xt7sn00zqw0c https://exploreuk.uky.edu/dips/xt7sn00zqw0c/data/mets.xml Agricultural Experiment Station, Department of Agricultural Economics, University of Kentucky 1970 journals kaes_research_rprts_03 English University of Kentucky Contact the Special Collections Research Center for information regarding rights and use of this collection. Kentucky Agricultural Experiment Station Research Report 3 : February l970 text Research Report 3 : February l970 1970 2014 true xt7sn00zqw0c section xt7sn00zqw0c V Effect of Burley Tobacco Prices and Allotment Levels
On Profitable Farm Adjustments
ln Four Areas of Kentucky
L Verner N. Grise and James F. Thompson
U
RESEARCH REPORT 3 : February l97O
A University of Kentucky :: Agricultural Experiment Station
g Department of Agricultural Economics
= Lexington

PREFACE
This study is the first of two studies dealing with optimum
adjustments to changing conditions in the four major burley-tobacco
producing areas of Kentucky. The research on which this publication `
is based was a part of a joint effort between the U. S. Department ¥
of Agriculture and twelve Land Grant colleges under Southern Regional
Project 5-42, "An Economic Appraisal of Farming Adjustment Opportunities
to Meet Changing Conditions." These studies were to determine and
evaluate the agricultural adjustments needed in the Southern Region.
The methods and procedures used in each of the states are similar so
that comparisons of the results may be made among states.
_ Regional Project 8-42 is financed in part from Research and
Marketing Act funds and is a cooperative effort of the following
state Agricultural Experiment Stations: Alabama, Arkansas, Georgia,
Kentucky, Louisiana, Mississippi, North Carolina, Oklahoma, South
Carolina, Tennessee, Texas, and Virginia; the Economic Research Ser- `
vice, and the Cooperative State Experiment Station Service, Department
of Agriculture. Dr. John W. White, Vice President for Agriculture,
- University of Arkansas, is administrative advisor for the project,
and Dr. James White, University of Arkansas, is chairman of the pro-
ject regional technical committee.
The Southern Farm Management Research Committee, sponsored by
the Farm Foundation and the Southern Agriculture Experiment Stations,
was helpful in the development of this regional project.
` For purposes of studying adjustments needed in the burley belt,
a Burley Tobacco Subcommittee consisting of agricultural economists
from the Kentucky, Tennessee, and Virginia Agricultural Experiment Sta-
tions and the Southern Field Group, Farm Production Economics Division,
Economic Research Service, U. S. Department of Agriculture, was es-
— tablished. This subcommittee developed the general framework for the
analysis of adjustments in the burley-tobacco area. ,
The authors gratefully acknowledge the services of Wayne F.
Ewbank and others at the University of Kentucky, who contributed to
this project. The valuable criticisms and suggestions of the Review
committees at the University of Kentucky and the Economic Research
Service are acknowledged.
iii

TABLE OF CONTENTS
Page -
A PREPACE ............................ iii
LIST OF TABLES ........................ vii J
LIST OF ILLUSTRATIONS ..................... ix
INTRODUCTION ......................... 1
Purpose and Objectives .................. 1
Methodology and Procedures ................ 2
Description of the Study Areas .............. 3
Sampling Methods, the Farm Sample, and the Use of Agri-
cultural Stabilization and Conservation Service Data . . 5
Method of Developing Representative Farms ......... 6
Aggregation Procedure ................... 13
Qualitatively Homogeneous Resource Groups 58.8—Cent
Tobacco Price, Outer Bluegrass ............. 13
I ASSUMPTIONS .......................... 13
Variables Analyzed .................... 13
Resources ......................... 14
Price and Cost Estimates ................. 16
AGGREGATION RESULTS FOR STUDY AREAS .............. 17 i i
General Adjustments to Different Burley Price and Allot-
ment Levels in Four Study Areas ............. 17
Aggregate Price Response of Burley Tobacco Production . . . 18
Aggregate Response of Other Products ........... 21
Aggregate Enterprise Leve1s——Four Areas Combined ..... 32
Resource Use ....................... 34 ’
Net Returns to Resident Labor and Management, and Land . . 35
I Resource Use——Four Areas Combined ............. 36
Aggregate Net Returns to Resident Labor and Management,
and Land for Four Study Areas Combined ......... 37
SUMMARY AND CONCLUSIONS .................... 37
APPENDICES .......................... 40
A. Description of Livestock Enterprises ......... 40
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_ { § Page
{ · 3 B. Assumed Yields per Acre of Specified Crop Enter-
§ Q i prises for Selected Areas of Kentucky ........ 42
é g C. Assumed Prices Received and Paid by Farmers, Blue-
{ g grass and Western Pennyroyal Areas, Kentucky .... 43
i § D. Resource Availability, Resource Use, and Aggregate
Q Returns for 15 Tobacco Price-Allotment Combina-
i . Q tions ........................ 46
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LIST OF TABLES
Table Page
l. Land and Labor Available on Farms in the Inner L
Bluegrass——l959 .................... 7 .
2. Land and Labor Available on Farms in the Intermediate
Bluegrass--1959 .................... 8
3. Land and Labor Available on Farms in the Outer
Bluegrass--1959 .................... 9
4. Land and Labor Available on Farms in the Western
Pennyroyal--1959 ................... l0
5. Land and Labor Composition of Qualitatively Homo-
geneous Resource Groups at the 58.8—Cent Tobacco
Price in the Outer Bluegrass Area ........... I4
6. Burley Prices and Allotment Situations Included in the
Analysis ....................... I5
7. Arc Price Elasticities of Burley Production, Four
Areas Separately and Combined ............. 20
8. Optimum Aggregate Levels of Specified Enterprises for
15 Price—Allotment Combinations, Inner Bluegrass »
Area, Kentucky .................... 22
9. Optimum Aggregate Levels of Specified Enterprises for
15 Price-Allotment Combinations, Intermediate
Bluegrass Area, Kentucky ............... 25
10. Optimum Aggregate Levels of Specified Enterprises for {
15 Price-Allotment Combinations, Outer Bluegrass
Area, Kentucky .................... 28
ll. Optimum Aggregate Levels of Specified Enterprises for
» I5 Price-Allotment Combinations, Western Pennyroyal
Area, Kentucky .................... 30
l2. Optimum Aggregate Levels of Specified Enterprises for
I5 Price—Allotment Combinations, Bluegrass and Western
Pennyroyal Areas Combined ............... 33
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LIST OF ILLUSTRATIONS
Figure Page
I. The Area of Study, Bluegrass and Western Permyroyal
Areas, Kentucky ..,............,..,, 4
2. Qualitatively H0m0gene0us Groups 0f Farms ........ I2
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EFFECTCN?BURLEY'TOBACCOIUHCESON`ALLOTMENT
LEVELS ON PROFITABLE FARM ADJUSTMENTSIN
FOUR AREASOF`KENTUCKY
by
Verner N. Grise and James F. Thompson*
INTRODUCTION
Burley tobacco is a major enterprise on many farms in Kentucky.
Forty to forty-five per cent of the gross income from agriculture in
Kentucky is derived from this crop. Any variation in prices and allot-
ments of tobacco, therefore, has a very important effect on Kentucky
agriculture and resources devoted to it.
Purpose and Objectives
The purpose of this publication is to present and evaluate
optimum farm adjustments under alternative price and allotment com-
binations in four major burley—tobacco producing areas of Kentucky.
Optimum farm adjustments are defined as farm organizations in which
the enterprises and the resources used in producing these enterprises
p are combined in such a manner that returns to resident labor and p
management, and land are maximized. Information concerning optimum
farm adjustments is useful to farmers, policymakers, and the general
public in the sense that it can be used as a general guideline in
decision—making.
In this study, estimates of the optimum enterprise levels, the
resources used and the net returns obtained from the resources of resi- ,
dent labor and management, and land were investigated for 15 different
tobacco allotment and/or price combinations. These included three
sets of estimates for three tobacco prices without allotment restric-
tions. ln addition, l2 sets of estimates were determined for four
p *Agricultural Economist, Farm Production Economics Division, Economic
Research Service, U. S. Department of Agriculture, formerly stationed
at the University of Kentucky and former Associate Professor of Agri- K
cultural Economics, University of Kentucky, now Professor of Economics,
Murray State University, Murray, Kentucky.
l

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1 § .
i 5
3 2
4 .
1 E 5 tobacco prices together with prespecified acreage allotments. The ef-
1 3 fects of the changes in tobacco allotments and/or prices are evaluated
P 1 in terms of their effects on enterprise levels, resource use, and net
1 . 3 returns to resident labor and management, and land.
1 § This study has three major objectives:
1 » 1. To determine the nature and magnitude of resource-use adjustments
5 which would achieve the most profitable system of farming under
1 alternative price and allotment levels of burley tobacco and
1 the effects of these adjustments on the aggregate output and in-
Q Q come of the Kentucky areas under study.
i - .
1 g 2. To determine the effect upon total agricultural production, farm
E ‘ é income, and the labor and land used in agriculture for the four
1 § Kentucky areas under consideration, if all farmers adjusted to _
g 1 g their most profitable farming systems.
1 1 3 3. To estimate optimum representative farm relationships and to ag-
§ ’ g re ate t ese to etermine ro uction, income, an resource-use
. 1 g g h d P d d
1 1 g estimates for each of the four areas under study.
1 . S
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2 Q R
1 3 METHODOLOGY AND PROCEDURES
1 1 A Several articles have been written concerning methods for es-
1 ` timating supply functions.l The two techniques most often used to
1 ` estimate supply are: (1) regression of time-series data, and (2) linear
1 programming. Regression techniques have been used mainly in the analy-
1 B Q sis of short-run su 1 res onse concernin henomena for which histor-
x , _ _ PP Y P 8 P
1 ‘ ical data are available. Linear programming is used largely in
1 a evaluating the effects of variables for which there is little or no
g _ historical basis for estimating supply response. Several regional ad-
. 1 ` g justment studies have used linear programming as a basis for estimating
1 regional outputs, income, and resource use or, in essence, supply re-
1 § sponse. The procedure used in this study consists of:
1 Q 1. Stratifying the region into areas that are similar with respect to
1 , Q production alternatives, resources, and techniques of production. A
1 :
1 1 § 2. Using a sample survey in each area, together with information from
1 ` S the Agricultural Stabilization and Conservation Service, to estimate
1 . §: the labor and land resources.
· 1
1 Q
~ 1 Q lSee: Marc Nerlove and K. L. Bachman, "The Analysis of Changes in Agri-
1 2 cultural Supply: Problems and Approaches," Journal of Farm Economics, A
1 XLIl:53l-554, August 1960; and R. Barker and B. F. Stanton, "Estima—
1 tion Aggregation of Firm Supply Functions,“ Journal of Farm Economics,
1 47:701-712, August 1965.
§ 1 5
; 1 E

3
3. Constructing representative farms. V
4. Solving representative farm linear—programming models with a series
of alternative tobacco allotments and prices to obtain optimum
enterprise and resource-use levels.
5. Summing the enterprise and resource—use levels of the individual .
representative farms to obtain aggregate or regional estimates.
A description of the above steps is presented in this section.
The major difference in the procedure used in this study and other
8-42 studies is the method used in constructing representative farms.
The use of labor-land ratios, discussed subsequently, is designed to
reduce aggregation error.
Description of the Study Areas
The areas covered in this report are the Bluegrass region and
the Western Pennyroyal region of Kentucky. The Bluegrass region is
divided into three parts: the Inner, Intermediate, and Outer Blue-
grass areas. Although all four areas are well suited to burley—tobacco
production, they are different in such respects as topography, soil
types, farm sizes, enterprise combinations, labor availability, and
burley allotment sizes. Because of these differences, each area is
considered separately with different production and cost coefficients,
‘ land—labor ratios and allotment restrictions. The four areas are
shown in Fig. 1.
Inner Bluegrass _ T
The Inner Bluegrass is the most productive part of the Bluegrass
region. This is a gently sloping upland area of approximately 1,700
square miles centrally located in the Bluegrass region. The surface
I soil of the Inner Bluegrass is a brown or faintly reddish-brown silt
loam, grading into a reddish—brown silty clay beneath. Phosphatic
V fertilizers are not needed in this area due to the high phosphatic I
content of the Maury silt and Mercer soils dominating the area.
Almost all the Inner Bluegrass can be used for either cropland
· or pasture. About 41 per cent of the farmland is suited to row-crop
production, about 75 per cent can be used for small grain production,
and about 95 per cent can be used for hay and pasture. Burley allot-
ments are larger relative to farm size in the Inner Bluegrass than any
of the other three areas.
Intermediate Bluegrass
The Intermediate Bluegrass is a thoroughly dissected plateau
of approximately 3,300 square miles consisting of many narrow, winding

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I ‘·‘5<¥§}— l b \ $ I
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E g § FIG. l.--The Area of Study, Bluegrass and Western
¤ 3 § Pennyroyal Areas, Kentucky.
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2 i . . .
l 3 ridges and valleys. This is a hilly area with the hills ranging in
i . slopes from 25 to 35 per cent. Eden and Fairmount silty clay loams
g are the main soil types of this area. These soils are fairly high °
_ I ` in phosphorus and high in lime and potassium. Unlike the Inner
i . Bluegrass, only about 9 per cent of this area can be used for row
` l 3 crops and only 2l per cent for small grains. About 65 per cent of
this region can be used for hay and pasture. The remaining 55 per
cent consists of timber and wasteland. Burley—tobacco allotments
{ » a in this area are smaller than the two other Bluegrass areas, but
{ T § larger than the Western Pennyroyal area.
I
I 1 S
I Outer Bluegrass
1 5
l I The Outer Bluegrass consists of 3,000 square miles which en-
` 5 circle the Inner and Intermediate Bluegrass areas on the west, south, »
i S and east in a horseshoe fashion. This area is quite similar to the
I [ Inner Bluegrass except that the topography is more rolling, the soils
I Q contain less calcium phosphate, and the internal drainage of the sub-
é 5 soil is not as good. The important soil types of this area are Shelby-
! § ville and Lowell silt loams. These soils are brown silt loams on the
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surface and shade into brownish-yellow silty clay loam to silty clay ·
underneath. Approximately 29 per cent of the farmland in the Outer
Bluegrass is suited to row-crop production, and about 44 per cent is
usable for small grains. Approximately 79 per cent of this area can
be used for hay and pasture crops. The other 2l per cent consists of
wasteland and forest. The burley allotments in this area are gener-
ally smaller than those in the Inner Bluegrass but larger than those q
in the Intermediate Bluegrass and Western Pennyroyal areas. ‘
, Western Pennyroyal
LX The Western Pennyroyal area consists of 4,200 square miles
se forming a broad horseshoe with the bend at the southern boundary of
‘_/ the Western half of the state and the ends extending north, except
/ that the east end is discontinuous. The important soil types of
this area are Baxter, Pembroke, Decatur, and Dixon. The area is
undulating to rolling with many sinkholes and is well adapted to
general farming when the soil is limed and phosphated. Approxi-
mately 50 per cent of this area is suited to row-crop production
and 70 per cent to small-grain production. Almost the entire area
is suited to some sort of farming or pasture production. The burley
allotments for this area are much smaller than those of the other
‘ study areas included in this analysis.
Sampling Methods, the Farm Sample, and the Use of Agricultural
. Stabilization and Conservation Service Data
Sample "communities" were selected from Agricultural Stabiliza-
tion and Conservation Service (hereafter referred to as ASCS) records I
for each of the study areas. All farms with 20 or more acres were then
completely enumerated by farm size. This enumeration provided esti-
mates of the relative importance of different sizes of farms.
‘ Following this enumeration, a random sample of farms was sur-
veyed in the four study areas to obtain information on present farm
sizes and resident labor supplies. Two counties were selected from )
each study area as representative of that area. Each county was di-
vided into area segments the boundaries of which were determined large-
ly by natural landmarks. Each of the segments was numbered and random
procedures were used to determine those to be used in the survey.
Once a segment was selected, all farms within it were enumerated.
More than l00 observations were obtained from each of the four study
‘ areas with a total of 445 drawn for the entire study area.
1, Since the sampling rate was quite small, the farm sizes obtain- I
ed in the sample of farms are subject to considerable sampling error.
iS For this reason the much more extensive information provided by the
i- ASCS records was used to determine the importance of different farm
1DY- Sizes. The ASCS data, however, contained no information on labor
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§ 3 supplies, so sample data alone were used to determine the amounts of
Q § resident labor available on farms of different sizes. ASCS farm-size
Q E data were used to compute weights which were then applied to the rel-
I ative farm-size frequencies obtained from the sample survey data.
§ Thus, the relative farm-size frequencies from ASCS data were imposed
2 ri on the sample data while, within each farm-size class, the distribu-
E tion by resident labor was left unchanged.
s
5 Due to the large number of different farm sizes and the vari-
T ations in the amounts of resident labor associated with them, the
I entire array is not presented here. Instead, the number of farms, the
§ land in farms, the resident labor on farms, and the range in the supply
i g g of resident labor to farms is broken down by farm-size groups for each
Q · area (Tables I-4).
!
€ E
2 . . .
; Method of Developing Representative Farms
1
[ x
Q In this study, a universe of farms was delineated. A number
§ of farms were then selected to represent the entire universe of farms.
_ Q ¤ Optimum enterprise and resource-use levels were developed for each of
E g the farms selected to represent the universe of farms. The enterprise
E _ § and resource-use levels obtained by linear—programming procedures on
Q g § the representative farms were then expanded to obtain aggregates for
p Y S the universe. The difference between the results obtained by this pro-
3 a g cedure and those obtained by programming all farms is defined as ag-
; gregation error.
E g An attempt was made to reduce aggregation error by grouping
{ farms on the basis of homogeneous resources.2 Farms were classified
§ . E on the basis of the amounts of resident labor and land available to
Q 3 3 them since these resources tend to be the most immobile resources V
I ; In making this classification, it is assumed that, with a given level
{ V Q of management, farms with similar resource bases use similar techno- °
. } V logy.
‘ 3
l ° Groups of "qualitatively homogeneous" farms were determined
` { for each area. Qualitatively homogeneous farms are defined as those
I Q that contain the same enterprises in their optimum programs.3 From
Q i g each of the groups of farms containing the same enterprises a single
Q ——————
i ‘ g 2See: James F. Thompson, Defining Typical Resource Situations, Southern
: , ' Cooperative Series Bulletin 56, pp. 32-43, 1958; G. E. Frick and R. A.
‘ ’ 3 Andrews, "Aggregation Bias and Four Methods of Summing Supply Func-
~ ` Z tions," Journal of Farm Economics, 47:696-700, 1965. Also, for an
g Q overall review of studies relating to the aggregation problem see:
I Q Thomas A. Miller, "Aggregation Error in Representative Farm Linear
p E E Programming Supply Estimates," unpublished Ph.D. Thesis, Iowa State
i University, 1967.
5
I 3See Miller, Ibid., for a discussion of "qualitatively homogeneous"
@ farms.
Q I I `
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TABLE 1
LAND AND LABOR AVAILABLE ON FARMS
IN THE INNER BLUEGRASS——1959 ·
Resident Range in Resident
Farm Number Land in Labor on Labor Available
Sizea of Farms Farmsb Farms to Farms€
(acres) (acres) (1,000 hrs.) (hours)
20 - 49 1,022 36,039 1,841 590 — 2,950
, 50 — 74 730 43,233 1,341 590 — 3,245
75 — 99 529 45,201 1,560 885 — 5,900
100 - 139 839 98,139 2,584 1,475 - 5,900
140 — 179 547 85,108 2,213 1,180 — 7,375
180 - 219 273 54,296 1,134 2,950 - 6,785
220 — 259 347 80,900 2,758 3,540 — 11,800
260 — 499 694 235,778 4,691 1,475 — 13,275
Total 4,981 678,694 18,122
aFarms with less than 20 acres and more than 500 acres were excluded.
Farms with less than 20 acres were considered to be basically rural
residences and not apt to adjust. Farms with more than 500 acres
were excluded due to the fact that the low sampling rate used in the
~ survey resulted in unreliable estimates of the needed data for such
_ farms.
bApproximate1y 95 per cent of this land is open land.
CEach man-equivalent was assumed to supply 2,950 hours of labor per
year. *

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g Q 3 TABLE 2
1 g LAND AND LABOR AVAILABLE ON FARMS IN
Q ‘ THE INTERMEDIATE BLDEBRABB--1969
E Resident Range in Res1 ent
Farm Number Land in Labor on Labor Available
, Sizea of Farms Farmsb Farms to Farmsc
3 i (acres) (acres) (1,000 hrs.) (hours)
l é é 20 - 49 2,366 85,516 6,629 885 - 3,246 A
g 4 2 60 - 74 2,1B1 134,226 6,113 885 - 3,836
Q § 3 75 - 99 2,393 206,469 5,066 BBB - 6,7BB
Q , g 100 - 139 2,964 347,669 9,025 885 - 6,785
Q : i 140 - 179 1,829 290,976 7,229 BBB - 7,0B0
5 3 Q 180 - 219 1,020 201,980 4,247 1,47B - 5,900
$ g 220 - 259 669 160,229 2,824 2,950 - B,B60
g 3 260 - 499 1,195 406,293 7,3B9 1,476 - 12,6BB
» 3 E
3 ; T6ta1 14,697 1,831,238 46,622
, Q 3
a · A
g 3 aFarms with less than 20 acres and more than 500 acres were excluded.
; E Farms with less than 20 acres were considered to be basically rural
E residences and not apt to adjust. Farms with more than 500 acres
1 5 5 were excluded due to the fact that the low sampling rate used in the
B § § Q survey resulted in unreliable estimates of the needed data for such
§ farms.
E 3 g bApproximately 65 per cent of this land is open land.
· E 1 a CEach man-equivalent was assumed to supply 2,950 hours of labor per
{ i year.
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TABLE 3
LAND AND LABOR AVAILABLE ON FARMS A
IN THE OUTER BLUEGRASS——1959 ‘
Resident Range in Resident
Farm Number Land in Labor on Labor Available
Sizea of Farms Farmsb Farms to Farmsc
(acres) (acres) (1,000 hrs.) (hours)
J 20 — 49 1,844 58,826 2,419 590 — 2,950
50 — 74 1,844 116,674 4,318 590 — 5,900
75 — 99 939 87,757 2,311 590 - 3,805
100 — 139 1,977 233,347 6,047 855 - 6,755
140 - 179 1,307 214,213 4,417 855 - 5,900
180 — 219 939 181,988 4,050 1,180 - 11,800
220 - 259 636 150,626 2,845 2,950 — 5,900
260 — 499 1,174 395,050 6,332 2,950 — 11,800
Total 10,660 1,438,481 32,739
aFarms with less than 20 acres and more than 500 acres were excluded.
Farms with less than 20 acres were considered to be basically rural
residences and not apt to adjust. Farms with more than 500 acres p
were excluded due to the fact that the low sampling rate used in the
survey resulted in unreliable estimates of the needed data for such
farms.
bApproximately 79 per cent of the land is open land.
CEach man—equivalent was assumed to supply 2,950 hours of labor per
year. '

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f { TABLE 4
l LAND AND LABOR AVAILABLE ON FARMS IN
1 THE WESTERN p5NNYR0YAL--1050
i
€
i
j Resident Range in Resident ,
Q = Farm Number Land in Labor on Labor Available
S 3 3 Sizea of Farms Farmsb Farms to Farmsc
Q 3 q (acres) (acres) (1,000 hrs.) (hours)
Q i § 20 - 49 2,105 97,015 2,540 295 - 2,950
1 , 1 50 - 74 1,005 85,450 5,102 885 - 2,950
; Q i 75 - 00 1,548 110,405 4,048 1,180 - 7,575
3 100 - 150 1,851 215,841 5,812 1,180 - 5,785
5 l 140 - 170 1,155 159,950 5,740 1,475 - 8,250
3 , _ 180 - 219 776 157,421 4,074 2,550 - 8,850
f _ 220 - 259 454 105,604 2,071 1,475 - 5,000
1 g 260 - 400 1,074 551,507 5,050 2,950 - 14,750
A 3 1 500 - 550 184 104,055 1,552 5,000 - 15,570
2 3 i Totals 10,050 1,408,057 54,508
l g K aFarms with less than 20 acres and more than 660 acres were excluded.
V 5 g g Farms with less than 20 acres were considered to be basically rural
g 5 3 residences and not apt to adjust. Farms with more than 660 acres
i 3 were excluded due to the fact that the low sampling rate used in the
E g survey resulted in unreliable estimates of the needed data for such
_ ( 1 farms.
-
‘ Q bApproximately all this land is open land.
Q g CEach man—equivalent was assumed to supply 2,950 hours of labor per
`;é year.
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farm was selected to represent all the others. A parametric program- f
ming procedure was used to isolate ranges in the relative combinations
of resident land and labor within which the enterprises in the optimum
programs did not change.
The procedure used in determining the ranges over which the rel-
ative combinations of resident labor and land could vary without any
change occurring in optimum programs or the marginal value product of {
land was to set resident labor equal to two man-equivalents and to ·
examine the range over which the quantity of land could vary without
affecting the enterprises contained in the optimum program. With
` slightly more land than that at which the enterprise composition
changed, and with resident labor held constant at two man-equivalents,
a new solution was generated. Solutions were generated with slightly
more land than that at which the enterprise composition changed for
each enterprise-composition change until the marginal value product of
land reached zero. Beyond this point no additional land is used and
no further changes occur in the optimum enterprise composition. This
procedure is graphically shown for the 58.8-cent tobacco price in the
Outer Bluegrass area (Fig. 2).
b All the farms with land-labor ratios falling between two boun-
dary lines (lines I, ll, etc. in Fig. 2) contain the same enterprises.
The optimum enterprise levels associated with each land and labor
level within the boundary lines depend on the point within the boun-
dary lines at which these land and labor levels fall. However, if
the resources of the farms falling between two boundary lines are
averaged and an optimum program determined by means of linear program-
ming for the average resources, this program can be multiplied by the
number of farms in the group and the results will be the same as if
optimum programs had been determined for the farms separately and
added together. When the boundaries were very close, some combinations
_ were made in constructing average land-labor ratios. The procedure
described above provides a basis for linear aggregation that greatly
reduces error in the aggregation process itself.
It should be pointed out, however, that the technical coeffi-
cients used in the programming are those for average—sized farms within ,
each area. To the extent that coefficients on large farms are dif-
ferent from those on small farms and these in combination do not equal
those of average—sized farms, aggregation error arises.
The parametric programming procedure described above was car-
1 ried out for each of the four tobacco price levels in each study area
since the resource ratios over which the optimum programs remain con-
stant change as prices are varied. Consequently, four sets of repre-
sentative farms were used in each study area. Six to thirteen
representative farms were used for each price, depending on the re-
source ratios over which the optimum programs did not change.

I
§
I
1
2 E §
2 I 3
E
3
I » I .
_ 2.0 I II III I\".`\'I \`l1 WU
a I
I 5 .
1.5
- 3 .:2
Z e =* <¤
I A
I *4-4
: g O
3 3
3 5 51.0 V
2 vg
2
I . 0.5
I 3 .
I 1
I . 2
g E O
I _ g 100 200 300
I Q Acres 0f Land
' Q I Figure 2.——Qualit;atively Hcmogeneous Groups 0f Farms
2
I I
I § 3
i
j Q
’ I
& I g
5 I
~ Ii I . ........

13
Aggregation Procedure j
The aggregation procedure used in this study involved the
translation of representative farm estimates into area estimates.
The mechanics of the aggregation procedure involved estimation of
the aggregation weights in such a way that the aggregate acreage
in the farms as determined by the use of these weights was approxi-
mately equal to the total acreages as determined for the ASCS data. i
The sum of land in farms in each qualitatively homogeneous group *
was expressed as a percentage of the land in all farms in the survey
for each study area. The total acreage in the study area represent-
ed by each qualitatively homogeneous group was then obtained by mul-
tiplying the total land in farms of the study area by the respective
group percentages. The amounts thus determined were divided by the
acreage of the single representative farm of each study group to
i determine the number of such farms which could be included in each
qualitatively homogeneous group. The aggregate enterprise levels
were then estimated by multiplying the optimum enterprise levels for
each representative farm by the number of farms represented by it and
T summing overall representative farms to obtain the aggregates for
each study area. The area aggregates were then totaled to estimate
the production for all the areas included in the study.
Qualitatively Homogeneous Resource Groups
’ 58.8-Cent Tobacco Price, Outer Bluegrass
Nine qualitatively homogeneous resource groups were shown in
Fig. 2 for the 58.8—cent tobacco price in the Outer Bluegrass area.
The average quantity of land, the total acreage of land, the average
quantity of labor, the number of farms represented by each qualita- . `
tively homogeneous resource group, and the average quantity of land
available for each man—equivalent of labor is shown below (Table 5).
ASSUMPTIONS
The results of a study of this nature and the conclusions
which it yields are highly conditioned by the major assumptions on
which it is based. The assumptions with respect to the variables
analyzed, resources, enterprises considered, and the coefficient
· assumptions and derivations are presented below.
Variables Analyzed _
The analysis in this publication is centered on the effects of
tobacco price and allotment variations on optimum enterprise combinations,
returns, and resource—use levels. Three burley—tobacco price levels were
considered under the assumption that tobacco production was not restricted

\ 11
E E
= 1
( 14
E E TABLE 5
l 3
i § LAND AND LABOR COMPOSITION OF QUALITATIVELY HOMOGENEOUS
( _ § RESOURCE GROUPS AT THE 58.8—CENT TOBACCO PRICE
j Q IN THE OUTER BLUEGRASS ARE