ADAPTATION OF THE THEORY OF THE FIRM TO THE OPERATION OF A SINGLE-ENTERPRISE DAIRY FARM IN NORTHEASTERN PENNSYLVANIA

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The Pennsylvania State College i

The Graduate School Department of Agricultural Economics and Rural Sociology

ADAPTATION OF THE THEORY OF THE FIRM TO THE OPERATION OF A SINC-LE-ENTERPRISE DAIRY FARM IN NORTHEASTERN PENNSYLVANIA

A Thesis by WILLIAM TAYLOR BUTZ

Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 1951

Approved:

3,/fJ7

325 pounds of total digestible nutrients from all feed sources other than pasture.

The method by which this estimate was

obtained was considered more reliable because of its inherent flexibility in considering substitutability of feeds on any one farm.

Consequently,

the estimates of the pounds of total digestible nutrients obtained per cow from each of the three sources (silage, hay and grain) were lowered proportionally so that the sum of the three individual estimates was equal to the estimated total of 4,325 pounds.

With this adjustment, each

cow obtained 1,106 pounds of total digestible nutrients from silagej 1,941 pounds from hay, and 1,278 pounds from grain. One additional adjustment was made in which the estimates of the pounds of total digestible nutrients derived from each source were altered slightly, but the sum of the parts remained unchanged.

To feed

each cow the amount of hay required to provide 1,941 .pounds of total digestible nutrients would have resulted in insufficient quantities of hay being available to supply the minimum requirements of dry roughage for other livestock.

For this reason, the estimate of total digestible

nutrients' derived from hay was reduced from 1,941 to 1,700 pounds.

The

reduction in pounds of total digestible nutrients derived from hay was

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

23 replaced by Increasing the estimated pounds obtained from silage and

21 concentrates to 1,157 and 1,4.68 respectively • The final step in the procedure was to reconvert the final estimates from pounds of total digestible nutrients (derived from each kind of feed) to pounds of the particular feed.

Final estimates of the

quantities of roughage and grain fed per cow and the toted amounts fed all cows are shown in Table 6. Bull - Following the same procedure described above, the sum of the total digestible nutrients obtained from individual sources (silage, hay and concentrates) was 2,589 pounds.

Adjusted to the control value

of 2,04-3 pounds, resulted in estimates of 563 pounds of total digestible nutrients from silage, 1,007 pounds from hay, and 4-73 pounds from pur­ chased grain. A portion of the hay reallocated from the cows was fed to the bull.

The increase in pounds of total digestible nutrients derived from

hay was offset by a decline in pounds obtained from grain.

The final

estimates of total digestible nutrients obtained by the bull, by sources, were:

563 pounds from silage, 1,067 pounds from hay and 413 pounds from

grain.

The pounds of particular kinds of feed represented by the pounds

of total digestible nutrients are given in Table 6. In total, the bull obtained 3>54-9 pounds of total digestible nutrients from all feed sources, including pasturage j 1,506 pounds ~y\' . This adjustment may be considered another instance in which an "average" concept failed to provide a "representative" value. The justification for the adjustment stems primarily from the attempt to synthesize % farm organization having the characteristics of existing farm businesses in the area studied. It is contended that the final estimates were more representative of the typical objective in allocating feeds among live­ stock than were the previous estimates.

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Table 6 - Kinds and amounts of home grown and purchased feeds allocated to livestock, Representative farm, 1941-42. Corn silage

Livestock Kind

Cows

Average number

13.3

Mixed hay

**ec* Per head

Total amount fed

Amount fed per head

Total amount fed

(pounds)

(tons)

(pounds)

(tons)

6,800*

45.2

4,000*

26.6

Purchased Oats concentrates Amount Total Amount Total fed per amount fed per amount head fed head fed (pounds) (pounds) (bushels) (pounds) 1,957*

26,028

—

—

Heifers, one year or older

3.4

3,434

5.3

1,385

2.4

325

1,105

—

—

Heifers, less than one year

4»1

1,800

3.7

550

1.1

225

922

—

—

Bull

1.0

3,312

1.7

2,510

1.3

551

551

—

—

Horses

2.0

~

—

4,612

4.6

—

36.0

28,606

Total amount fed, all livestock

56.4

2,832

177.0 177.0

*The components of the ration assigned to each cow on the representative farm may be compared to the ingredients of the average ration estimated by Barr in the 1941-42 Cost Study. In that study, the average amounts of roughage and concentrates fed per cow in Wayne and in Lackawanna counties were calculated. Weighting these estimates by the number of farms in the sample drawn from each county (ll from Wayne and four from Lackawanna), the amounts of silage, hay, and concentrates fed per cow were 7,400, 4,480 and 1,909 pounds respectively.

25 were derived from pasture and 2,04-3 from all other sources. 00

son, Morrison

For compari-

has recommended an average of 10*3 pounds of total digesti­

ble nutrients daily (3,750 pounds annually) for a 1,200 pound mature dairy bull. Horses - The ration fed to horses consisted of hay and oats. No silage or pasture was allocated to the horses.

The sum of the total

digestible nutrients derived per horse from hay and oats was 3,699 pounds; 1,996 were obtained from hay and 1,703 pounds from the oats consumed.

The

first adjustment, as before, was to correct these estimates proportionally so as to equal the control value, 3,94-3 pounds.

This adjustment produced

estimates of 2,128 pounds of total digestible nutrients from hay and 1,815 pounds from the hame grown concentrate feed, oats.

The second ad­

justment, by which more hay was made available for the young stock and the bull, consisted of reducing the estimated total digestible nutrients de­ rived from hay to 1,960 pounds and increasing the total digestible nutrients obtained from oats to 1,983 pounds.

Estimates of pounds of the hay and

grain fed per horse converted from pounds of total digestible nutrients, are shown in Table 6.

According to the Morrison^ standard, a 1,200 pound

horse requires 4-,236 pounds of total digestible nutrients during a 12 month period consisting of 182 days of idleness and 183 days of medium hard work.

22Morrison, F. B. Feeds and Feeding. 21st edition. Morrison Publishing Company. Ithaca, New York. 1948. P» 114-8• 23Ibid.

p. 1151.

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26 Heifers, One Year or Older - Estimates of the pounds of total digestible nutrients fed to young stock were based, in general, upon recommendations furnished by dairy husbandrymen

• A total of

1,4-50 pounds of total digestible nutrients, excluding pasture, was recom­ mended for heifers over one year.

In the present synthesis, heifers were

fed 1,417 pounds of which 584 were obtained from silage, 589 pounds de­ rived from hay and 244- pounds from grain.

Pounds of each feed repre­

senting the pounds of total digestible nutrients obtained from each source are given in Table 6, Heifers Less than One Year - A ration totaling 768 pounds of total digestible nutrients was recommended for a heifer less than one year of age.

On the representative farm, the sum of the total digestible

nutrients acquired from the various feed inputs allocated to each calf under one year was 761 pounds.

This total represented 306 pounds from

silage, 234 pounds acquired from hay, 169 pounds from grain and 52 pounds from milk.

The pounds of roughage and concentrate to which the

pounds of total digestible nutrients refer are given in Table 6.

The

52 pounds of total digestible nutrients supplied by mjlk were obtained from 324 pounds of milk consumed by each calf raised as a replacement. Bedding - A total of 4.8 tons of oat straw was available for bedding livestock.

Straw was distributed between kinds of livestock as

follows:

^Handbook of Basic Information for Planning Pennsylvania Farm Businesses. Department of Agricultural Economics and Rural Sociology. The Pennsylvania State College. 1950.

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27 (tons) Cows

3*2

Heifers, oneyearor more

*5

Heifers, lessthan one year

.5

Bull

.2

Horses

.4

Salt and Minerals - From the information available from the records of the 15 farm businesses, it was estimated that 16.2 pounds of salt and minerals were consumed per animal unit.

The same rate of

consumption was assigned to livestock on the representative farm.

The

quantity of salt and minerals consumed by all livestock was estimated at 333 pounds. Utilization of Milk Produced The total quantity of milk produced by the cows kept on the representative firm was estimated at 872.48 hundredweight of four per cent fat-corrected milk.

This quantity was the product of l) the average

number of cows kept during the year, 13.3j and 2) productivity per cow, 65.60 hundredweight of four per cent fat-corrected milk. The relative quantity of milk marketed was determined by dividing the pounds of four per cent milk marketed by the total pounds of milk produced on the 15 farms.

The percentage amounts of milk used in

the home and fed to calves were estimated in the same manner.

According

to this method, the representative farm marketed 94*6 per cent of the milk produced, used 3.5 per cent in the home, and fed 1.9 per cent to calves.

In absolute amounts, the quantities were 825.37, 30.54 and 16.57

hundredweight of four per cent milk respectively.

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28 The 16.57 hundredweight of milk fed to calves was utilized as follows:

l) 10 pounds per day for four days^ to each of the nine

calves sold, or a total of 3*60 hundredweight j 2) 324*25 pounds to each of the four heifer calves retained for replacements, or a total of 12.97 hundredweight.

All of the milk fed to calves was marketable.

The

colostrum milk consumed during the first three days following birth was not included in estimating feed inputs allocated to young stock. Labor Force The method by which the labor force of the representative farm was determined paralleled closely the procedure followed in calcu­ lating other characteristics of the farm business.

Initially, the

number of man equivalent months worked by each component of the labor force (operator, unpaid family help and hired laborers) was summed for each of the 15 farms. and the mean

The total numberof months per farm was arrayed

of the middle third of the values was calculated.

By this

method, it was estimated the labor force worked 21.1 man equivalent months on the farm business and the farm home. By each segment

arraying the number of man equivalent months worked by of the labor force, and computing themean for each segment,

the number of months worked, by kind of laborer, was:

operator, 12 months;

unpaid family 7.3 months; hired help, 3*4 months. Operator - The operator of each farm in the sample stated that he had worked 12 months on the farm.

Consequently, on the representative

25

Assuming an average selling age of seven days, marketable milk was consumed four days beyond the period during which colostrum milk is normally yielded.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

29 farm, it was assumed that the operator's labor accounted for 12 man equivalent months.

By subtraction, 9*1 man equivalent months were worked

by other laborers. Unpaid Family and Hired Help - The separate estimates of"months worked by unpaid family labor (7.3 months) and hired help (3.4- months) were reduced proportionally in order to equal the sum of 9.1 months.

As a

result, the estimated numbers of months worked by these two components of the labor force were 6.2 months by unpaid family labor and 2.9 months by hired labor. The total number of man equivalent months worked by all members of the labor force included labor time expended in gardening and in caring for poultry. family labor.

It was assumed that both chores were performed by unpaid The total labor time for both tasks was estimated at .2 man

equivalent months

26

, thus reducing unpaid family labor time expended on the

farm business to 6.0 months.

For the same reason, the number of man

equivalent months worked by all members of the labor force was reduced from 21.1 to 20.9 months, consisting of 12 months by the operator, 6.0 months by unpaid family help and 2.9 months by hired help.

Equipment The methods by which pieces of equipment were assigned to the representative farm were less objective, consequently more difficult to explain, than methods used to determine other physical characteristics of the.representative farm organization.

Decisions relevant to the equip­

ment to be included in the representative farm business were influenced

26Calculated at the rate of .18 man work units per hen or a total of 22 man hours for poultry, and 28 man hours for gardening.

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30 considerably by the frequency with which a piece of equipment was found on the 15 farms studied.

This basis of selection provided the synthetic

farm with the non-specialized equipment usually found on comparable farms. Several pieces of specialized equipment were assigned to the farm.

The

selection of specialized equipment was more arbitrary, however, inasmuch as each piece assigned to the representative farm was not found on a majority of all farms.

In determining the specialized equipment owned by

the synthetic organization, consideration was given to the kind and acreage of crops, kind and number of livestock and typical farm practices as well as to the frequency of ownership. Power - A H but one of the farms in the sample had one or more kinds of power equipment ■— truck, tractor or auto. combination was a truck and a tractor.

The most frequent

Hence, these two kinds of power

equipment was assigned to the representative farm.

Other - Following the procedure described above, the equipment listed below was selected for the farm:

ensilage cutter, manure spreader,

binder, grain drill, wagon with racks, mower and rake, plows, corn planter, cultivator, harrdw, horse harnesses and miscellaneous dairy equipment. The dairy equipment did not include a milking machine nor an electric or 27 ice milk cooler , Limited information was available with which to determine the permanent equipment installed in the barn on the representative farm. All that can be stated is that the barn was equipped with stanchions. 27 Of the farms observed, two had milking machines, both electric, and four had electric mriHc coolers.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

31 Drinking cups and manure carriers were not installed in a sufficient number of bams to be considered typical equipment. Financial Organization of the Representative Farm The primary objective in recasting the physical organization into value terms was to compute the total cost of producing the milk

2 8 marketed by the representative farm.

Cost data refer, of course, to

the same time period as did the physical organization, i.e., JJay 1, 1941 through April 30, 1942*

Furthermore, the cost data relate to the opera­

tion of the farm business, per se, as distinct from the farm business plus the farm homeo Classification of Costs This study followed the conventional practice of classifying total costs into fixed and variable categories.

The criteria by which

the cost of any one productive service was classified as fixed or varia­ ble were not conventional, however.

The fixed category included all

costs except the cost of grain purchased for cows.

In turn, the sole

variable input was the quantity of grain fed to cows.

All concentrate

29 feeds consumed by the cows were assumed to be purchased * This classification of costs did represent a simplification of the real opportunities available to producers to vary costs.

That is,

several minor expenses such as fertilizer cost, hired labor expense and

28The product of the firm was considered to be the milk that was marketed, not the produced. Specifically, then, the cost to be estimated was the cost per unit of output, i.e., cost per hundredweight of four per cent milk marketed. 29 This assumption was fairly well vindicated by typical feeding practices. On the 15 farms studied, 12 did purchase all concentrates fed to cows. At least 84 per cent of the grain fed was purchased on each of the three other farms. -

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i

32 the costs of operating power equipment, which are truly variable in the short run, were considered fixed according to the methods used in this study.

But it is contended that this abstraction did not seriously dis­

tort the actual conditions facing specialised dairy operators in the area. Grain was the really important input capable of being varied by producers during the short run and the grain cost was correctly classified.

In

addition, the derivation of a production function from the law of variable proportions permitted variation of one productive service only, at any one 30 time . Grain was not only the most important variable input, but'also the sole input for which a production function had been experimentally derived.

No such functions, adaptable to the area observed, were available

for other "variable" productive services.

Furthermore, the costs which

are traditionally considered variable but which were treated as fixed costs in this analysis did not comprise the bulk of the total fixed costs. The largest single fixed cost was the imputed value of family labor, and this input cannot be varied significantly within a 12 month period.

Costs

of maintaining the human agent continue regardless of the family's contri­ bution to the labor force of the farm.

But the labor input of the family

remains relatively constant (within a short time span) as a consequence of long tern commitments in capital items, and family and community ties.

Factor Costs The cost of an individual resource was computed by following either of two methods.

By the first method, the total factor cost was

estimated as the product of an average rate (price) per unit of the 30 This is not to state that methodological limitations restricted the analysis to one variable input. Iso-product (product indifference) curves could have been used to analyze a problem in which the quantities of two inputs were varied simultaneously.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

33 factor and the number of physical units utilized.

According to the

second method, an expense for a particular resource was determined by arraying the individual costs reported by each of the 15 farms and com­ puting the mean of the five median costs.

The latter method was followed

only when the basic data provided no information with which to estimate the number of physical units of a particular resource used by the repre­ sentative farm. Interest on Average Investment - Total investment in the representative farm, based on average inventory values, was $7,329*00, Table 7.

Interest on average investment was charged at $366.4-5 on the

assumption that a five per cent return, could have been realized from some financial venture other than the farm business. Total investment was estimated in the same manner as other values computed in this study, i.e., the mean of the total investment reported by each of the five median farms.

Inventory values for real

estate, livestock, equipment and feed and supplies were determined simi­ larly.

The latter investments were adjusted proportionally in accords

ance with the total investment calculated by arraying total investment per farm. The depreciation of real estate represented the amount by which average repairs necessary to maintain the value of real estate were greater than the repairs

31

made.

Estimated average repairs for

land and buildings were $14*20 and $38.18 respectively.

The dollar

value of repairs made are discussed below.

31 For land, repairs consisted primarily of fence upkeep.

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Table 7 - Inventory value of resources, by kind, Representative farm, May 1, 1941 - April 30, 1942. Resource

--

Real estate Land Buildings

Beginning value $4, 339.00

955.50

2,052.00

2,001.00

976.50

966.00

24.7.00 729.50

268.00 698.00

36.90

43.10

40.00

$7,281.4.0

$7,376.59

$7,329.00

Feed and supplies Total investment in farm business

$4,322.00 $2,119.00 2,203.00

1,950.00 289.00 666.50

Average value

$4,304-99 $2,116.70 2,188.29

$2,121.30 2,217.70

Livestock Equipment Power Other

Ending value

Table 8 - Inventory value of livestock, by kind, Representative farm, May 1, 1941 - April 30, 1942. Livestock Cows Heifers, one year or older Heifers, less than one year Bull Horses Total investment in livestock

Beginning Value per Total head value $ 96.00 57.00 23.00 73.00 135.00

$1,344-*00 171.00

92.00 73.00 270.00 ’ $1,950.00

Ending Value per head

Total value

$100.00 63.00 25.00 91.00 136.00

$1 ,4.00.00 189.00 100.00 91.00 272.00 $2,052.00

Average Value per Total head value $ 98.00 60.00

$1,372.00 180.00

24.00

96.00

82.00 135.50

82.00 271.00 \ $2,001.00

35 Data vere available with which to calculate the beginning and ending values per head of livestock, and these inventory data are sum­ marized in Table 8. Inventory values of power and other equipment were established in much the same manner as real estate values.

Separate estimates of

depreciation from use and obsolescence could not be determined from the information collected in the original study by Barr, however.

The net

appreciation of "other” equipment resulted from the purchase of new equipment.

The value assigned to each piece of equipment is indicated

in the accompanying table. Table 9 ~ Average inventory value of equipment, Representative farm, May 1, 1941 - April 30, 1942. Item Power equipment Tractor Truck Other Ensilage cutter Manure spreader Binder Seed drill Wagon with racks Mower and rake Dairy equipment Plows Harnesses Corn planter Cultivator Harrow Other Total, all equipment

Value $268.00 $179*00 89.00 698.00 128.00 75*00 68.00 67.00 65.00 64*00 55*00 35*00 34*00 30*00 20o00 18*00 39.00 $966.00

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36 The feed component of the feed supplies inventory consisted solely of home grown f e e d s .

Only two farms reported silage on hand

at either the beginning or end of the inventory period, consequently, silage was not included in either inventory account of feed and supplies prepared for the representative farm.

For other home grown feeds, it

was assumed that the physical quantities on hand May 1, 1941 were equal to the quantities at the end of the accounting period.

This assumption

simplified the accounting procedure slightly, but more importantly, the information available did not justify any alternative assumption. Quantities of feed and straw on hand at the beginning (and end) of the inventory period were: ton.

hay, 2.25 tons; oats, 15 bushels; straw, .75

By this method of accounting, consumption (of home grown roughage

and grain) equaled production during the accounting interval.

The

inventory increase of the feed and supplies account resulted therefore from

l) rises in unit price of home grown feeds, and/or

2) increases

in physical quantities and/or prices of supplies. Insurance - The total cost of insurance was estimated at $13*29, representing annual premiums of $10.78 for fire and $2.51 for livestock insurance.

In the 1941-42 study, the cost of fire insurance

for the whole farm, home and business, was tabulated for each farm.

In

the present analysis, the fire insurance cost allocated to the farm busi­ ness was based on the proportion of total investment in buildings accounted for by the investment in farm business buildings.

None of the 15 farms studied reported purchased concentrates on hand at the beginning or end of the inventory period.

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37 The cost of insuring livestock was determined by arraying this expense as reported by each of the 15 farms, and calculating the mean of the five middle observed values* Taxes - The real estate tax bill reported by each farm in 1941-4-2 represented taxes imposed on the whole farm.

The farm busi­

ness share of the taxes was calculated by the same procedure used to estimate the farm business share of the fire insurance expense* Real estate taxes were estimated at $41*40. Real Estate Repairs - The total expense of repairs to real estate amounted to $18.37, of which $9.60 represented repairs to land (fence upkeep) and $8.77 repairs to buildings.

Each of these estimates

was determined by arraying the cash repairs reported by the farms in the sample and determining the mean by the method described previously.

Cost of Operating Power Equipment - The total expense of operating the tractor and truck assigned to the representative farm business was $93*29-^.

The cost of separate items and services in­

cluded in the total expense were:

gasoline, $38.17j tires, $12.54;

license, $11.76} repairs, $10*80} insurance, $10,73; oil, $6.23; and mis­ cellaneous costs of $3*06.

Each of the individual expenses as well as

the total expense, was calculated by the array method.

Repairs on Other Equipment - Cash repairs on other than power equipment were estimated at $15*09*

This amount wascalculated from an

array of dollar repairs reported by the farms in the sample. 33 The data from which this estimate was derived reflected only the farm share of the cost of operation, i.e., the home share of the operating cost had been deducted.

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38 Purchases of Other Equipment - No attempt was made to set down the items of equipment purchased.

The equipment purchased by the 15

farms varied from a wagon valued at $15.00 to a binder costing $175*00. The representative farm was estimated to have acquired equipment valued at 165.15 during the 1941-42 period. General Expenses - Among the more important expenses in this group were the costs of electric power, telephone service, horse shoeing, veterinarian service, disinfectant, whitewash and milk pads.

The total

of these and other miscellaneous costs were estimated at $78.57*

General

expenses, in total and particular, were established by arraying indivi­ dual values and calculating the mean of the median third observation^. Seed - The cash cost for seed amounted to $29*4.0. mate was obtained in the following manners

This esti­

l) the seed cost per acre

for each kind of crop was calculated for each farm in the sample,

2) costs

per acre were arrayed and the typical cost determined for each crop, 3) the typical cost per acre was multiplied by the number of acres of each crop grown on the representative farm.

The estimated cost of grass

seed was computed on the basis of six acres sown annually.

No cash cost

was calculated for oat seed inasmuch as most of the farm enterprises studied used home grown seed.

Fertilizer and Lime - The quantity of commercial fertilizer and lime applied to field crops and pasture was valued at $49*83.

In the

probably the least reliable of any costs calculated in this analysis. The total of the general expenses, computed by the compounding of many separate expenses subject to rather wide variation between farms, was considered more representative than the particular costs comprising the total. Estimated costs of operating power equip­ ment were subject to the same criticism.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

39 original study, the combined value of fertilizer and lime purchased per farm was tabulated, hence no division of total cost could be made for the representative farm.

The estimated cost was derived from an array^of total

cost reported per farm for fertilizer and lime*

Salt and Minerals - The 333 pounds of salt and minerals consumed by all livestock were charged at the rate of $*01 per pound, or a total cost of $3*33*

The representative price was estimated by the array method* Labor - Man labor represented the highest single cost in the

farm organization.

The total cost, imputed and direct, of the labor force

employed on the farm business amounted to $1,622.50.

The operator's labor

and management were valued at $84.0.00, unpaid family labor expense was estimated at $360.00, and the cost of hired help at $157.30.

In addition,

farm privileges valued at $265.20 were available to the operator's family. The yearly value of the operator's time was calculated from an array of each farmer's estimate of the value of his labor and management, as reported by the owner-operators of the farms studied.

It was estimated

above that the operator devoted full time, 12 man equivalent months, to the farm business; thus the full amount ($840.00) was charged as a business expense. The cost of unpaid family help was determined by multiplying the number of man equivalent months (6.0) worked by the monthly rate assigned to the unpaid family component of the labor force.

The monthly

rate was estimated at $60*00, based on an array of imputed values assigned to unpaid family help on each of the 15 farms. The cost of hired labor was also calculated from the number of man equivalent months (2.9) worked and a monthly wage rate.

In the 1941-42

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .

40 study, wages paid to hired help were reported both by day and/or ty month, with or without board.

These data were used in the present analysis

to construct a composite wage rate per month for each farm.

The composite

rate was calculated from the dollar wage paid and the cost of providing board for hired help. wage.

That is, the composite rate was a dollar equivalent

The representative monthly wage rate was derived from an array of

the composite rate calculated for each farm.

According to this method,

the cost of hired labor was $54.24 per man equivalent month. The privileges to the operator’s family included the milk used in the home which was valued at $85.20, and the imputed rental value of the dwelling, estimated at $180.00.

The value of milk used in the home

was determined by multiplying the quantity used by the unit price assigned to milk used.

By a previous estimate, 3,054 pounds or 1,420 quarts, were

consumed in the farm home.

This milk was valued at $.06 per quart.

The

array method was used to estimate this price. The rental value of the dwelling was calculated by arraying the imputed rental values reported by the 15 farmers.

Inasmuch as this study

has consistently separated the farm home from the farm business, it would appear that the shelter privilege should not have been included in com­ puting the labor cost of the farm business.

The decision to include the

rental value of the dwelling as a labor cost was influenced considerably by the manner in which farmers were asked to value their time in collecting data for the 1941-42 study.

Each owner—operator was asked what it would

cost him to hire some one to come on the farm and have the same responsi­ bilities of labor and management and be supplied with the same privileges as the present operator.

It seemed realistic to assume that the operator

in appraising the value of his time did not base his estimate upon the

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .

f

A1 separation of home and business that has been adopted in the jr-esent analysis.

On this basis, the rental value of the dwelling should be con­

sidered a cost in computing the value of the operator1s labor and management.

Concentrates Purchased for All Livestock Except Cows - The cost of purchased grain fed to the young stock and the bull was estimated at $55.17.

This expense was the r esult of number of pounds fed to the stock

multiplied by a representative price per pound.

These animals were esti­

mated to have consumed 2,578 pounds of concentrates, all purchased, (see Table 6).

Concentrates were priced at $2.14- per hundredweight or $.0214-

per pound. The price per hundredweight of grain was estimated from the prices 35 paid by farmers for a 20 per cent dairy mix as reported in the basic study.

This price represented the net cost after the refund for returned

feed bags had been deducted.

The typical gross price was $2.20 and the

typical refund was $.10 per bag.

Not all bags were returned, however.

average refund per bag purchased was estimated at $.06.

The

This estimate was

calculated by dividing the total amount received for returned sacks by the number of 100 pound sacks of feed purchased by the representative farm.

Concentrates Purchased for Cows - The cost of grain consumed by cows was estimated at $557.00.

This sum was obtained by multiplying the

35 A mixed dairy feed containing 20 per cent protein was fed more commonly on the farms studied than either a 16 or 24- per cent urif, On several farms, other grains purchased included a fitting ration and/or f»al-P meal. Either of these accounted for a relatively minor part of the total concentrates purchased. Furthermore, in the few instances in which a fitting and/or a calf ration was fed, the price per hundred­ weight of these feeds varied only slightly from the price of 20 per cent dairy feed. Hence it was assumed in this analysis that a 20 per cent feed was the only concentrate purchased.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .

U2 number of pounds purchased (consumed) by the price per pound. The former value was estimated at 26,023 pounds (see Table 6).

The price assigned

to concentrates fed to cows was the same, $.0214- per pound, as that used to calculate the cost of concentrates fed to other livestock.

Credits to Costs Several direct and imputed returns, other than the receipts for milk marketed, accrued to the representative farm during the accounting period, May 1, 1941 through April 30, 1942*

Inasmuch as

this analysis was directed primarily at deriving the cost functions of a single product (marketed milk) enterprise, it was necessary to treat incidental returns as credits to costs of producing marketed milk rather than as receipts for separate products. Livestock Sales - The numbers and kinds of livestock sold were shown in Table 5.

Total returns from the sals of these animals amounted

to $252.00, of which $139.00 was obtained from the sale of three cows, $18.00 for the heifer calf sold, and $45*00 for nine bob calves sold. The unit price for each kind of livestock sold was estimated from an array of the prices received per head by each of the farms in the sample.

Value of Manure - Manure valued at $160.00 was recovered from the animals kept on the representative farm.

The total value was the

Nproduct of the number of tons of manure recovered and the value per ton. Each fluimal unit^ was assumed to produce 12 tons of manure of which

^^Each head of livestock, except young stock, was considered an animal unit. Heifers and heifer calves were counted at .5 animal unit. On the basis of average inventory numbers, the livestock represented 20.0 animal units.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

43 37

eight tons were recovered

for use on cropland..

Manure was valued at

$1*00 per ton.

Increase in Inventory - This credit was obtained from'Table 7. The sum of the ending inventory values of all resources was $95.19 higher than the total beginning inventory value.

Value of Milk Used in Home - This sum was calculated previously in estimating the value of the operator's labor and management.

On

balance, the value of the milh used in the home does not affect net costs of production.

The value of the milk was considered a cost in computing

the total labor expense but was also entered as a credit since'it represented a product other than the product of the farm0

Miscellaneous Receipts - Government payments accounted for the largest share of the receipts in this category with total returns from all sources estimated at $4-9*42.

This amount was calculated by arraying

the total miscellaneous receipts reported by farms in the sample and computing the mean of the five middle observations.

Cost of Producing Milk Marketed A summary of the costs of producing the milk marketed by the representative farm during the period May 1, 1941 through April 30, 1942 is presented in Table 10. of

ttHT-V

The total cost of producing the 82,537 pounds

sold was $2,367.03; fixed costs totaled $1,810.03 and variable

cost amounted to $557.00, according to the procedures followed in this study.

Fixed costs were calculated as the net of total fixed costs

minus creditsj thus, $2,351.64- minus $641.31.

■^Unpublished data. Department of Agricultural Economics and Rural Sociology. The Pennsylvania State College. 1950.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

Table 10 - Costs of producing milk marketed, Representative farm,

190 -42.__ ______ Item

Cost or credit

~

(dollars)

Costs Fixed costs: Interest on average investment Insurance Buildings Livestock Taxes Real estate repairs Land Buildings Power equipment, operating costs Other equipment, repairs Other equipment, purchases General expenses Seed Fertilizer and lime Salt and minerals Labor Concentrates purchased for all livestock except cows Total fixed costs

'366,45 13.29 10,78 2,51 0.4-0 18,37

93.29 15.09 65.15 78.57 29,40 49.83 3.33 1,622,50 55.17 2,451.84

Variable cost: Concentrates purchased for cows

557.00

Total gross costs

3,008.84

Credits Livestock sales Value of manure Increase in inventory Value of milk used in home Miscellaneous receipts Total credits Total net costs

252.00 160.00 95.19

85.20 49.42

641.81 2,367.03

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

45 Product Price Received by the Representative Farm The price calculated for this analysis was the price received at the farm.

An annual average price of $2.49 psr hundredweight of four

per cent milV was established for the period May 1941 through April 1942. The price was computed from monthly prices weighted by the quantity of Tn-nv sold each month.

The procedure followed is described below*

The value of Tn-nv and the physical quantities of milk and 38 butterfat marketed monthly by each farm in the sample was tabulated in the original study.

The first step was to compute the total value and

the total quantities of in-nV and butterfat marketed monthly by all farms in the sample.

Second, a monthly price per hundredweight was calculated

by dividing the aggregate value by the aggregate hundredweight.

Third,

the percentage of butterfat in the milk marketed each month was deter­ mined by dividing the total pounds of milk marketed into the total pounds of butterfat.

The monthly price computed above was associated, therefore,

with a hundredweight of milk containing the percentage of butterfat cal­ culated in the third step.

The next adjustment in determining a monthly

price was to correct for butterfat content.

Each monthly price was cor­

rected to a hundredweight price for four per cent milk by using a $.04 39 butterfat differential for each .1 per cent variation from 3.5 per cent. Finally, the unit price at the farm was established by deducting a repre­ sentative hauling charge.

The hauling charge was estimated by arraying the

charge paid b7 each of the 15 farms and calculating the mean of the middle five values observed.

The hauling charge to be assigned to the representative

33 In the 1941-42 study, these data were obtained directly from the dealers’ handling the m-Hlr marketed by each farm. 39 All dealers to whom milk was sold by the 15 farms paid a $.04 differ* ential during the period studied.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

46 farm was $.12 per hundredweight according to this method.

The data

suggested further that no variation in rate occurred from May 1941 to April 1942 inclusive. The following methods were used to estimate the quantity of mi TV marketed monthly by the representative farm.

The total quantities

of miTIr and butterfat marketed each month by the 15 farms had been determined previously.

First, the monthly quantities were corrected to

pounds of four per cent milk.

Next, the total pounds of four per cent

mi Hr marketed during the year by all farms was determined.

Third, the

amount of milk marketed in each month was calculated as a per cent of the total quantity marketed annually.

Finally, the monthly percentages were

used to distribute, by months, the 825.37 hundredweight of four per cent milk marketed during the year by the representative farm. The annual price was calculated by weighting the monthly prices by the quantity sold each month.

As stated above, the farm price was

estimated at $2.49 per hundredweight of four per cent milk.

Total Product Function of the Average Cow on the Representative Farm The prime analytical tool utilized in this study was a parti­ cular expression of the law of variable proportions.

The specific input-

output relationship adopted was proposed from an investigation^ carried out jointly by the United States Department of Agriculture and 10 Agri­ cultural Experiment Stations,

This study focused on establishing physi­

cal relationships between feed inputs and milk output.

One of the input-

output relationships established from this research was selected as the relevant production function for the present analysis.

^Jensen, E. et.al. Input-Output Relationships in Milk Production. Technical Bulletin 815. U.S. Department of Agriculture. Washington, D.C. 1942.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

47 The Experimental Production Functions In one phase of the physical experiments, information was collected on the output responses of cows at various levels of feeding. Cow records in that particular analysis were sorted into four groups on the basis of inherent producing ability.

For identification purposes,

the groups were labeled:

poor cows,

good cows,

1) low stations —

3) nigh stations —

2) low stations —

poor cows, and 4) high stations —

good cows.

This two-way sort was made in an attempt to eliminate variations in output associated with environmental differences between stations cooperating in the study.

"Poor" or "good" were identification terms referring,to the

productivity of a cow in relation to the general productivity of all cows. Inasmuch as the general level was fairly high, there was scarcely a really low producer among the cows in the experiments. Within each "basic producing ability" group, output responses of cows at six levels of feeding were observed.

Different levels of

feeding were accomplished mainly by varying the amount of concentrate fed. To the six observations obtained for each group, a curve was fitted mathematically, indicating the relationship between feed inputs and milk output.

Thus, four production functions were constructed —

one for each

group of cows having approximately equal inherent producing abilities.

The "Low Stations — to which the "low stations —

Poor Cows" Function - The observations poor cows" function was fitted are shown

graphically in Figure 14 of Bulletin 815^, and the statistical data for the six observations are included in Table 11 of the Bulletin^. Output responses were corrected to four per cent milk, and feed inputs were

a ibid., page 42. ^Ibid., page 43. R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

4 .8

presented in terms of total digestible nutrients fed above the maintenancerequirement

4.3 of a cow.

All cow

recordswere standardized to a 302

day lactation period and a 60 day dry period.

Neither the milk produced

nor the feed consumed during the three days immediately following calving were included in the data. The generic formula^ describing the functional relationship between feed inputs and milk output for any one cow in the "low stations poor cows" group was:

Y = A(l-rx), in which:

I = output of four per cent milk A = a constant representing the asymptote of the function, even though it may be impossible to feed a cow enough to reach this maximum output r = a constant representing the ratio of increments of output < & > associated with equal absolute increments of input x = total digestible nutrients fed above the maintenance requirement. The values of A and r were not published nor could they be obtained from the agricultural bureaus that conducted the investigations.

By a series

of approximations, however, the values of A and r were estimated at 86.5 and .94-5 respectively, when Y and x were expressed in hundredweights. The values of A and r were stated in three digits because limitations in the estimating procedure made additional calculations unreliable / O

The maintenance requirement was based on the Haecker standard. Haecker' revised standard recommended a daily maintenance ration of 7.925 pounds of total digestible nutrients for a 1,000 pound cow. The revised standard rather than Haecker's original recommendation of 7.000 pounds of total digestible nutrients was used in the feeding trials, according to information supplied the author by the Bureau of Dairy Industry of the U.S. Department of Agriculture. ^Also the formula for the function fitted to observations in each of the three other "basic producing ability" groups. R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

49 statistically.

Hence the particular equation representing the input-

output relationship per cow in the ”low stations — was:

poor cows” group

I = 86.5 (1-.945X ) when: I = hundredweight of four per cent milk produced x = hundredweight of total digestible nutrients fed above the maintenance requirement. In the feeding trials, Y varied from 59*38 to 78.93 hundredweight;

x was varied from 19*08 to 35*61 hundredweight

. As indicated above,

x was varied primarily by altering the amount of grain fed.

The high­

est level of output was associated with the highest feeding level, but the lowest output resulted from the next to the lowest feeding level. It may have been significant that the lowest output occurred at that feed­ ing level in which the total ration contained less grain than any of the five other levels of feeding, but the authors offer no explanation for this discrepancy.

One reviewer^ of the study suggested that the first

observation (the lowest level of feeding) should have been eliminated from the results because the observation was out of place for reasons other than nutrients fed. By expressing feed inputs as pounds of total digestible nutrients fed above maintenance, the authors tacitly assumed that, within the range of the feeding trials, perfect or nearly perfect substitutability existed between kinds of feed inputs.

This assumption was necessary in adapting

the law of variable proportions to the analysis, for this law presumes heaogeneity between units of the variable input.

^Based on a calculated maintenance ration of 2,834 pounds of total digestible nutrients during 362 days0 ^Headley, F. B. Mathematical Relationship Between Production of Dairy Cows and Nutrients Consumed* Nevada Agricultural Experiment Station* 1943* Mimeo*

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

JflH

50 The Production Function for Cows on the Representative Farm The first step in adapting the experimental function to the present analysis was to compare the input-output relationship of the average cow on the representative farm with the "low stations — - poor cows" function developed from the feeding experiment.

To accomplish

this comparison it was necessary to restate the physical input and output data of the 1941-42 observation, with reference to the condi­ tions under which the feeding experiment was conducted.

The methods

by which the provisions of the experiment were imposed on the empiri­ cal observation

follow.

The kinds and quantities of feed, other than pasture, consumed by each cow on the representative farm were presented in Table 6. Pounds of total digestible nutrients obtained, per cow, from pasture were given in Table 4-, and the yearly ration per cow, converted to pounds of total digestible nutrients is summarised in Table 11. Pounds of total digestible nutrients fed during the first three days after calving were deducted from the annual ration in order to make the empirical observation comparable to the procedure followed in the experiment.

It was estimated that a cow consumed 4# pounds^

of total digestible nutrients during this interval.

Thus the total

ration fed per cow during 362 days was reduced to 5,786 pounds.

Calculated at rate of 16 pounds of total digestible nutrients daily which was the average daily rate for the year, i.e.. 5,834 pounds divided by 365. Furthermore, it was presumed that the cow obtained all total digestible nutrients consumed during these three days from sources other than concentrates.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

51 Table 11 - Total digestible nutrients fed per cow, by source, Representative farm, 1941-4-2. Source

Quantity fed

Total digestible nutrient content

(pounds)

(per cent)

Corn silage Mixed hay Concentrates Pasture

6,800 4,000 1,957 —

Total digestible nutrients (pounds)

17.0 42.5 75.0 —

1,157 1,700 1,468 1,509

Total digestible nutrients consumed

5,834

The maintenance requirement for each cow on the representative farm was calculated by the same procedure used in the experiment.

At

the rate of 8.718 pounds of total digestible nutrients per day for an 1,100 pound co\/'8, the maintenance requirement for 362 days was esti­ mated to be 3,156 pounds.

Thus the cow consumed 2,630 pounds of total

digestible nutrients above her maintenance requirement. Productivity per cow on the representative farm had been esti­ mated above at 6,560 pounds of four per cent milk.

Accordingly, the empiri

cal values of Y and x were 65.60 and 26.30 hundredweight respectively. These coordinates defined a point which was closer to the experimental function than five of the six observations in the experiment.

The

closeness of the fit suggested that the experimental function could be used to estimate the input-output relationships of cows kept on the representative farm. One final adjustment was made.

The experimental function with

an A value of 86.5 and an r value of .94-5 did not pass through the point defined by the coordinates developed from the empirical study. __

See footnotes 15 and 4-3.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig ht o w n er. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

52 Consequently, the second step in adapting the experimentally derived function to the present analysis was to adjust the curve so that the coordinates of the empirical investigation defined a point on the experi­ mental function —

that is, a curve which passed through a point described

by a I value of 65.60 hundredweight of four per cent milk and an x value of 26.30 hundredweight of total digestible nutrients. This adjustment

was accomplished by lowering

constant A from 86.5 to 84.7.

the

value ofthe

The value of r (.94-5) was not changed.

Changing the value of A was the only method by which the curve could be lowered, within the limits of the estimating procedure followed in the analysis. effect on

A two per cent reduction in A (from 86.5 to output as a .03 per cent change in £.

in r would not have altered the third digit of £•

But a

84-.7) had .03

the same

per centchange

Hence, within three

digits for each constant, additional precision in the formula had to be' acquired by lowering the value of A.

The experimentally derived formula

[I = 86.5 (l-.94-5Z)] for cows in the "low stations — was modified, therefore, to:

poor cows" group

Y = S4-.7 (l-.94-5X)> and the latter relation­

ship was considered the total product function for each cow on the representative farrn^.

A graphic illustration of this function is pre­

sented in Figure 1.

^"Several consequences of lowering the curve should be noted. Originally, it was assumed that the product function for "poor" cows at low stations could be used as the function for cows on the representative farm. The justification for this assumption has already been stated. This assump­ tion inferred that the same maximum output was approached by "poor" cows and representative cows. By lowering A, however, this inference was no longer valid in a strict mathematical sense, for the function for representative cows has an asymptotic value lower than the experi­ mental function for "poor" cows. In short, for any given value of 2, the slope of the function used in this analysis is slightly lower than the slope of the function developed for "poor" cows at low stations. The difference in slope between the two functions was of the order of smalls, and fop all practical purposes, the best estimates of output responses of cows on the representative farm to increased feed inputs could be derived from the equation: Y = 84.7 (1.-94-5*)» R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

FIG. I - T O T A L

PRODUCT

F U N C T I O N , PER

r e p r e s e n t a t iv e :

D AI RY

COW,

farm

O U TP U T o r M IL K (1000 POUNDS 4/4 FCM)

L E V E L OF O U T P U T I 941 - 4 2 \

RANGE

Or P H Y S IC A L

a

2

E X P E R IM E N T

4

A BOVE M A I N T E N A N C E ( 1 0 0 0 POUNDS TDN )

rEED

&

5

6

54 To derive this function, the pounds of total digestible nutrients fed above maintenance were varied within the same range as established in the feeding experiments; i.e.. the value of x was varied from 19*00 to 36.00 hundredweight.

This function further paralleled the experimental

methodology in that all variations in feed inputs were accomplished by altering the quantity of grain fed.

One other restriction was recognized

in determining the limits over which feed inputs were varied.

In the

feeding trials, grain accounted for at least 21 per cent of the total digestible nutrients in the total ration (maintenance and production) fed per cow.

At the lowest level of feeding (19*00 hundredweight of total

digestible nutrients) in the present analysis, grain accounted for 15 per cent of the digestible nutrients in the total ration.

At x values of

20.00, 21.00 and 22.00 hundredweight, grain made up 16, IS and 19 per cent respectively, of the pounds of total digestible nutrients in the total ration.

For these four observations only was the concentrate

content of the ration less than the minimum (21 per cent) fed in the feeding experiments.

Although little evidence exists to the contrary,

the assumption of perfect substitutability between kinds of feed may not apply to levels of feeding at which grain constitutes less than 21 per cent of the total ration.

This deviation in sources of feed between the

empirically and experimentally derived functions should be recognized, nevertheless, for modification of the substitutability assumption may alter slightly the value of Y obtained for each value of x between 19*00 and 22.00 hundredweight.

In deriving the cost functions, unit costs were

computed only for values of x between 20.00 and 36.00 hundredweight inclusive.

Thus, the relevant portion of the total product function lies A I

between x values of 20.00 and 36.00 hundredweight, not 19.00 and 36.00 hundredweight.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

V

55 Derivation of Cost Functions Mich of the physical, financial and. theoretical data presented previously was utilized in deriving the average and marginal cost functions*

For convenience, therefore, the information related directly

to the derivation of the schedules has been brought together below.

With

respect to the physical characteristics of the representative farm, the following data were presented: a) product of the farm:

marketed milk

b) average number of cows:

13*3

c) hundredweight of grain fed per cow, all of which was purchased:

19.57

d) hundredweight of grain consumed by all cows: e) total digestible nutrient content of grain:

260.28 075

f) hundredweight of total digestible nutrients consumed above maintenance requirement, per cow:

26.30

g) hundredweight of four per cent milk produced per cow:

65.60

h) hundredweight of four per cent milk produced by all cows:

872.48 i) hundredweight of four per cent milk utilized in farm home or fed to calves:

47.11

j) hundredweight of four per cent milk marketed:

825.37

The relevant financial information included: a) total cost of producing 825*37 hundredweight of milk marketed:

$2,367.03

b) total fixed costs: c) total variable cost:

$1,810.03 $557.00

d) price paid per hundredweight of variable input:

$2.14

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

e) pries received per hundredweight of four per cent milk marketed:

$2*4-9

The chief theoretical concept was a particular statement of the law of variable proportions, expressed for this analysis in the equation: Y a 84-.7 (l-*94-5x), where: Y a hundredweight of four per cent milk produced per cow, and x = hundredweight of total digestible nutrients each cow was fed above the maintenance requirement.

Average Cost Functions The first observation for which average costs were computed was the level (825.37 hundredweight) at which the representative farm operated in 1941-4-2* For this level of operation, average total costs, average fixed costs and average variable costs were determined by dividing the relevant cost datum by the output

50

marketed*

The procedure by which

the various cost elements at other levels of output were calculated follows The value of x in the mathematical formulation of the pro­ duction function was varied by intervals of 1.00 hundredweight of total digestible nutrients over a range from 20.00 to 36*00 hundredweight.

The

value of Y, representing the quantity of milk produced per cow, "was cal­ culated for each level of feeding.

Production per cow multiplied by the

average number of cows represented the total production of the farm at a given feeding level.

Output of the representative farm was obtained by

subtracting a constant (4-7.11 hundredweight) from the total production associated with a given level of feeding.

-^Henceforth, the term output will refer solely to quantity marketed as distinct from quantity produced*

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

57 Average Fixed Cost Function - The fixed cost per hundredweight at any given level of output was determined by dividing total fixed costs, $1,810.03, by the relevant output. Average Variable Cost Function - The average variable cost associated with any given level of output was calculated by dividing output into total variable cost.

Total variable cost was obtained by

multiplying the hundredweight of grain fed to all cows by the price paid per hundredweight, $2.14-, for the variable input (grain).

The quantity

of grain fed to all cows was calculated as follows: a) for any given value of x (hundredweight of total digestible nutrients above maintenance), the deviation of that value of x from 26.30 was computed b) this deviation, expressed in terms of hundredweight of total digestible nutrients, was converted to hundredweight of grain by dividing by ,75•

The quotient therefore

represented the deviation in hundredweight of grain from 19*57 (the hundredweight of grain fed per cow at an x value of 26.30) c) the hundredweight of grain fed per cow at any value of x , was computed by adjusting 19*57 in accordance with 1±te deviation calculated'in b) d) the hundredweight of grain fed to all cows was calculated by multiplying the hundredweight of grain fed per cow by 13*3

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r re p ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

58 Average Total Cost Function - The total costs associated vith a given level of output represented the sum of the total fixed costs and the total variable cost at that level.

The average total cost*^- vas

calculated by dividing this sum by output.

Marginal Cost Function The marginal cost per hundredweight of milk at a given level of output was calculated by dividing the increment in total cost by the corresponding increment in output.

Although the marginal output

referred to the increase in output between two levels of output, the marginal cost was plotted in the following diagrams at the higher of the two levels of output.

This practice vas followed in order that each

optimum output position, represented by the intersection of the marginal cost schedule with the marginal revenue (price) schedule, could be demonstrated*^ graphically.

One disadvantage resulting from this pro­

cedure was evident, hoveverj the marginal cost function of each cost structure illustrated did not intersect the average total cost function at the minimum cost position.

The procedure was retained, nevertheless,

because the demonstration of optimum output positions was more closely allied with the central objective of this study. ^"Alternatively, the sum of average fixed cost and average variable cost at any level of output. ^%his problem arose as a result of the discrete series used. Both mar­ ginal values (cost and output) were "average” marginal concepts. That is, the addition to total cost between two levels of output represented the cost increment associated vith an increase of several units of output. If a marginal value had been plotted at the mean of the two relevant outputs, the graphically demonstrated optimum output position would have differed (been lower) from the mathematically determined solution noted in the text.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

59 COST STRUCTURE OF THE REPRESENTATIVE FARM IN 19-41-4-2 The cost and revenue

functions^

of the representative dairy-

farm for the 1941-42 period are presented in Figure 2.

Unit costewere

calculated for outputs ranging from 716.44- to 932*63 hundredweight. The minimum output was associated with a feeding level of 20.00 hundred­ weight of total digestible nutrients above maintenance, whereas the higher output was obtained by feeding each cow 36.00 hundredweight of total digestible nutrients above maintenancec

Cost Elements

Average Fixed Cost Schedule Fixed costs per hundredweight of four per cent milk marketed totaled $2,193 at the level of output attained in 1941-4-2.

Over the

full range of the schedule, average fixed costs declined $.586 —

from

$2,526 at an output of 716.44- hundredweight to $1,940 at an output of 932.83 units.

At the optimum output, fixed costs per hundredweight

were $2,210.

Average Variable Cost Schedule The average variable cost at the level of operation was $.675* Variable cost per unit of output increased $.548 when output was varied from 716.44 to 932.83 hundredweight.

At the optimum output of 818.88

hundredweight, the average variable cost was $.660.

Average Total Cost Schedule At 825.37 hundredweight, the output of the representative farm in 1941-42, the average total cost was $2,868.

The most significant

^The relationships were based on annual data.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .

60

FIG.2 -T H E

SHORT R U N GOST STR U C TU R E, REPRESENTATIVE FARM, 1 9 4 1 - 4 2

PRICE OR COST PER CWTi OF A / FCM < DOLLARS;

L E V E L OF OPERATION 1941-42

4.0 0 MC

3 .0 0

ATC

PRICE £ .4 9

AFC

2.00

1.00 AVC

700

750

M IL K

800 818.88 M A R K E TE D

85 0 82537 CCWT.

900 OF

4 /

950

FCM)

___________________

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n er. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .

*dla

61 characteristic of this function was its proximate linearity.

The highest

average total cost ($2,970) occurred at the lowest output for which costs were computed, namely, 716.44- hundredweightj and the minimum cost out­ put was 848.78 hundredweight, where average total cost was $2,865* Cursorily the explanation for the approximately constant cost configuration of this function can be obtained from a re-examination of the average fixed and variable cost schedules.

As indicated above, average fixed costs

declined $.586 over the full course of the function.

This decline was

offset almost completely by an increase of $.548 in average variable costs over the same range. A more thorough explanation for the near linearity of "the average total cost curve would require a reappraisal of the justification and methodology by which factor costs were classified and calculated.

In­

sofar as reclassification and recalculation of costs would not change sig­ nificantly the slopes of the average fixed and average variable cost schedules'^, the configuration of the average total cost function would be subjected to slight variation only. The position of the level of operation along the average total cost schedule did suggest nevertheless that, given the cost relationship as determined herein, the representative specialized dairy farm of northeastern Pennsylvania was organized in 1941-42 to produce market milk at nearly minimum cost0 Such an observation comes as no surprise to farm management specialists who have long claimed that farm operators in a given type of farming area have, mainly by trial and error, achieved considerable technical efficiency in the organization of their operations,,

54This would appear to be the more plausible case in view of the number and relative importance of those costs classified as fixed in this study but which are realistically variable in the short run.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

62 Marginal Cost Schedule Marginal cost per unit varied from $1,791 at 716.44 hundred­ weight to $4*449 at an output of 932.63 hundredweight. achieved in 1941-42, the marginal cost was $2,536.

At the output

The slope of the

marginal function was determined primarily by the position and shape of the production function.

The position of the marginal cost curve

was determined by the price paid per unit of variable factor.

Optimum Output Position Given an annual average price of $2.49 per hundredweight, the representative farm could have minimized its losses by producing 818.88 units of output.

At the optimum, a loss of $.380 per unit of output

would have been incurred; at the level of operation, the loss amounted to $.378 per hundredweight of milk marketed'*'*.

For all practical purposes,

therefore, the representative farm was in short run equilibrium in the 1941-42 period. The disclosure that average total cost exceeded price at the level at which the representative farm was operated in 1941-42 was not unexpected.

In the 1941-42 study, Barr had estimated that the costs of

producing and marketing a hundredweight of milk were higher than the

55 Both the optimum and the operational levels of output were within the declining phase of the average total cost function, consequently the operational output (the larger output) was associated with a lower average total cost. The total loss (loss per unit multiplied by output) however, was greater at the attained level of output because of the larger volume of output.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

63 returns per hundredweight

56

. The result whereby average total costs

were higher than price in this study was attributed primarily to the imputed value of the family labor.

This did not imply necessarily

that the operators (of farms in the sample) had overvalued their time. The result suggested only that the return for labor expended by the family was less than the cost estimated by the opportunity principle.

^ The average loss per hundredweight for all farms enumerated in Wlayne county was $.15 while in Lackawanna county, the average loss amounted to $.51 per hundredweight. These data were not directly comparable with the estimated loss of $.378 per hundredweight calculated for the representative farm, however. In the original study, quantities of milk were not corrected to four per cent milk, and in addition, the costs included the marketing expense per hundredweight. The marketing expense was not a relatively important cause of the variation in losses between the 1941-42 study, and the present study because the higher price received would offset somewhat the added cost.

R e p ro d u c e d w ith p erm is sio n o f th e co p yrig h t o w n e r. F u rth e r rep ro d u ctio n p ro hib ited w ith o u t p erm is sio n .

64 AN OPERATIONAL SYSTEM FOR THE SHORT RUN The preceding analysis was directed at the construction and interpretation of cost functions for the representative farm for the period May 1, 1941 through April 30, 194-2•

The primary objective of

this study, however, was to appraise the theory of the firm as an instrument with which to explain output behavior of a particular type of agricultural firm in the short run.

Annual data for the 1941-4-2 period

represented only one observation of the response of the specialized dairy farm to product price.

To determine output response of the farm

to a change in price, required two or more observations.

For this

reason, the two 12 month periods immediately following the 1941-42 period were selected for study.

The dates of these intervals were

May 1, 1942 - April 30, 1943 and May 1, 1943 - April 30, 1944.

Cost,

output and price data comparable to that prepared for the 1941-42 period were calculated for each of the 12 month periods.

Thus three observa­

tions, 1941-42, 1942-43 and 1943-44 were available. Methods:

Cost Structures for 1942-43 and 1943-44

The 1941-42 observation provided the physical setting for all three years.

That is, the physical organization of the representative

farm was assumed to be constant through time.

Crop yields, numbers and

kinds of livestock kept, labor force and all other physical attributes of the farm business in 1941-42 were carried unchanged to the 1942-43 and 1943-44 analyses.

The input-output relationship established for each

cow in the analysis for 1941-42 was assumed to be the relevant production function for 1942-43 and 1943-44 also.

According to these assumptions,

shifts in the cost function-^ for the two latter years resulted solely e are presented in the upper chart of Figure 5. The general pattern of seasonal output associated with a spring-summer 71 dairy was clearly outlined in the output series. year period, however, no distinct trend was evident.

Over the entire three In brief, the out­

put series suggested that output was relatively stable.

Data presented

on an annual basis confirmed this proposition; for as was indicated, out­ put in the three observations varied^ between 807.71 hundredweight in 1943-44 and 851.45 units in 1942-43. The price series, on the other hand, exhibited a marked upward trend in the 1941-44 period.

Milk prices were counter cyclical to the

output series through the fall of 1942; but thereafter little semblance

"^"Defined here as a dairy business in which: l) output in the low quarter (on a ;calendar year basis) was less than 70 per cent of output in the high quarter, and 2) the output peak occurred in the second or third quarter. These criteria were adapted from, Economic Analysis of Feeding Practices on 720 Pennsylvania Dairy Farms, 1945-46, by W. F. Gregory; unpublished manuscript, The Pennsylvania State College, 1948. ^^The magnitude of the variation (43.74 hundredweight) represented slightly more than five per cent of the average annual output (828.18 units) for the 1941-44 period.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

FIG. 5 -P R IC E -O U T P U T SERIES OF REPRESENTATIVE FARM A N D IN D E X OF M IL K -F E E D P R IC E RATIO . BY MONTHS. MAY 1941 - APRIL 1944 M IL K MARKETED (CWT. OF 4 7. ---FCM)

PRICE PER CWT — I OF 4 X FCM ( DOLLARS )

IOO

OUTPUT

/ PRICE

75

300

• 5C

200

40

IN D E X

MAY 1941 = 1 00

105

100

95

1942

1943

1944

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

91

of the usual price pattern through the seasons was displayed.

As a

result of the upward trend in the monthly series, the annual average price rose from $2.49 in 1941-42 to $2.88 in 1942-43 and to $3.49 in 1943-44. It would appear from the output and price series that output was comparatively unresponsive to price changes.

And the level and

pattern of the milk-feed price ratio7^ during the 1941-44 period sug­ gests a plausible explanation for this (price) inelasticity.

The pattern

traced by the index of this ratio, shown graphically in the lower chart of Figure 5, outlined neither an upward nor a downward trend during the period Since the price of milk was rising during the period, the feed price must have been rising at approximately the same rate; thus reducing the index of the ratio to a zero or near zero trend. Under these conditions, there was little incentive to expand (or contract) output. It is contended, therefore, that the representative farm was not unresponsive to changes in the price of milk.

The relatively constant

levels of output attained in 1941-42, 1942-43 and 1943-44 were economically rational responses to rising costs and prices over which the operator had no control.

This proposition gains greater respect when actual (estimated)

levels of output are compared with optimum output positions.

Output Predictions, 1941-44 Output solutions predicted in each set of cost structures (1941-42, 1942-43 and 1943-44) are illustrated74- in Figure 6.

This

7^The ratio represented the number of pounds of concentrates equal in value to a hundredweight of milk. The monthly prices of feed were adapted from Bulletin 500 of The Pennsylvania Agricultural Experiment Station; the price series was developed from reports issued by the Pennsylvania Federal-State Crop Reporting Service. May 1941 was selected as the base period in constructing the index. 74The relevant portions of Figures 2, 3 and 4 have been magnified in order to demonstrate optimum output positions with greater precision. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

FIG 6 —OPTIMUM OUTPUT POSITIONS, REPRESENTATIVE FARM, 1941-42, 1 9 4 2 -4 3 , 1 9 4 3 -4 4

P R IC E OR COST PER CWT OF 4 / . FCM | f DOLLARS t I 4 .0 0

MC l9 4 2 -4 3 i

3 .5 0

ATC 1943-

1943-44

PRICE

ATC 1 9 4 2 -4 3 3.00 ATC 1 9 4 1 -4 2

1 9 4 2 -4 3 PRICE ,

2 .5 0

__ I 9 4 1 -4 2 P R IC E

2.00

1.50

700

7 50 M IL K

800 M A R K E TE D

900

850 CCW T

A /.

950

F C M)

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

illustration demonstrated the relative movements of the schedules through the short run.

The marginal function shifted upward solely as a result

of increased cost3 of the variable input, grain.

The average cost function

76 shifted through time as fixed and variable costs increased, although rising grain costs accounted also for most of the increase in average total costs at any given level of output. The optimum output solutions indicated that the representative farm would have minimized losses (or maximized profits) by contracting output slightly in successive years.

Contractions in output in 1942-43

and 1943-44. were dictated by the movements of the marginal cost schedule in relation to price movements during the same periods.

That is, at any

given price (marginal revenue), an upward shift of the marginal cost schedule would have lowered the income-maximizing output.

On the other

hand, for any given marginal cost schedule, an increase in price would have increased the optimum output.

Thus the lower levels of output

predicted by the model in 1942-43 and 1943-44 indicated that the mar­ ginal cost function shifted upward a little more rapidly than price over the period.

In effect, the price of grain increased at a slightly

77 higher rate (between observations) than the price received for milk • "^This schedule was, of course, not necessary to define the levels of output at which profits were maximized. The average functions were included in the operational structure for two reasons: l) to illustrate the minimum cost positions in relation to attained and predicted levels of output and 2) to provide a more realistic setting for the analysis. 76 Fixed costs were varied for those factors classified herein as fixed but which are realistically variable in the short run, as explained in the preceding section. ^The price of grain rose 16 per cent ($2.14 "to $2.49) between the 1941-42 and 1942-43 observations, whereas the milk price rose 15 per cent ($2.49 to $2.66) over the same period. Between 1942-43 and 1943-44, comparable rates were feed, 46 per cent and milk, 40 per cent. These rates were consistent with statements above concerning the trend of the index of the milk-feed price ratio in Pennsylvania.

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94 This result was apparent especially in the movements of the cost and price schedules from 1942-43 to 1943-44 positions. Comparison of Attained ana Predicted Levels of Output A comparison of the levels of operation vith the optimum out­ put solutions provided some measure of the accuracy vith which the theory of the firm provided estimates of the output responses of the representa­ tive farm. Table IS.

Actual and predicted levels of output are summarized in The first and third predicted values varied from the observed

values by less than one per cert, vhile the optimum output in 1942-43 vas approximately four per cent below the attained output for that period.

Varia­

tions between actual and predicted levels of output were so slight during 1941-42 and 1943-44 that the farm was considered to have been operated in short rim equilibrium during these two periods.

Failure of the model to

predict more accurately in 1942-43 cannot be overlooked, but neither is this variation sufficiently large to discredit the whole analysis.

This

deviation may be attributed primarily to the lack of data vith which to describe more accurately the organization and practices

78

of the repre­

sentative farm dui’ing the 1942-43 and 1943-44 periods. Table 18 - Levels of output, attained and predicted, Representative farm, 1941-42, 1942-43 and 1943-44. Period

Output level Attained Predicted (cwt.)

Deviation of predicted from attained level (per cent) -0.8

1941-42

825.37

(cwt.; 818.88

1942-43 ;

851.45

816.05

-4.2

1943-44

807.71

804.26

—0 *4

78Particularly the effect of crop yields and pasture conditions on levels of feeding.

« Reproduced with permission of the copyright owner. Further reproduction prohibited without permission

95 STOiM&Hr AND GENERALIZATIONS The foregoing interdisciplinary analysis has attempted to unite two areas of interest and inquiry —

economic theory and farm management —

to explain output responses in the short run.

A functional approach was

developed from the analytical tools^ of theoretical economics, whereas the unit of analysis was designed with reference to the management of real farms by real farmers.

The results of the study indicated that the

solutions rendered by the theoretical model approximated closely the actual output levels.

That is, the empirical data suggested that the particular

type of agricultural firm studied did behave in the manner expounded in the traditional theory of the firm. The principal contribution of the study, then, was its modest verification of the theory of the firm.

The study, therefore, substantiated

the tenets as well as the functional method of analysis proposed in this theoretical formulation.

Maximization of income represented the basic

motivating force in the theoretical setting and the preceding analysis has shown that the levels of output at which incomes would have been maximized varied only slightly from the actual levels of operation. Through the 1941-44 period, marginal cost and revenue schedules were shifted upward at such rates that optimum output levels could have been achieved by relatively small adjustments in physical output.

Observed

output responses during the period intimated that the representative farm recognized the cost-price relationships and was reasonably successful in adjusting output to the optimum levels. Of greater significance than the results obtained, however, was the support established for the general methods of analysis incorporated

^Including, of course, the experimentally derived input-output relation­ ship in milk production. jM < R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

in micro-economic theory. behavior of the firm —

By definition, the theory predicted the output

the representative firm.

Tools of analysis, re­

presented by functions expressing physical and value relationships, were developed to examine the representative firm with reference to output responses over a series of product prices.

Inasmuch as actual output

levels of the representative farm -were derived from a group of comparable farms, the similarity between actual and predicted levels of output through time appeared to justify the representative concept as a useful unit of analysis in this study at least. The functional type of analysis provided a rigorously defined setting for the investigation.

But this theoretical formulation resulted

in abstraction from error as well as from reality.

The production function

for instance, was an exact definition of the increase in milk resulting from increments of feed.

Without question, each of the cows kept on the

representative farm did not respond precisely as indicated by the function. Yet the relationship adopted was the best estimate of the expected response The fixed cost function, likewise, represented an attempt to depict accur­ ately and realistically, within the strictures of the analysis, the cost of resources the quantities of which were fixed within each accounting period.

This also was a simplification technique.

A few of the factors

(assumed fixed in amount) would have varied with output.

But these inputs

were relatively unimportant in the financial organization of the farm. The crucial costs in this analysis were imputed value of family labor and the cost of grain and it is maintained that the methods adopted re­ flected the interpretation placed on these costs by operators in the area studied.

It is not here implied that the end justified the methods of

analysis^ the available means were limited by the state of development

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97 of the science of economics.

It was within this schema that the analysis

was conducted.

Generalizations This study has indicated that the marginal cost function for each observation did provide a fairly accurate schedule of intentions to produce.

Generalizations drawn from this analysis need be limited, however,

to single-enterprise farm businesses or close approximations thereof.

Thus

the implications of the investigation had greater significance for highly specialized than general types of farming areas.

Within the former areas,

this analysis has provided one example of the capabilities of the theory of the firm as a predictive tool. Generalisations from this study were subjected to one other limitation.

The known variation in quality of productive factors, even

within relatively small areas, would suggest that the physical character­ istics of a representative unit be described cautiously.

A two variable

input-output relationship presumes homogeneity between units of the fixed input and between units of the variable input.

Variations in quality

would distort the physical relationship, hence the cost structure.

The

importance of theoretical formulations with which to predict output responses of agricultural firms hinges largely, consequently, on the develop­ ment of input-output relationships within production sciences.

Without

these technological data, little practical significance can be attached to micro-economic analyses. This limitation of theoretical investigations can be easily magnified to false proportions, however. within frames abstracted from reality.

Economic analyses are conducted As such, they present maps of

reality not detailed portraits of the real world.

A simplified model

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98 is required if progress is to be made in explaining realityj and those who criticise theoretical formulations because such hypotheses (models) are unrealistic fail to grasp fully the purpose of economic analysis. The important details of reality were considered in the present study. Thus within fairly well-defined limits: specialized dairy farms of the area,

l) the farm was typical of

2) the production function provided

the approximate relationship for the quality of cows kept on the represent­ ative farm, and

3) the cost structures presented plausible descriptions

of the economic situations pertinent to the profitable operation of the individual farm firm.

Within this framework, the preceding analysis has

offered empirical verification of the theory of a special type of agricultural firm. The methodology and results of this study are not above criticism, of course.

Single causality, expressed in the theory of the firm as profit

maximization, is rarely a complete explanation of human behavior.

Hence

this investigation is not proposed as a self-contained explication of observed output responses.

In addition, this study does not disprove other

explanations of output responses.

That is, the relative stability of out­

put over the period observed may be explained by causes other than those expounded in the theory of the firm.

The study suggested merely that the

tools of micro-economic analysis are additional instruments useful for prediction. Implications for Further Studies The present analysis was based almost entirely on information collected for purposes other than the expressed objectives of this study. As a result, some of the data were adjusted in order to establish the type of information required to conduct the theoretical investigation.

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The

99 study was not strengthened by this procedure.

Future studies should be

privileged, therefore, to draw upon data collected for the specific pur­ pose of analyzing the objectives of these studies. Second, the study has pointed out a need for further investi­ gations designed to develop physical input-output relationships.

These

experiments should be constructed and conducted under the joint super­ vision of physical and social scientists in order to give promise of results useful to inter-disciplinary analyses.

In selecting relationships

to be established, priority should be given to productive services which represent the more important variable inputs to a given area.

Furthermore,

functions should be formulated for several quality grades of the fixed factor. Finally, the preceding analysis can, at best, be considered but one test of the adaptability of the theory of the firm to an agri­ cultural enterprise.

Further studies, drawing upon information developed

as stated above, are required to evaluate more accurately the method of analysis suggested by this investigation.

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