Joel Dean

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research
Volume Title: The Relation of Cost to Output for a Leather Belt Shop
Volume Author/Editor: Joel Dean
Volume Publisher: NBER
Volume ISBN: 0-87014-447-2
Volume URL: http://www.nber.org/books/dean41-1
Publication Date: 1941
Chapter Title: Conclusions
Chapter Author: Joel Dean
Chapter URL: http://www.nber.org/chapters/c9258
Chapter pages in book: (p. 49 - 52)in
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particular shape of the cubic function, i.e., the costs associate(1 with high
and low outputs, were likely to be inadequately rectified for price and
quality changes, the bias being in the direction that would create a cubic
total cost function.
The four observations lying above the fitted line at the highest out-
put levels were in December 1q36, and March, April, and May, iqs7
(Chart ii). Thus they occurred at a cyclical peak, when defects in rectifi-
cation would be expected to overstate deflated cost. The six observations
lying below the fitted line at the lowest recorded outputs were depression
monthsJanuary to June i 938a period in which the rectification de-
vices may not have accounted adequately for price anti quality fluctu-
ations.
The negative intercept of the total cost curve, and the COIISC(1UCDt
illogical behavior of the average cost curve within the range of observa-
tions, cast some further doubt on the validity of the cubic function.
Moreover, as pointed out in Section i and discussed in Section 2, there
are indications that thetechnical structure of the production process
does not correspond to that assumed in the cubic model.
In view of all these considerations, the curvature within the observed
range does not seem to substantiatedecisively the hypothesis that the
total cost function is curvilinear.
8 Conclusions
The statistical evidence presented in Section 7 gives some support to
the conclusion that marginal cost is constant within the range of output
examined in this study. The findings of such an investigation asthis
that are most significant for economic theory can be presentedadequately
by considering solely the behavior o marginal cost; for, if the courseof
the marginal cost function is known, the shape of the total costfunction
is apparent. (Supplementary information is needed todetermine the
magnitude of fixed cost and the behavior of average cost.) Somecaution
must be observed, however, in comparingthe marginal cost function of
a model firm under static competitiveconditions with marginal cost
function derived by statistical methods from empirical data.The ob-
servations that are the basis of the statistical estimate may nothave been
adequately purged of the influence of extraneous variablesby the sam-
pling, rectification, and correlation analysis procedures.To the extent
that dynamic factors are present in the cost and outputobservations the
empirical curves will not be a precise counterpart of the curvesdescribed
in theory. It appears likely, however, that the most importantdynamic
influences were eliminated in the data adjustments.
On the assumption that our statistical techniqueshave successfully
isolated the static marginal cost curve, it is desirable to attemPtto ac-
49count for the particular results observed. Theexplanations will beCon-
sidered Uflder the following headings: (i)possibility of excesscapacity;
(2)segmentizeci organization of plant;() conventional rigidities.
Possibility of excess capacity
The most obvious explanation forthe constant marginalcost observed
for the belt shop is that onlyone portion of the marginal costcurve was
examined. A rising phase of marginalcost is, therefore, not disproved
and, on the other hand, is almostcertain to occur as physical plantca-
pacity is approached. It is likely, however,that the majorpart of the
possible variation of outputwas explored. The index of outputranged from40to 135, with four observationsover io. The largest output oh-
served had not been exceeded duringthe preceding tenyears of opera-
tion; plantmanagers expressed the opinion that thisoutput represented
'practical' plant capacity. Thismay be interpreted to mean thatsome- where beyond therange of observations marginalcost would rise
markedly.
Since excess capacity ofan economic sort is indicated,an exploration
of its causesmay lead to a better understanding ofthe implications of
the findings. Were itpossible to assume that thefirm was in long-run
equilibrium, so that its long-runaverage cost curve wastangent to a falling demandcurve, the firm would be operatingon the descending
phase of its short-runaverage cost curve. In sucha situation, visualized
in theories ofmonopolistic competition,excess capacity could be ascribed
to imperfections ofcompetition. Suchan assumption, however, would
be highly unrealisticand unjustified byany available informationcon- cerning the firm. Morevalid explanations mightbe found ina shrinkage of demand subsequentto the time investment in fixedplant was made,
oFover-investmentas a result of optimisticexpectations. Thesecauses. the first of whichseems important, would beoperative in a non-equi-
librium situation. Theshrinkage in demandevident in the firm'ssales
records is explained by theencroachment of chain drivesand rubber belts on a fieldpreviously dominated byleather belting.l)espite the general secular decline indemand, some furtherreasons must be sought to explain why, in viewof the large seasonaland cyclical shifts in(IC- mand, the plantwas not forced tooperate in the area of risingniarginal cost. Two possible explanationsmay be mentioned. First, thepossibility of anticipating peaksin sales andmanufacturing for stock intimes of slack demandmay have made itunnecessary to force productionbeyond the critical level. Thisis especiallytrue of leather beltingmanufacture
49 Demand for leatherbelting has declined sinceabout 1923 in a secularmovelnelit transcending the business cyde, thepeak of 1929 being lowerthan that of iq2, and thepeak of 1937 much lower than that ofiqag.
50since sales peaks can be forecast and the product can easily be stored.5°
Second, the declining trend of industry demand may have shifted the
firm's individual demand function to the point where sales fell so far
short of original expectations that even seasonal and cyclical peaks do
not strain the plant's capacity.
Segmentized organization of plant
Constancy of short-run marginal cost is, as pointed out in Section i,
consonant with the technical organization of this plant and of similar
mechanized operations. Segmentation of this plant into a number of
similar operating units, each of which can be withdrawn from operation
without influencing the efficiency of the others, tends to result in constant
marginal cost up to the point where all units are fully utilized. Variation
in the time these units are operated, attained either by changing the
number of shifts or the length of the work week, will accomplish the
same end.51 Two further questions are whether all the fixedplant and
equipment can be segmented and whether the essential labor force is
homogeneous. Concerning the first, it is likely, in practice, that segmenta-
tion of certain parts of a fixed plant is not possible. while a high degTee of
segmentation is feasible for other parts. if machinery and operating
equipment are segmented, even though the buildings, etc. remain in-
divisible, all physically fixed plant relevant for marginal cost behavior
may be considered to be segmented.The second question, concerning
the homogeneity of the factors of production can best be treated as a
part of the question of conventional rigidities.
Conventional rigidities
If the management of this firm had been perfectly free to adapt the or-
ganization of production to variations in output by taking full advantage
of the differences in efficiency in the segmented units, it isdoubtful that
the tendency to increasing marginal cost would be socompletely offset
as the statistical findings indicate. Althoughneither machines nor oper-
ators are of uniform efficiency, to select theunits of the various factors
with a view to employing them in the order of their efficiency was pos-
sible only within nan-ow limits. Seniority rights, repair programs,hu-
manitarian and other considerations apparently deterred the manage-
ment from taking full advantage of differencesin efficiency. For these
reasons, the hierarchy of efficiencythat undoubtedly existed was not
reflected in rising marginal cost with more intensiveutilization of plant.
iSO The costs of storage, insurance, and interest on inventories of finished goods were notcharged
to current production since they are caused by uneven distributionof demand and are more
properly attributable to cost of selling.
51 Variation in the quality of labor inputs as a result of longer hours and night shiftslies outside
the compass of static cost functions, although the effects of such influences aredifficult to remove
in empirical investigations.
51Restrictions of this kindtherefore constitutea type of rigidity2
that prevents the employerfrom Selecting theminimum COSt combi
tioll of factors fora given Output.a As we know thatCOIlvenhional rigidi- ties are present,we conclude that there is effectivehomogeneity of segments.
Thus the possibility of chronicunder-utilization of plant,the exist- ence of segmentation, conventionalrigidities and thereforeeffective fac- tor homogeneity furthersubstantiate the findings ofconstant marginal cost. The implication of thisstudy, an implicationof interest to indus- trialists as wellas to economists, is thatconstant marginal Costwithin the usual range ofoutput may be more prevalentunder modernoperat- ing conditions thanhas been implied bymuch economic theory.
52 Apart from thesecouventiottal rigidities, evidence oftechnical rigidities was to hefound in the behasior of one consponeiof cost, overhead cost. Asignificant telation of overheadCOSt to magni- ttide and direction of change inoutptit fi-om the precedhig monthwas ol)scrvett, after the infltaence of output itself had beenretnoved. It usight have beenexpected that if Otttputwere tinchatiged for two successive periods,overhead cost seotilci he less,because of the longer timeallowed for adjustment, than if a givenoutput followed either loweror higher outputs. As alnauer of fact, increases in outputwere accompanied by loweroserlsea(l cost, while decreasesin output were more costly (see Chart 7). Onepossible interpretation is thatincreases in outputcall he attained by temporarily overloadingthe staff, which results ina low cost per unit, while, whenotltptit is reduced it is dillictilt to adjustthe personnel immediately.Thcrc are usany indicationsthat over- head cost reductiotis inthe face of outputcotitractjois (especially whenpersonnel changes are involved) occur less easilytitan Cost increases whenoutput is increased. The lack ofevidence of rigidities us the behaviorof consbined costcan he attributed only to therelatively small im- portance of overhead cost intotal combitsed cost.
3 Although suchconventional rigidities cannot beclassed as dynansic forces,they may Cause even greater deviations from thestatic model. Forpurposes of prediction, however,empirical cost curves possess some advantageover cost curves predicatedupon (lie existence of a nsinimumcost complex of factors atevery output because of theircloser approximatiomi toreality.
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The Relation of Cost to Output for a Leather Belt Shop

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