production Function Scale Parameter C-D .842 CBS 0 6 GPF .735 31 The results for the production functions are: Standard errors are listed in parentheses under their respective coefficients. C-D constant 81 B2 B3 B4 6.92 .52 .037 .05 .24 (.889) (.073) (.022) (.100) (.135) D.W.=1.626 [inconclusive], F-Ratio=794 with 4 and 6 d.f. CES p 6 0“31 0‘82 0‘83 0‘84 -.8 .6 —.39x10‘14 -.15x10‘14 .33x10"13 .28x10'14 ------ (105x10‘l3) (.33xio'l4) (.93x10'l4) (.16x10’14) D.W.=l.342 [inconclusive], F—Ratio=535 with 4 and 7 d.f. GPF 8 constant 81 B2 B3 B4 5 4 2 2 .0001 -1.05x10 6.03x10 5.62x10 6.52x10 1.37x102 --- (8.6x103)(7.11x102)(2.12x102)(9.76x102)(l.32x102) D.W.=1.601 [inconclusive], F-Ratio=899 with 4 and 6 d.f. The coefficients of the CES and the GPF functions are clearly out of the range of economic meaning. However, it is believed that further iterations would bring the coefficients into a reasonable zone. The CES function showed signs of converging between 0 = .6 and 5 = .8 . GPF showed signs of converging as 8 tended towards zero. 56 These results must be viewed with some hesitancy, however. While they indicate the existence of increasing returns to scale, the results might be clouded by a simul- taneous equation bias. The estimated equations assume that factor inputs are independent of the stochastic error term. However, if one were to take account of an hypo- thesized objective function of cost minimization, it would be seen that factor inputs are a function of the level of output, and thus of the stochastic term. Hence, the factor inputs and the error term are not independent. This being the case one cannot show that the ordinary least squares estimates obtain any of the desired large or small sample prOperties. To obtain more defensible estimates, it will be necessary to consider the production function in light of a reasonable objective function main- tained by the USPS. This is done in the next section. B. Postal Cost Functions and Factor Demand Equations An alternative approach to direct production function estimation is an estimation of the production relationship by using the firm's cost function. For the sake of our analysis, let us assume the USPS has an ob— jective function and that that objective function is to minimize costs within the level of its technical and managerial competence. To specify the concomitant 57 relationships and to derive the desired functions for estimation, let us first define some variables: DC = Delivery Capability WL = Price of Labor ED = Exogenous Demand _ . . L = Labor ‘ WK — Price of Capital K = Capital Equipment WS = Price of Space S = Space _ . T = Purchased Transportation WT _ Price Of Purchased _ Transportation C — COStS U = The stochastic error Q = Mail Volume i term R = Load Factor Further, let us specify the following relationships: DC = F(LIKISIT) ED = G(QIR) = + A C WLL + WKK + WSS WTT DC = ED The basic delivery capability production function is assumed to be stochastic. The stochastic error is attributed to vagaries in weather, population densities, service quality, etc. The problem facing the Postal Service, then, is to minimize expected costs to the constraint of the ex- pected delivery capability production function. For estimation purposes, ED can be substituted for the un— observed DC. To cast the problem in a form such that estimat- able relationships can be derived let us assume the 58 following functional relationships: DC = AL K S T O B B B B — E(DC)= AL 1 K 2 S 3 T 1 e 2 C + . + WLL + WKK WSS WTT ED = QRw The lagrangian function for minimization is, then: 81 B2 B3 B4 % A = WLL + WKK + WSS + WTT + m(E(DC) - AL K S T e ) and the first order conditions are: AL = WL — mBl(E(DC)/L) = 0 AK = WK - m82(E(DC)/K) = 0 AS = WS - m83(E(DC)/S) = 0 AT = WT — mB4(E(DC/T) = O O AA = E(DC) - ALBl K62 883 T84 e E = 0 Taking the log of each equation, moving the endo— geneous variables to the left hand side of the equation 32The error term eU is distributed log normally O . 2 . O 0 . . . With mean = e and variance = e (e —l). This implies that U is distributed normally with mean = O and vari— ance = O . Further, it is assumed that Ui and U. areiJr- dependent for all i # j. J and the exogenous relationships in matrix form, and noting that we see that: 1n S or H Y = BX, where respective matrices. model. Noting that: H—1 = where Z H m + it is seen that MIH m H the reduced form is 1n T 1n K 59 WKK E(DC)B2 IlnBZ-lnBl) <1n02-1n03> (lnBZ-ln84) fi-ln A + g) l H I [—4 -1 0] variables to the right, putting the . 1 A 1n W 1n W 1n W 1n W K L S T 3nE(DCL H,Y,B,X take on the values of their This is the structural form of the Y 6O or: . _ 1 [- 1n L] a 82 Y1 B3 B4 1 1 T 1n WK 1“ S 1 b B2 81 Y2 B4 1 1n wL ln T Z c 82 81 B3 Y3 1 1n WS 1n W 1n K d Y B B B 14 T L 3 _ 4 1 3 4 [ln E (DC)_ where Y1 = ‘(82 + 83 + 84) Y3 = "(81 + 82 + 83) Y2 = "(81 + 62 + 84) Y4 = -(81 + 83 + 84) __ _ _ _ O a — lenB2 +(82+83+B4)1n Bl B3ln B3 B4ln B4 1n A + 2 _ _ _ _ _ E b — 821n82 81 1n 81+(Bl+82+84)1n B3 B41n B4 1n A + 2 O c — -821n82~8l 1n Bl-B3ln 83+(Bl+82+83ln 84- 1n A + 2 d _ O From this we see that the resultant delogged factor demand equations are: -(82+B3+B4) 82 B3 B4 l _ z ‘z‘,’z" ‘2‘- '2' L — Z BlWL WK “S WT E(DC) E1 E2. _‘Bl+82+84’ El 1 Z Z Z Z Z = '7 - ' S .. BJWL WK WS WT E(DC) 51 5.2. E; (81%”? _1_ T=ZBW Z[77,214] 22W Z E(DC)}: 61 El _(Bl+83+84) 83' 83 _ z z z X K — z BZWL WK wS WT E(DC) where By multiplying each factor demand equation by its respect- ive factor price and summing, we derive the resultant ex- pected cost function: 8_1_ E2. 32 .811. l _ z z . z \ X g 2 E(C) — Z(Bl+52+63+84) wL WK NS NT E(DC) These relationships cannot yet be estimated, however, since E(DC) is not directly observable. Making use of the relationship DC = ED = QRw 1n E(DC) = 1n (DC) - U + kflQ the factor demand equations can be represented as: m -‘82+B3+B4) E2. .3 _4. .1. l _ - Z , Z Z Z Z 2 -u L _. B 81 WI. WK WS WT Q R e .83. £12 -‘Bl+82+84) 5:1. .1. Y S = B 8 K1 2 vv 2 iv 2 w 23 Q2 R2 e_u 3 L K S T 62 51 5.2. _B_3 -‘BfoW l T _ Z Z Z Z Z 2 -u T — B B4 WL WK WS WT Q R e i -(81+B3+B4’ .83 El. 1 1 _ Z Z Z E -u K — B 82 WL WK WS WT Q R e And the cost equation is representable as: .81 32. E1 _B_4 1 11’ _ z 2: ‘ z z z: z -u C -— B(Bl+ 82+ 83+ 84) WL WK WS WT Q R e where “HQ Since all variables on the right hand side of the equation are statistically independent of the error term, the re- lationships can be estimated by OLS. All relationships are estimated by applying OLS to the logged equations. 63 The estimated cost equation, then, is: = * ' \ .. lnC A +dlanL+d21nWK+d3anS+d4anT+d51nQ+d6lnR U and a representative factor demand equation is: :** ~ . .. lnL A +YlanL+y21nWK+Y31nWS+y4anT+y51nQ+y6lnR U The results from estimation are contained in Tables 5 and 6-933 33This model does not explicitly take account of the fact that postal space is separable into two compo- nents: one which is leased or rented from private sources and one which is provided by the government and for which no price is paid. A model taking account of these differ— ences is reported in Appendix B. The results are similar to those reported here. 64 TABLE 5 COST FUNCTION PARAMETERS Standard errors are listed in parentheses under their respective coefficients. Cl 0!. 0!. 0L (1 (I l 2 3 4 5 6 .6610 -.2256 -.O699 .1783 1.3293 .0311 (.1562) (.0530) (.0938) (.0950) (.2481) (.0661) F Ratio = 1139 with 6 and 4 degrees of freedom. D.W. = 2.34 [Inconclusive] R2 = .998 TABLE 6 LABOR DEMAND EQUATION Standard errors are listed in parentheses under their respective coefficients. Y1 Y2 Y3 Y4 Y5 Y6 .0455 .0461 -.2063 -.0826 .7430 .1503 (.1284) (.0435) (.0771) (.0781) (.2039) (.0543) F Ratio = 634 with 6 and 4 degrees of freedom. D.W. = 2.82 [Inconclusive] R2 = .993 TABLE 7 SPACE DEMAND EQUATION Standard errors are listed in parentheses under their respective coefficients. Y1 Y2 Y3 Y4 Y5 Y6 3.4874 3.5100 -2.l328 —.8705 -l.6655 .3678 (.8332) (.2825) (.5003) (.5069) (1.3231) (.3526) F Ratio D.W. R2 77 with 6 and 4 degrees of freedom. 2.41 [Inconclusive] .978 65 TABLE 8 TRANSPORTATION DEMAND EQUATION Standard errors are listed in parentheses under their respective coefficients. Y1 Y2 Y3 Y4 Y5 Y6 —.5363 .1881 .5847 .0496 2.0531 -.0080 (.2711) (.0919) (.1628) (.1649) (.4305) (.1147) F Ratio = 197 with 6 and 4 degrees of freedom. D.W. = 2.37 [Inconclusive] R2 = .993 TABLE 9 CAPITAL DEMAND EQUATION Standard errors are listed in parentheses under their respective coefficients. Y1 Y2 Y3 Y4 Y5 Y6 -.0391 ~1.1022 -.0973 -.5696 .7657 -.4576 (1.3620) (.4618) (.8178) (.8286) (2.1628) (.5764) F Ratio = 32 with 6 and 4 degrees of freedom. D.W. = 2.51 [Inconclusive] R2 = .953 66 TABLE 10 RETURNS TO SCALE ESTIMATESd Economy of Scale Return to Scale Parameter Parameter Cost Function 1.3604a .7350a Labor Demand Function .8933b 1.1194b Space Demand Function (xxxx)C (xxxx)C Transportation Demand Function 2.0539a .4889a Capital Demand Function .3081b 3.2456b aEconomy of scale parameter significantly greater than one, return to scale parameter significantly less than one. bEconomy of scale parameter not significantly less than one, return to scale parameter not significantly greater than one. c . . Estimated parameters are negative and thus are not economicall; meaningful. d I I Economies of scale parameters are estimated as as + d6 , etc. and the returns to scale parameters are l estimated as ——————— 0‘5 + 0‘6 , etc. 67 The returns to scale parameters are indicated in Table 10. They indicate the existence of significant diseconomies of scale. The estimates of the labor and capital demand equation cannot be shown to reject the hypothesis that constant returns to scale exist in defer- ence to the hypothesis that economies of scale exist. The results of the scale estimates of the space demand equation are negative and hence not economically meaning- ful. C. An Alternative Approach to Cost and Factor Demand Equation Estimation The estimates of the cost and factor demand equations in the previous section required obtaining information on total costs, factor prices, and required capacity. Due to poor data collection or a lack of in- formation, however, it might not be possible to obtain all the necessary data on factor prices. If information is available on factor inputs and on the percentage in- crease of at least one factor price, however, the cost equations can still be estimated. Let us assume the following model DC = AL K S T e ED = QRw = + + T C WLL + WKK WSS WT 68 Assuming that the firm minimized costs to the constraint of the expected capacity production function, solving the resultant first order equations of the lagrangian for factors and total costs, and applying the equilibrium conditions, we derive cost and factor demand equations similar to thoSe in the last section. The cost function is of the form: 0‘1 0‘2 0'3 0'4 0'5 0‘6 v C = A* WL WK WS WT Q R e where v = -U di = 2% (i = l, ..., 4) 0‘5 = E 0‘6 = H A* = B(B + B + B + B ) 1 2 3 4 and all other variables are as defined as above. Noting the first order conditions: WL = MBl (E(DC)/L) WK = M82 (E(DC)/K) Ws = M83 (E(DC)/S) WT = M84 (E(DC)/T) WLL and noting that M = W we can solve Noting further factor price, and I = this implies: where B = W l L for 69 W . This yields: tfl'm |-' N /"-\ Wlb 2 L'" B_3 (A) W 81 s L 54. (A) i, 81 T L that WL = WL IL where WL = the base the index of factor price changes, Substituting in the cost function we have: 0!. 06 CL C( (X. (X. — 1 L 2 L 3 L 4 5 6 v A*(WL IL) (B1(R)IL) (B2(§>IL) (B3(T>IL) Q R e C: or O l L _-_-* _ c D .L (K 70 where Thus, the cost function is case in terms of the index of labor's wage, factor input ratios, and the re— quired level of capacity. In a similar manner, the factor demand equations can be transformed. Making the appro- priate substitutions, we have: 0!. 2 3 4 d d _ B 8 B B (L) (L) (L) 5 6 v L — l 2 3 4 B T — — Q R e which reduces to: d d d L = F E 2 E 3 E 4 st RG6 V K S T ‘ e where -l E _ £1 F = A 2 e2 22 The other factor demand equations can be transformed in a similar fashion. The transformed equations are: -(a +a +a ) a a _ F E 1 3 4 E 3 E 4 Qas Ra6 eV K S T ' d -(d +d +d ) d 2 l 2 4 4 d d S = F (é) (g) (%) Q 5 R 6 ev K o T 7: l 71 Thus, the factor demand equations can be estimated solely in terms of factor input ratios and the level of required capacity. The cost and factor demand equations were estimated by running OLS on the respective logged functions. The results of the estimation are in Tables 11 through 15. It should be noted that there is a striking and curious simi- larity among the coefficients of the various factor demand equations.34 The scale results are reported in Table 16. As shown, the results indicate significant diseconomies of scale. TABLE 11 COST FUNCTION Standard errors are listed in parentheses under their respective coefficients. 51 062 0‘3 0‘4 0‘5 0‘6 .7390 -.1228 .3141 -.2299 1.0950 .0955 (.0860) (.0257) (.0957) (.1186) (.1029) (.0512) F Ratio = 1925 with 6 and 4 degrees of freedom. D.W. = 3.039 [Inconclusive] EZ = .999 34 Differences between Tables 11—15 and Tables 5-9 could stem from errors in measurement of the factor prices for K,S, and T. 72 TABLE 12 LABOR DEMAND Standard errors are listed in parentheses under their respective coefficients. a2 a3 d4 a5 a6 .0387 .0009 .3042 1.1044 .0766 (.0278) (.1320) (.1571) (.1101) (.0687) F Ratio = 443 with 5 and 5 degrees of freedom. D.W. = 1.505 [Inconclusive] £2 .995 TABLE 13 CAPITAL DEMAND Standard errors are listed in parentheses under their respective coefficients. -(al+d3+d4) d3 d4 d5 d6 -.9613 .0009 .3042 1.1044 .0766 (-.0278) (.1320) (.1571) (.1101) (.0687) F Ratio = 2680 with 5 and 5 degrees of freedom. D.W. = 1.505 [Inconclusive] E2 = .999 TABLE 14 SPACE DEMAND Standard errors are listed in parentheses under their respective coefficients. a —(d +d +a4) d a d 2 l 2 4 5 6 .0388 -.9991 .3042 1.1044 .0766 (.0278) (.1320) (.1571) (.1101) (.0687) F lkatio 1393 with 5 and 5 degrees of freedom. ELVV. 1.505 [Inconclusive] —2 R = .996 73 TABLE 15 TRANSPORTATION DEMAND Standard errors are listed in parentheses under their respective coefficients. d2 d3 —(dl+d2+d3) d5 d6 .0388 .0009 -.6958 1.1044 .0766 (.0278) (.1320) (.1571) (.1101) (.0687) F Ratio = 634 with 5 and 5 degrees of freedom. D.W. = 1.505 [Inconclusive] fi2 = .996 TABLE 16 SCALE PARAMETERS Returns to Scale Economies of Scale Cost Function .840 1.191 Labor Demand .847 1.181 Capital Demand .847 1.181 Space Demand .847 1.181 Transportation Demand .847 1.181 D. Productivity Measures Information on the technical relationships among factor inputs and outputs, and particularly information on the nature of the returns to scale parameter, can be inferred from productivity measures. The measure of "productivity" employed in this study is the quite familiar Kendrick measure. Kendrick's measure of productivity change 18 defined as dP yl / yo _.. = -1 P E W. V . Z W. V . 74 where yo = Quantity produced in time period 0 y1 = Quantity produced in time period 1 V0 = The ith input in time period 0 Vl = The ith input in time period 1 Wi = The ith factor price (common to both time periods) When an underlying homogeneous of degree one production function is assumed,35 %? can be inferred as the increase of "technological knowledge" over time.36 The results of a time series measurement of pro- ductivity is given in Table 17 and the graph of producti- vity change in terms of a 1961 base year is shown on Figure 2. Factor inputs were aggregated as weighted by a base year price. Labor was priced out in terms of the 1966 average wage and all other costs were deflated by the wholesale price index. Output was defined as Y = QRW where w was derived from the cost function relationship. If the production function was homogeneous of degree one and if no technological advance occurred, then 35An underlying production function for a two factor input model consistent with this measure is: Q = tKL 1 (CLD + dkp)p where K,L are factor inputs; and t,C,d, are parameters. See Kendrick and Sato (40). 36See Nadiri (63). 75 the measure %; would equal zero, for all increase in "output" could be attributed to an increase in factor inputs. If there were technological advancements, then the measure would be positive, indicating that propor- tionally fewer factors were necessary to produce a higher level of "output". For the USPS, however, the measure of productivity increases slightly from 1961 to 1962, stays relatively constant through 1966 and then decreases. The measure comparing 1961 and 1971 is (-.O365). This indi- cates that "productivity" decreased 3.65% over the eleven year span. Since it is difficult to accept a decrease in the level of technological knowledge, one might infer that the underlying postal production function exhibited characteristics of decreasing returns to scale rather than constant returns to scale. TABLE 17 PRODUCTIVITY MEASURE Productivity Productivity Year Coefficient Year Coefficient 1961 17.4094 1967 17.2697 1962 17.8920 1968 17.2011 1963 17.6753 1969 17.2284 1964 17.6649 1970 16.8284 1965 17.7802 1971 16.7749 1966 17.6903 E. Qualifying Remarks The results thus far, while tending to indicate the existence of diseconomies of scale and declining 76 _-—-—_—_—-------_—--—_—_-——-—-_- Hw. Ho. Ho; Hm. Hm. Hm. HmL Hm: Ho. Ho. Ho; .QH .qo wow you too rmm ya» .mw 1mm ImH 10% -10% FIGURE 2 PRODUCTIVITY CHANGE OVER TIME (196l=0) 77 productivity, are premised on several assumptions. While it is hoped that the assumptions are fair representations of reality, they should be reviewed to seek out any sources of serious bias. (1) The Aggregation of Output To obtain a single valued mail volume representa— tion for each year, it was necessary to assume some trans- formation function among the various mail classes and services. While simple summation of "mail pieces" and "special service transactions" would qualify as a trans- formation function, such an approach would be misleading. A piece of first class letter mail and a second class magazine or a fourth class parcel have very different physical characteristics and are not processed in the same manner. However, simple summation implies equal weighting factors of one for all mail classes and ser- vices. This would indicate that a mail flow of all first class letter mail, a mail flow equally divided among the various classes, or a mail flow of all parcels (assuming an equal number of pieces in each case) would have the same output value and would require the same amount of factors. This does not appear to be a reasonable assump- tion, and thus is not used in this study.37 37This approach is used by the USPS in reporting its measures of productivity. See the Postmaster's General Annual Report (93 (1971)). 78 An alternative approach was employed by Merewitz. In his study he assumed a transformation function of the form A x ml x a2 x a3 1 2 3 ° ' where Q = weighted mail volume x1 = first class pieces x2 = second class pieces x3 = third class pieces, etc. The coefficients of the transformation function were es- timated from the reduced form cost function. While this approach has much merit, it could not be employed in the time series study due to a lack of observations. The approach used in this study is to assume a transformation function of the form: Q = E wi xi where Q = mail volume X. = the ith class 1 th Wi = the i weight The weights, obtained from the Postal Cost Ascertainment 38 See Merewitz (59). 38 79 System, represent the ratio of the allocated unit costs of the ith class or service to the allocated unit costs of first class mail.39 This approach thus assumes con- stant returns to scale for all classes,40 and assumes the transformation holds equally for all years. If there exists instead, increasing returns to scale in the true transformation function; or if the weights have varied from year to year such that W. < Wi then the in- t-l t crease in mail volume is understated. This could imply that constant or increasing returns to scale might exist. (2) Disembodied Technological Change and Factor Quality The results of the analysis thus far are premised on the assumptions that there has been no disembodied technological change and that input factor quality has remained constant. The direction of the findings would be questionable if there had in fact been a negative change in disembodied technology or if the quality of the inputs had deteriorated. It is difficult to accept the possibility of a decline in the level of disembodied technology. The more likely case is that there has been 39As indicated in Appendix A, this measure is not substantially altered by using weights derived from any single year, an average of the years, or by using like weights developed from the USPS concept of "attributable costs". 40That is ox' = 2 xi wi A and r = 1. i 80 a positive change. If there had indeed been a positive change, the scale results would tend to be strengthened. Measuring factor quality presents a difficult problem. It is doubtful that the "quality" of floor Space or transportation has varied over the period. It is likewise doubtful that the quality of capital has declined. Since there has been an increase in the capital account, one may assume that more and more new equipment is being added to the USPS stock. In addition, it is reasonable to assume that the new equipment is of at least equal quality to like older equipment. There is a possibility that the Service has systematically and increasingly em— ployed inappropriate equipment, but this is doubtful. The major factor input is labor, and it is con- ceivable that the quality of the postal employee has declined over time. One potential measure of employee quality would be the ratio of average postal wage to average wage of industrial or manufacturing workers. This measure is premised on the assumption that a higher rela- tive wage will entice higher quality employees to the Service or induce them to stay with the Service. The wage ratios are presented in Table 18. 81 TABLE 18 RATIO OF POSTAL WAGE TO WAGE OF ALL PRIVATE INDUSTRY year ratio year ratio year ratio 1961 1.23 1965 1.27 1969 1.27 1962 1.19 1966 1.27 1970 1.31 1963 1.23 1967 1.27 1971 1.39 1964 1.24 1968 1.26 Source: Postal wage was derived as the ratio of total wages divided by total man years. The data was obtained from the Postmaster General's Annual Report and the Budget of the United States Government. The wage for all private industry was obtained from the BLS report, Employment and Earnings: United States 1909-1971 (Bulletin No. 1312-8). As the table indicates, the ratio has increased from 1961 to 1971, but was fairly constant for 1965-1969. This does not tend to indicate that labor quality has deteriorated. (3) Managerial Quality Though management is also a factor input in the postal production process, it was assumed that it could be subsumed as a part of the labor component and that the quality of management was constant over time. The di— rection of the findings could be questioned if there had been a deterioration of the quality of management over time. There are no available measures of managerial quality, so the question remains open. It might be speculated, on the other hand, that there is an 82 "observation effect" among managers. That is, as manage- ment came under greater scrutiny by outside bodies (par- ticularly bodies with authority to change the basic structure and function of the Postal Service) the tendency for managers to improve their behavior would increase. Certainly, as postal revenue deficits have increased over the last decade, outside observation has increased. Thus, the "observation effect" might tend to moderate any sup- posed deterioration in postal management. (4) Quality of Service Another assumption made in this study is that the quality of postal service has remained constant over time.41 If, instead, the quality of service had increased, then these findings might not be interpretable as demon- strating the possible existence of diseconomies of scale. Increased postal costs might be attributable to increased service quality rather than only to increased volume and factor wages. As with other items in this section, a comprehensive measure of mail service quality is not available. However, since 1966 the USPS has measured the amount of time it takes a piece of First Class (or Air Mail or a parcel) to move from the point of entry into the Postal Service to its point of destination. These times are indicated in Table 19. 41Quality of service includes speed of delivery, damage rate, reliability of delivery, etc. 83 TABLE 19 QUALITY OF POSTAL SERVICE FOR SELECTED CLASSES OF MAIL Average Days Average Days to Delivery to Delivery First Air First Air Quarter ' Class Mail Quarter Class Mail Sept. '66 1.39 -e- III — 70 1.7 2.3 III - 68 1.5 2.1 IV - 70 1.7 2.2 II - 69 1.6 2.2 I - 71 1.8 2.2 III - 69 1.5 2.1 II — 71 2.0 2.4 IV - 69 1.4 2.0 III - 71 1.8 2.2 I - 70 1.6 2.1 IV - 71 1.7 2.1 II — 70 1.8 2.3 The table does not indicate any systematic in- crease in service quality over time. Thus, the possi- bility of serious bias because of this assumption is discounted. (5) Number of Households and Population Density Another source of bias is that of the nature of the delivery route. For this study, it was assumed that postal routes have not changed in such a manner as to introduce significant bias. Over the period 1960-1970, however, the number of households has increased from 52,799,000 to 62,874,000 [80 pg. 37]. This increase indicates that there might have been a concomitant in- crease in the number of delivery points for carriers. Such an increase might explain part of the increase in postal costs. However, along with the rise in the total $1.... 1. 1. 84 number of households, population density has also in- creased. In 1960 there were 42.6 people per square mile and in 1970 there were 57.4 peOple per square mile [80 pg. 5]. An increase in population density, all other things being equal, should reduce the costs of postal service. It is assumed that these two changes, taken together, contributed to no significant net change in postal costs. CONCLUSIONS AND POLICY IMPLICATIONS The United States Postal Service is an extremely important market venture. It is important because of its sheer size, the nature of the material it handles, and its position in, and impact on, the larger communications and transportation markets. Its employment practices affect a significant portion of the labor force. Its procurement policies affect a wide range of suppliers. The manner in which it performs its task of delivering the mails affects both personal habits and the manner of economic intercourse. Its service offerings, pricing, and product policies affect not only users, but a broad range of competitors as well. Thus, problems which face the Postal Service are of major significance, since a disruption or deterioration of service will have a multi- plying effect on the users, suppliers, and competitors of the Service. As noted by its several critics, the list of problems besetting the Postal Service is gargantuan. Postal management has been charged with being inadequate, inept, and non—innovative. Local managing units, as well as the national staff, have frequently lacked the authority 85 I4... 86 or information necessary to fulfill their responsibilities. Postal facilities have been criticized as being out-moded and inadequate. The Service's capital intensification program, some feel, has been insufficient and misdirected. Supply and transportation procurement practices have been questioned, as have been the quality of the labor force and the nature of the management-labor relationship. Patrons have complained of rising costs and prices, and of a decrease in the quality of service as manifested in the speed and reliability of delivery, the damage rate, and postal employee-customer relationships. Competitors complain of unfair competition emanating from the dis- criminatory practices of the USPS. The problems of the Postal Service are due in part to the institutional con- ditions surrounding the postal organization. But in large part they are an outgrowth of the technical nature of the Service's own production process. Policies which in- crease mail volume through price discrimination have re- sulted not only in a situation in which competitive ser- 3 vices are cross subsidized by revenues from monopoly services, but also in an increase in costs and a deterio- ration of service quality. In the face of diseconomies of scale, increased volume will lead to higher unit costs, or a lower standard of service, or both. The increased costs, further, result in a greater degree of cross 87 subsidization as the Service attempts to raise additional revenue without impairing its competitive position. A. The Pricing Question The Commission's criteria for pricing are set forth by Congress in the Postal Reorganization Act. The criteria listed, however, are numerous and not succinctly defined (see pp. 24-25 above). Thus, the Commission has a fairly wide latitude in the adoption of policy. The Commission must establish rates so that all relevant postal costs are recovered. In determining its rate structure, the Commission may consider the costs, the demand charac- teristics and the social value of the various mail classes and services. In addition, the Commission may consider the impact of alternative rates upon both the users and competitors of the Postal Service. The determination of the relative social value of a class of mail is a difficult, if not impossible, task. For example, while some segments of society may consider third class circulars as "junk mail" and an unnecessary nuisance, others value it highly as a con- venient means of information distribution. The ability of the Commission to "sense" the public's relative eval- Iiation of the classes is limited by the nature of its E>osition. The Commissioners are neither elected offi- C=ials nor appointees who must be approved by a 1". 88 representative legislative body. Further, the budget of the Commission is not subject to direct Congressional review. Thus, the opportunity and directive mechanism for public guidance on the "social value" issue is limited. Recognizing the virtual impossibility of the task, the Commission has attempted to limit its considerations to more technical and tangible areas. But the more "technical and tangible" areas are far from being clear and unambiguous. Holding social considerations aside, the Commission must weight the considerations of cost, demand, and impact so as to de- rive a rational and beneficial rate structure. In devel— oping an acceptable rate structure which meets the cri- teria and constraints of the Postal Reorganization Act, it is necessary for the Commission to demonstrate that any elements of discrimination are not "undue" in nature. Two pricing models which either rely upon or result in a price discriminatory set of rates have at various times been suggested as applicable to the postal pricing prob- lem. These models are the Boiteux-Baumol model and the classic economies of scale model. In its simplest form, the Boiteux-Baumol model presents an appealing pricing guideline anchored firmly in rationality. As simplifying assumptions are removed, however, a theoretically pleasing rule tends to become 89 administratively implausible. Due to the nature of the service offerings, it cannot be assumed that cross- ) elasticities are in fact zero. Due to the customer mix, it cannot be assumed that the Feldstein "distribution characteristics" of the various classes are equal. Thus, the measurement problem is greatly increased beyond that which is needed to measure marginal costs and own-price elasticities. If the pricing policy affects the level of competition, and if the level of competition in turn af- fects the costs of the public enterprise, then these fac- tors must also be measured. In addition to the measurement problem, other difficulties may arise in the Boiteux-Baumol approach. The analyses of Boiteux and Baumol, as well as that of Feldstein and others, does not consider the pricing re- action of direct or indirect oligopolistic competitors. If competitors did react to a new Postal Service rate schedule by changing their set of prices, then there could be a change in the level of consumer surplus derived from the price and demand patterns for the competitors' ser- vices. If the change in the level of the consumer surplus derived from the demand for the competitor's product was negative and of sufficient magnitude, then any supposed welfare gain for Postal Service customers could result in a welfare loss for society. Likewise, price changes by 90 suppliers of products which are complementary to postal products could also affect the total welfare level and thus should not be ignored. Consequently, in addition to the measurement factors, a commission seeking to justify its pricing on the basis of maximizing welfare would have to bring into its considerations the probable price re- actions of competitors and suppliers of complementary products, and the resultant change in the levels of the respective consumer surpluses. Since the various simplifying assumptions are inapplicable to the postal situation, the measurement and information requirements necessary to implement a rate structure become monumental and, in all probability, far beyond the capabilities of the respective parties. Our discussion of the limiting Boiteux-Baumol case has been, as Lord Keynes noted with respect to other problems: . . . not so much in finding logical flaws in its analysis as in pointing out that its tacit assumptions are (not applicable), with the result that it cannot solve the economic problems of the actual world." (44 pg. 378) Quite apart from the Boiteux-Baumol approach, it has been argued that a price discriminatory pricing struc- ture can benefit all customers, or can at least benefit some of the customers without detriment to the others. CDhis argument is based on the existence of economies of sscale in the postal process and in the ability to shift 91 the total demand for postal products by means of a change in the relative structure of rates. If economies of scale do exist, this argument for price discrimination is well worth consideration. The existence of economies of scale is an empirical question. Thus, the applicability of this model can, in part, be determined through empirical investigation. B. Results From The Investigation of The Postal Production Process An investigation into the technical relationships of the postal process was conducted to determine the nature of the Service's scale economies. The investiga- tion indicated that the hypothesis of economies of scale could not be accepted, and that the hypothesis that dis- economies of scale exist tends to be borne out by the separate analysis of production functions, cost functions, and input factor demand functions, as well as by the con- sideration of Kendrick type productivity measures. The analysis was based on the time series data for the total postal system. An independent study (59) found that the large individual postal processing centers which handle a large portion of the mail volume operate in the range of decreasing returns to scale. The results of this study cannot be taken to in- dicate that economies of scale are forever beyond the III. 92 Postal Service's reach. Improving technologies, changes in the patterns of processing, and improvements in manage- ment and factor quality might over time extend the range in which economies of scale can be realized to include the actual level of production. However, the realization of any such future economies is speculative. What the present study does demonstrate is that the available data do not support the hypothesis that the Postal Service has been or is operating in a region where economies of scale are realized. C. Implications for PricingiPolicy The findings of the technical analysis tend to indicate the existence of diseconomies of scale in the relevant production region. This indicates that the pricing implications of the economy of scale model are inapplicable to the postal situation. Thus, without economies of scale, without the technical ability to mas- ter the information and measurement problem arising from a Boiteux-Baumol approach when relevant assumptions are brought into line with the postal circumstances, and absent any other compelling argument to the contrary, a price discriminatory rate structure appears to be neither beneficial nor justifiable. Unfortunately, these findings do not solve the postal pricing problem. Rather, they tend to limit the extent of the consideration to be 93 given to the "value of service" aspect of the relevant criteria. However, it is possible to give suggestions as to the direction in which future work should go. As- suming costs and cost relationships will play a major role in the development of the rate structure, the present methods of determining the cost of an individual class of mail or service, or groups thereof, are in definite need of improvement. For years the Post Office Department made a full allocation of its costs to the various classes of mail and service. The allocation attempted to dis- tribute "accounting costs" to the classes on the basis of various factors which were held to have an impact upon costs. The system of allocation, however, was criticized for making seemingly arbitrary cost allocations.42 At- tempting to improve upon its old system, the USPS embarked upon what has become known as the Incremental Costing System. Whereas the old system allocated all costs to mail classes, the new system allocated only those costs which were felt to vary directly with volume and to be directly associable with a single class. Under this system approximately half of the costs are "attributed" to the classes of mail. The remaining portion, which is categorized as "institutional costs," is spread among the classes on the basis of market and pricing factors. The new system of costing has also been severely criticized I 14;. 94 (note particularly 103 pg. 20-30 and 70 p. 90-165). Both approaches can be criticized because of the allocation factors they employ and because neither approach indicates the degree to which costs vary with volume in the relevant range of production. The allocation problem can be im— proved in part through a functionalized cost analysis, i.e., an analysis which identifies the costs by key pro- cessing functions and which allocates costs based on the alternative functional steps through which various classes pass. Serious statistical cost analysis will be of value in identifying the class's cost variability with volume, a necessary step if incremental or marginal costs are to be derived. Proper cost identification by class of mail or service is necessary for rational pricing. Without ade- quate cost information, the determination of the discrim- inatory nature of the rate structure will be all but im- possible. If, after the cost analysis process, there re- mains a portion of costs which do not vary with volume and which cannot be related to an individual class or group thereof, or if pricing on the basis of incremental costs results in either more or less revenue than is allowed by the statute, it will be necessary to analyze alternative methods for "equitably" allocating these cost or revenue differences to the various classes. Given an inability 42For a critique of the system, see (29 Chapt. 4, 5 and appendix B). 95 to justify price discrimination, or an ability to put it into effect in a proper manner, alternative methods of "equitable" allocation should be investigated to deter- mine the range of rate structure possibilities. Given that a set of cost based-equitable rate structures is possible, various performance standards (e.g., impact on competition, effect on costs, etc.) and administrational standards (i.e., the need to construct and implement an understandable and uncomplicated rate schedule) may be relied upon to choose among alternatives. D. Imwlications For Broader Public Policy The findings of the production function analysis raise the question of the appropriateness of the Private Express Statutes. If the Service were able to realize cost improvements through the exploitation of economies of scale, then it might be necessary to protect certain mail classes from outside competition. The ability to price discriminate to increase volume and thereby lower unit costs would be limited if competitors were permitted to carry the "monOpoly" class or classes of mail. Absent eccmomies of scale, however, such a rationale for pro- tecting the Service from competition is without substan- tial merit. Indeed, the impact of the Private Express Statutes is to enable the Service to implement pricing 96 and processing policies which are detrimental to the monopoly classes. The Private Express Statutes enable the Service to compete unfairly in those markets where it does not have legal protection by cross subsidizing the operations of the competitive services with excess revenues from the monopoly service. Such legal protection has had not only a detrimental effect upon the monopoly service, but also a chilling effect upon competition. The forestalling of competition could well result in a deterioration of service standards, sluggish technological advancement and innovation, an increase in processing in- efficiencies, and a host of other performance problems. Thus it would be desirable to lift the legal prohibition against competition in the letter mail market, as well as the other restraints to competition with the USPS. 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APPENDICES APPENDIX A APPENDIX A Review of Relevant Literature Due to its size, importance, and data resources, the performance and productivity of the Postal Service has long been studied. In 1932, Witt Bowden developed a statistical estimate of labor productivity changes (12). Henry Lytton expanded the output base of Bowden's Study and measured labor productivity for 1967-1958 (49). Baratz considered the behavior of postal costs for the total Service and by class of mail (5, 6). Three recent studies by Fred Dziadek, the Post Office Department, and Leonard Merewitz to bear closely upon my own work. A. Dziadek Dziadek was concerned both with the performance of forty-two post offices in 1954 and 1958, and with changes in the Post Office Department (POD) over time [24]. Intertemporally, he chronicled the growth of employment, expenditures, and mail volume. He noted various factors which might have borne on labor productivity over time (e.g., relative shifts in output from low to high pro- ductivity post offices, mechanization, the use of permit 106 107 mail, public investigations, and administrative changes). However, he made no systematic attempt to relate actual productivity changes to these factors. Cross sectionally, he compared labor productivity among 42 individual post offices as well as among the fifteen postal regions. ,He used various measures of per- formance. Among them were: 1. post office expense per hundred work units1 2. work units per supervisor and clerical man hour 3. incoming work units per letter carrier man hour 4. piece handlings2 per man hour. Using the Spearman correlation technique, Dziadek related labor productivity to post office size. He found a negative and significant relationship. This relation- ship, he suggested, could be due either to the existence of diseconomies of scale or to differences in the capital labor mix (he had found that the capital labor ratio was greater for smaller offices than for larger ones). Interregionally, he noted a significant variation in labor productivity (as defined above). This variation, he suggested, could arise from variations in the quality of mail service, the quality of the postal employee, 1A work unit was defined as the amount of work required to handle one machine cancelled letter. 2Total piece handlings was defined as the sum of all pieces handled at each mail sorting operation. 108 demographic characteristics (e.g., population density), managerial efficiency, or the capital output ratio. However, he made no attempt to relate systematically hypothesized cause and effect. B. Post Office Department The POD prepared its 1963 study of productivity as part of a Bureau of the Budget project to promote and guide the construction of productivity measurement systems for other agencies [27]. The study constructed indices, of inputs, outputs, and productivity for the POD as a whole as well as for major components of its manpower and major segments of its real costs (87). The indices cover- ed the period PFY 1953~62. Both total factor and partial factor productivity ratios were constructed. Two output indices were constructed. The first of these weighted pieces (mail) or transactions (special services) by the man hour per unit of output expended on the class or service in 1962. Man hours expended on a particular class or service were obtained from the POD's Cost Ascertainment Report. The second output index weight- ed pieces or transactions by real cost per unit expended on a class or service in 1962. Cost data were also ob- tained from the POD's Cost Ascertainment Report. The man hour components included window service and related main- tenance, and administration and related field services. 109 Total real costs included personnel costs, purchased transportation services, and building occupancy (rent - both actual and imputed). Indices were constructed for outputs and inputs for the years 1953-62. Using the appropriate indices, labor and total factor productivity indices were constructed. The POD report merely presents the productivity measures for the total postal system. No attempt is made either to construct productivity ratios for individual post offices or to eXplain the reasons for productivity changes. C. Merewitz Merewitz estimated the production functions for intra post office activity (mail processing and window services) as well as for extra post office activity (col- lection and handling)[59]. His data were drawn from 156 of the largest post offices in the United States. Merewitz used the derived cost function and factor demand equations to estimate the parameters of the production function of an individual post office. He also estimated both a Cobb—Douglas type and a CES type production func- tion directly. Regardless of the form of the production function, he found diseconomies of scale for both intra- and extra-postal activity. Breaking the sample up into small, medium, and large offices, however, he found 110 evidence of the existence of economies of scale in the smaller post offices but diseconomies of scale in the larger post offices. Merewitz also measured the relative performance , of the various individual post offices. His major measure of performance was "costliness", a comprehensive measure which, he felt, subsumed productivity (technical effi— ciency) and input effectiveness (price efficiency). He suggested that regional differences could be explained by differences in the quality of the postal employee. Em- ployee quality was measured indirectly through the dif— ference of the postal wage rate and the average regional market wage rate. Merewitz also tested degree of mecha- nization to see if it could explain inter post office costliness differences. However, he found that a positive relationship between performance and degree of mechaniza- tion could not be established. D. Production Functions, Cost Functions and Productivity Production function analysis dates back at least to 1928 and the seminal article by Charles Cobb and Paul Douglas (16). Though the original Cobb-Douglas production function was used to analyze macro or aggre- gate data, other economists quickly adapted the form to micro or firm data (13). In addition, the initial 111 restriction of linear homogeneity was quickly relaxed to allow analysis of returns to scale. (13, 23). The C-D form has continued to be a mainstay in countless empirical studies. (for a survey see 100 and 63). Certain restrictions implied in the C-D formula- tion limited its applicability certain problems. In 1961 Arrow, Chenery, Minhas, and Solow proposed a production function (CES) which maintained a constant elasticity of substitution among the factors of production but did not require the elasticity to be equal to one (2). Though the CES was originally formulated with a restriction of constant returns to scale, the restriction was soon re- laxed (l4). McFadden (57) and Uzawa (99) considered the implication of constant elasticity of substitution for three or more factor production functions. Dhrymes and Kurz (21), Gorman (32), and Mukerji (61) indicated how the CES could be specified for three or more inputs in such a way that the partial elasticities of substitution would not be restricted to the same value. The CES func- tion is a generalization of the C-D function. If the elasticity of substitution coefficient were equal to zero, then in the limit it could be shown that the CES reduced to C-D. If the elasticity of substitution were equal to one, and the scale parameter equalled one, then CES re- duces to a simple linear function of the inputs. 112 Another generalization of the C-D function is the variable elasticity of substitution function (VES).3 VES allows an elasticity of substitution coefficient which varies with the input factor ratio, though not with the scale of production. The VES function was not used in this study, however. The C-D and CBS formulations hypothesize a pro- duction function with a returns to scale coefficient which is constant over the range of production. Work by Zellner and Revankar demonstrated that functions with fixed re- turns to scale and a given elasticity of substitution could be transformed to obtain a function with the same elasti- city of substitution but having a return to scale coeffi- cient which varied with the level of output (106). The estimation of the C—D function is not a par— ticularly difficult task. A log transformation is all that is required to convert a seemingly non linear func- tion into one which is linear. And while OLS on the log- ged transformation does not obtain an unbiased estimate of the constant term, the estimates of the input para- meters can be shown to be unbiased when the error term behaves in a desirable manner (45). CES can be estimated leither through iterative least squares (the equivalent of DHJE) or by Kmenta's approximation (46). Also, CES can be €81zimated with a more complicated two phase method which 3VES, though a generalization of C-D is not a genearalization of CES. VES and CES have only three SPeCial cases in common. (See 71) 113 draws information from the cost function (see Dhrymes and Kurz 21). The GPF can also be estimated through iterative least squares. Though the estimation of the functions can be performed in a relatively straightforward manner, ques- tions have been raised as to proper specification. Marschak and Andrews in an article published in the 1940 noted that the relationship between outputs and inputs demonstrated not only the production function relation- ship, but the effects of managerial abilities and objec- tives as well (55). Though some had concluded that fail- ures to take the objective of the firm into account would lead to unreliable estimates of production coefficients when the production function was estimated directly, Zellner, Kmenta, and Dreze demonstrated that such is not the case (107). Applying the maximum likelihood technique and considering a profit maximizing firm with a stochastic production function, ZKD provided a Vindication for the straightforward OLS estimation technique on the C-D function. An alternative approach to estimating the pro- duction function coefficients is the derived cost function approach. For firms which are cost minimizers, a cost function can be derived in such a way as to provide es— timates of the production function parameters (64). 114 Shepard and Uzawa have shown the duality and one-to-one correspondence of this approach (76, 99). Nerlove (65) and Klein (47) among others have applied this technique to regulated industries. As noted above, Merewitz did the same with the single post office plants. The use of productivity measures has largely been fostered by the work of John Kendrick (40, 41). A thor- ough review of the theory and measurement of total factor productivity of the aggregate production process is given in a recent article by Nadiri (63). As an overall indica- tor, productivity measures the technical characteristics of the production process (elasticity of substitution, returns to scale, overall efficiency, etc.), technological change, and movements in relative factor prices. (See 63 pg. 1141) APPENDIX B APPENDIX B Data, Data Sources, and Methods of Compilation The data used for this study were derived from publicly available sources published by the USPS and its predecessor, the Post Office Department. The Postal Ser- vice is a convenient organization for technical analysis because, unlike equally large private corporations, its volume, input, and cost data are in the public domain. This appendix presents the data used in the study, iden- tifies the sources from which the data were obtained, and delineates transformation of raw data which were necessary for purposes of analysis. The data used in analysis are presented in the table at the end of this appendix. A. Time Frame Data employed in this study are yearly observa- tions of total Postal System cost, output, factor quan- tities, and factor prices. Data reported by the Postal Service in nominal terms have been deflated by the con- sumer price index to place them on a constant dollar basis. The data are from the years 1961-1971 inclusive. Cost and production function studies prior to this period 115 116 are difficult to perform, if not impossible, because the Postal Service did not keep a systematic record of its stock of, or yearly changes in, equipment capital. In- formation on the other factors prior to 1961 is, however, available. Though there are only a limited number of observations, eleven to be exact, estimation of respective coefficients is possible and sufficient degrees of freedom exist to test the significance of estimated coefficients. B. Output In order to construct a cost function, production function, or productivity indicator of the Postal Service, it is necessary to develop an output measure. As discussed above (see Chapter 4) the development of an output measure is difficult because (a) the Service does not "produce" mail, but merely provides a means of transporting it from sender to recipient, (b) the various mail classes differ greatly in physical characteristics and in their respective methods by which they are processed, and (c) the capacity which is produced by the Postal Service for the time period under analysis (i.e., a year) is in part a function of the peaking patterns of mail flow within the period. Thus, it is necessary to develop an adequate measure of mail volume and to develop a measure of the peaking pat- terns or actual yearly rate of capacity utilization. ln- 117 Three methods exist for deriving a measure of mail volume. The first is to simply sum the number of mail pieces and transactions for the various classes of mail and service. The second approach is to assume some functional transformation function among the classes and either to assume or estimate from other sources the para- meters of the transformation function. The third approach is to assume a functional transformation form with un- specified coefficients. The coefficients of the third approach would be estimated as a byproduct of the cost or production function estimation exercise. Though the first of the three methods is by far the simplest approach, and has been used by the Postal Service on occasion, it provides an unreliable volume measure. It tacitly assumes that an increase of the mail volume by one piece of first class mail would have the same affect on costs, or would need the same additional amounts of inputs, as an increase in the mail volume re- sulting from one additional piece of second class mail or one additional parcel. Due to the vastly different physi- cal characteristics of the mail classes, however, and due to the differing processing methods used for the different classes, such an assumption does not seem reasonable or tenable. 118 While the third approach is highly desirable, there is not a sufficient number of observations to allow its implementation. Thus, for purposes of this study, the second method of constructing a volume output was fol- lowed. The transformation function employed was linear, i.e., Q = X wi xi where 'Q is the weighted total mail volume wi is the weight for the ith class or service, and xi is the number of pieces or transactions for the ith class or service. The weights were derived on the basis of the USPS (or POD) cost allocations to the various classes of mail and service. To derive the weights used in the study it was first necessary to obtain the unit costs for each class of mail. These costs were obtained from the annual ngt Ascertainment Reports of the Post Office Department.1 They were derived simply by dividing the costs allocated to a class by the number of pieces or transactions in that class. The number of mail pieces and service trans- actions were obtained from the various issues of the Cpgt Ascertainment Report and the 1969, 1970, and 1971 issues of the Revenue and Cost Analysis reports. The weights were then derived as the ratio of the unit cost of any given class to the unit costs of first class mail, or lThe CAR were only published through 1968. 1969 and 1970 unit costs were derived from information submit- ted by the USPS in Docket No. R7l—l. 119 UCi th w. = ——— where w. is the weight of the i class, 1 UCl 1 UCi is its unit cost, and UCl is the unit cost of first class mail. Weights were derived separately for each of the years 1950-1970. In addition, a set of weights was derived based on the average of the yearly weights. Weights were deVeloped in a similar manner, using the USPS concept of attributable costs. The impact of employing the various weights2 is demonstrated on the Figure 3. As the graph demonstrates, there is a high correlation among the various weighted output vectors. The output data used for this study employed the average weights. Those weights are shown in Table 20. TABLE 20 OUTPUT WEIGHTS FOR MAIL CLASSES AND SPECIAL SERVICES Class Weight (First Class equals 1.00) Domestic Air Mail 2.66 Priority Mail 11.12 Second Class 1.27 Controlled Circulation 1.89 Third Class .97 Fourth Class 16.14 Official Mail .93 International Mail 5.87 Registry 19.22 Certified 6.74 Insurance 4.22 COD 19.93 Special Delivery 11.40 Money Order 7.44 Postal Savings 21.59 2Each set of weights were alternatively applied to all mail class volumes to derive an output vector. 120 110-. 100 d- A 90 m. B C D E 80 4- 70 .1 F 60 «- A = Ave. C.A. Weighting C.A. = Cost B = 1960 C.A. Weighting Ascertainment C = 1970 C.A. Weighting D = 1968 C.A. Weighting A.C. = Attributable E = 1972 A.C. Weighting Cost F = Unweighted 50 III- I [ 1 n l 1 I J_ _L n I 1 1 I V I V T I F I I I I H H H l4 H H H H H I4 la K0 K0 K0 KO KO \0 \0 KO KO KO \0 ON ON ON ON ON ON ON ON ON \I \l H N U) 04> U1 ON \1 00 \0 O I—‘ FIGURE 3 GRAPH OF AGGREGATED OUTPUTS BASED ON VARIOUS WEIGHTING SYSTEMS 121 The transformation employed assumes that inherent differences in the various types of mails and methods of processing them are affected in the costs allocated to each class. This approach is not novel. Similar pro- cedures have been used by other researchers (41) and by the former Post Office Department itself (87). The data vector representing the utilization rate of the postal system was derived from information in the Summary Financial and Operating Statements accounting period reports. The measure of capacity utilization is that of the familiar utility "load factor", i.e., 1 2 v.. Hi 13 R.= j max(V..) 1] Rj = The load factor for the jth year ..= The total mail volume for the ith accounting 13 . .th period of the 3 year th N = The number of accounting periods in the j year This measure is the average accounting period mail volume divided by the peak accounting period mail volume. 9.19.192; The major factor input, in terms of expenditures, is labor. Personnel costs accounted for 84.8 percent of total expenses in 1972 (93 (1972) p. 25). For the pur- pose of this study, the measure of the labor input com- ponent is that of man years. Since the employment of the 122 Service consists of regular employees and substitutes, the use of number of employees as a measure of labor's input would be misleading. If regular employees were replaced by substitutes working on a part time basis, total employment would increase, but the total work input would not necessarily change. Thus, it is necessary to place labor on an equivalent basis. The man year measure, then accounts for regular, substitute, and overtime work. Man year data for 1961—1970 are available in the Annual Report of the Postmaster General for the respective fiscal years. 1971 man years were reported in the 1973 Budget Request of the Postal Service. The wage for labor was constructed by dividing the total salary and benefits for any given year by the total number of man years worked. Data on salaries and benefits are available in the Annual Report of the Post- master General. Wages were deflated by the consumer price index, as reported in the 1972 Economic Report of the President. D. Equipment Capital Capital is the most difficult component of the production process to measure. Prior to FY 1961 the Post Office Department did not maintain, or at least report, accounting records of its equipment capital. In FY 1960, however, a substantial portion of the equipment was 123 placed under accounting control after a physical inventory held that year. Prices for equipment purchased prior to FY 1960 were estimated by applying the pertinent BLS wholesale price index to the estimated year of acquisition. After that time, new purchases were recorded at acquisi- tion cost (85 (1970) p. 77). The measure of the equipment capital input was measured as flow variable. It was constructed by summing the yearly deflated value of depreciation and the "oppor- tunity cost" of capital. The opportunity cost of capital was computed by multiplying the undepreciated book value of equipment times six percent. The deflation factor used was the consumer price index. The "wage" factor used for capital is the wholesale price index. This was deflated by the consumer price index. The measure is recognized as being weak. E. Space The measure of space used in this study is the physical square foot measure. Data on postal space are available in the various issues of the Annual Report of the Postmaster General. There are three basic types of postal space: interior floor space, platform space, and outside space. The total postal space was measured as a weighted sum of the three types of space. The weights used were similar to those employed in Merewitz's study 124 and those which were used by the Post Office Department. The Weights are: 1 sq. ft. interior space = 2 sq. ft. platform space 1 sq. ft. interior space = 5 sq. ft. outside space The price for postal space was computed as the ratio: ZwiRi P. = . i = 1,2,3 Zw.S. 1 1 where Si = Total leased and rented space of the ith type Ri = Payment for leased and rented space of the ith type 2 ll i space weights (wl = l, w = .5, w = .2) Data on expenditures on postal space were likewise avail- able in the various issues of the Annual Report of the Postmaster General. The price vector for postal space was deflated by the consumer price index. F. Transportation The measure for the transportation input was that of transported ton miles. The measure is limited to pur- chased transport. (Transportation provided by the Postal Service is via service owned vehicles, which are included in the equipment capital measure.) The major modes of transportation are air, rail, highway (star route contract), and water. Information on transportation ton miles was obtained from the various issues of the Cost Ascertainment Report and the 1969, 1970 and 1971 issues of the Revenue and Cost Analysis report. The price for transportation services was derived by dividing expenditures for 125 purchased transportation by the total number of ton miles. Expenditure data is available in the Cost Ascertainment Reports and the Annual Report of the Postmaster General. G. Total Costs The expenditures of the Postal Service are re- ported in the various issues of the Annual Report of the Postmaster General. Expenditure data used in the study has been deflated by the consumer price index. Though for purposes of deriving the cost and factor demand functions costs were defined as: = + + C WLL + WKK W S WTT S total costs (C*) were used for estimation. The following relationship between (C) and (C*) is assumed: C* = C d eu u where d = a constant, and e = random measurement error Using (C*) rather than (C) will affect the estimates of the constant term in the cost and factor demand equations, but will not affect the coefficients on the other independ- ent variables. To demonstrate this, consider the case of a simple cost function: 2This implies that funds other than for K,L,S,T are expended in fixed proportion to the costs of K,L,S, and T. 126 The function to be estimated is: ln C. 1n A + b 1n Z. + V. 1 1 1 The least squares estimator is derived as follows a '1 1n zi] . '1n oil "v11 8 =[b] X = E E 1n C = E V = 5 L1 1n ZN“ [in CN_ LVNd ln C = X B + V This implies B = (x'X)"l x' [1n C - V] and B = (x'X)"l x' ln c Z(ln Z.)2 - Zln 2:] . , -l _ 1 1 1 Since (X X) — 2 2 [Elm Zi N N E(ln zi) -(Zln zi) Then 2 A [E(ln Zi) ][Zln Ci] - Zln Zi Zln Ci ln Zi a = 2 2 N Z(1n Zi) - (2 1n Zi) and g = N E(ln Ci 1n Zi) — [Zln Zi][Zln Ci] N E(ln z.)2 - (Zln z.)2 1 l 127 The question is - does using (C*) affect esti- mates of a but not b ? To see that this is the case, consider the estimators a and b when C* is used for estimation. The function to be estimated is: or The estimators are obtained as follows: [1n C + 1n d + U] = x B + V This implies (x'X)"l x' [1n c + 1n d + U - V] II) I or 1 B = (X'X)- x' [1n c + 1n d] Thus 2 E(ln Zi) Zln Ci - (Zln Zi)(Zln Ci 1n Zi) a: 2 2 N E(ln Zi) - (Zln Zi) (ln d)(N)Z(ln zi)2 - (ln d) Z(ln 2i) Z(ln zi) + 2 2 N 2(1n zi) - (2 1n zi) 128 m2 II or a + 1n d and ~ N 2 1n C- ln Z. - Zwln C. 2 1n Z. b'= l 1 1 1 2 2 N 2(ln Zi) - (2 1n Zi) N(Z Z.) 1n d - (2 1n d) 2 ln Z. + l 2 2 1 N 2(ln Zi) - (2 1n Zi) or b = b Since N(ZZi) 1n d - (2 1n d)(Zln Zi) II 0 Thus using C* rather than C affects only the estimates of the constant term.3 3The ratio C*/C for the years 1961—1971 is: year C*/C ear C*/C year C*/C 1961 1.063 1965 1.067 1969 1.079 1962 1.060 1966 1.073 1970 1.079 1963 1.072 1967 1.081 1971 1.129 1964 1.072 1968 1.084 129 vhv.vmv.n mo.aa nm.aoa.~ Nan. «Ho.m muw.vm~.v www.mo Hmm.mma 0mm.oma Hmm.m~n man. m~m.mom.naa Hnma mmn.nom.m om.ma nm.-o.a ova. vmo.n me.vca.v mmo.vw «mm.mma omm.m0H mam.mmn mom. moo.anv.maa onma oo~.o~o.m mm.~H om.mmo.~ moo. mhv.h mm~.ma~.v mmm.mm mom.mna www.mm www.man mom. 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