Agricultural Production and Farm

Management
Eco 2115
August 2024

1
 Introduction
Role of Agriculture in Development
• Job creation
- %ge share of a country’s labor force in agriculture.
- Gender composition(ploughing, planting,
spraying, weeding, storage etc)
- Age distribution
- Paid & unpaid labour force
• Share of agriculture in a country’s total o/p.
• Generates income for hh/individual.
• agriculture & Infrastructure dev’t,
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• Importance of food production.- energy, health
• Agric vs industrial growth> forward & backward
linkages.
• Terms of trade- export promotion- foreign
exchange earnings- imports of raw materials &
pdts not produced locally.
• Shifting financial resources from the agricultural
sector
• Promotes econ growth, poverty reduction, food
security.
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 Characteristics of Agriculture in LDCs
• Dualistic
– Traditional ( large in employ’t & small in production)
– Modern ( small in employ’t & large in marketed o/p)
• Production units
– Family farms & share tenancy
– FOP (land, lbr & other inputs)
– Family labor
– Hiring in & out
– Type of technology – simple tools to advanced.

4
 Characteristics continued

• farm h/hs both producer & consumer ( home prodn)

– home consumption
– little taken to market
– lack of infrastructure
– lack of information
– lack of storage facilities
– Lack of marketing centres.
• Production functions
– seasonality affects the nature of inputs ( affects the inputs, high
economic costs)
– geographical dispersion
– land surface as the major FOP
– transportation ( linking producers & consumers)
– Perishable commodities produced.
– Price uncertainty ( affects what to grow & how many inputs to use)

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 Characteristics contid

• Economic behaviour of farmers ( utility maximization)

• Risk & uncertainty
yield uncertainty, drought, rainfall, pests & diseases, choice
of crops, price uncertainty
• Response
Changes in price for marketed o/p; Change in cash crops
relative to food crops; Change in rural –urban migration;
Change in agricultural inputs
• labor reward system
– Traditional - work & income;
– Modern - VMPl =wage rate
– low opportunity cost in traditional
– lack of information
– returns to labour lower in traditional
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 Challenges faced by the Agric sector
in DCs
External
• Our commodities have low income elasticity of DD
• They also have low price elasticity of DD (decrease in prices
does not lead to increase in dd for the c’dities
• Deterioration in terms of trade due to decline in world
commodity prices.
• Replacement by synthetics
• Imports not protected hence great stiff competition with
our exportables
• World recession
• High interest rates abroad ( Tight monetary policies debt)
• Tariffs & non-tariff barriers
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• Education
• Health
• Infrastructure (roads, electricity, telecom.),
storage facilities
• Research
• Extension services
• Credit facilities
• Declining soil fertility
• High losses dues to pests & diseases
• Uncertain land rights
• Inadequate institutional coordination & linkages
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• Negative consequences of climate change. Due to climate disturbances,
growing & harvesting seasons are increasingly unpredictable.
• Land scarcity, magnified by episodes of severe droughts & consequent
food shortages
• Rising population density.
• African rural hhs are imprisoned in a poverty trap, thus, they dont have
the money required to invest in income enhancing activities. This denies
them access to technical innovations that wld boast agricultural
production.
• In agriculture, women face particularly severe challenges. Although they
represent 47% of the labor force, they are prominently smallholder
farmers b’se the system tends to discriminate against them.
• Customary laws & rules governing ownership & transfer of land rights are
generally unfavorable to women in SSA, conferring title & inheritance
rights upon male family mbers.
• Women in agriculture also experience lack of access to finance, modern
inputs as well as lack of knowledge & skills of modern agricultural
practices.

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 Policy measures/initiatives
• Promoting private sector investment & raising
farmer productivity.
• Improving Access to Markets & Value Addition.
• Improving access to credit.
• Creating an Enabling Environment.
• Institutional Strengthening in the Sector.
• Promotion of Selected Strategic Enterprises.

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 Policy measures/initiatives contd

• Reverse costly environment degradation & better

adapt to climate change shocks. However,
sometimes there is a trade-off btn protecting the
environment & enhancing agricultural productivity.
• Connection of small-scale farmers to large business
farmers thru mutually beneficial contract farming .
• Facilitate famers’ access to inputs, financing, end-
markets as well as their participation in agriculture
value chains.
• Promote/strengthen farm groups.

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 outcome
• Rural incomes & livelihoods improved
• Household food & nutrition security improved.
• Factor productivity (land, labour, capital) in crops,
livestock, & fisheries sustainably enhanced.
• Markets for primary & secondary agricultural products
within Uganda, the region & beyond developed &
sustained.
• Improved access to high quality inputs, planting & stocking
materials
• Expanded network of rural market infrastructure
• Farmers’ organizations strengthened in management,
entrepreneurship, & group dynamics especially for
collective marketing.

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 Subject matter of Farm Management
Definition of Farm Management
• An art/science for organizing & operating a farm.
• An art of managing a farm successfully.
• Farm Management is a decision-making process
which coordinates FOP to produce desired o/p.
The functions of management includes:- planning,
organizing, directing & controlling. These are
explained in detail below.

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 Functions of Farm Management
➢Planning;- establish goals, identify resources.
➢ Organising;- acquire resources, devise workable
strategy to meet the goals.
➢Implementation/directing;- allocate the resources
to competing uses, coordinating/ supervision.
Management directs the operations to achieve
desired goal through motivation.
➢Control;- monitor results, record information, &
take corrective action as needed.
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Management Flow chart

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 Steps in Farm Management
1. Define the mission of the Farm
2. Formulate the goals for the farm and family
3. Assess the resources available to the farm (
land, labour, capital)
4. Survey the world surrounding the farm
enterprises (external scanning)
5. Identify and select appropriate strategies
6. Implement and refine the selected strategies
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 Scope of Farm Management
• Deals with allocation of resources.
• Deals with decisions that affect profitability of
the farm.
• Helps in decision making on what, how, how
much, when.
• Key for economic efficiency of the farm.

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 Managerial Performance
Successful managerial performance rests on three
basic elements –
➢leadership,
➢motivation , and
➢communication.
A successful farm manager is one who performs
the above functions efficiently

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 Characteristics of a Good Farm
Manager
In order to efficiently perform the above functions, a
manager must possess, the following characteristics:
✓ Be a goal oriented individual
✓ Possess a keen sense of observation.
✓ Possess an enquiring mind.
✓ Have analytical ability
✓ Be able to take initiatives
✓ Be a risk taker.
✓ Be a good leader.
✓ Be able to motivate workers.
✓ Be an effective communicator.
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 Characteristics of a Good Farm Manager contd…

✓ Be technically competent, i.e. know what to do and

how to do it.
✓ Be able to manage his time.
✓ Define his problems clearly after identifying them.
✓ Sort out problems into big & small, urgent & pending.
✓ Be able to take corrective steps.
✓ Be full of vigour, energy & readiness to face risk &
uncertainty.
✓ Be flexible, knowing that today’s decision may be
wrong for tomorrow.
✓ Face challenges of new technology & be ready to
learn and adapt if possible.
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 Relationship of Farm Management
with other sciences
• Physical and biological sciences( plant breeding,
soil science, engineering etc).
• Business principles ( book keeping).
• Economics –economic theory
• Statistics:- methods & procedures of data
manipulation.
• Psychology:- human motivations & attitudes
• Philosophy & religion:- certain pdts eg piggery
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 Common values among farmers
✓ A farm is a good place to raise a family.
✓ A farm should be run as a business.
✓ It is acceptable for farmers to borrow money.
✓ A farmer should have at least 2 weeks of vacation.
✓ It is better to be self-employed than to work for someone
else.
✓ It is acceptable for a farmer to also work off the farm.
✓ It is more enjoyable to work alone than with other people.
✓ Farmers should strive to conserve soil & keep water & air
✓ resources clean.
✓ A family farm should be passed on to the next generation.
✓ All family members should be involved in the operation.

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 Agricultural production
• It is concerned with the choice of production
patterns & resource use in order to maximize
the objective function of farmers.

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 Why study Agricultural production
• What is efficient production?
• How is most profitable amount of input
determined?
• How the production will respond to a change in
the price of output?
• What enterprise combinations will maximise
profits?
• How will technical change affect output?

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 Goals of Agricultural Producer
• Survival- peasant farmer
• Maximize profits- commercial farmer
• Maintain or increase standard of living
• Increase equity- various crops
• Maintain stable income
• Pass farm to next generation
• Increase free time
• Increase farm size (“growth”)
• Maintain or improve environmental quality
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 Goals of production Economics
1. To provide guidance to farmers in using available
resources.
2. To facilitate the most efficient use of resources .
3. Assist farm managers in determining the best use of
resources, given Δing needs, values & goals of society.
4. Assist policy makers in determining the consequences of
alternative public policies on output, profits, & use of
resources on the farm.
5. To evaluate the uses of the theory of the firm for
improving farm management & understanding the
behavior of the farm as a profit-maximizing entity.
6. To evaluate the effects of technical & institutional
changes on aquaculture production & resource use.

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7. To determine individual farm & aggregated regional
farm adjustments to output supply and resource use
to changes in economic variables in the economy.
8. To determine & define the conditions which provide
for optimum use of resources.
9. To determine the extent to which the existing use of
resources deviates from optimum use.
11. To analyze the factors or forces which are
responsible for the existing production pattern &
resource use.
12. To explain means & methods for changing existing
use of resources to the optimum level.

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 Focus of Agricultural production
➢Resource use efficiency
➢Resource combination
➢ Resource allocation
➢Resource management
➢Resource administration

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 PRODUCTION FUNCTION
• A systematic way of showing the relationship
between different amounts of inputs that can
be used to produce a product.
• Technical relationship between inputs and
output.
– numerically/Algebraic equation
– Tables
– Graphs
– Diagrams

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Production function depends on the following:
1. Quantities of inputs used
2. Technical knowledge of the producer.
3. Possible processes in production
4. Size of the firm
5. Nature of firm’s organization
6. Relative prices of factors of production.

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 Types of Production Functions:

• Continuous Production Function

• Discontinuous or discrete
Production Function
• Short Run Production Function
• Long Run Production Function

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 Basic production problems

• WHAT TO PRODUCE?
• HOW TO PRODUCE?
• HOW MUCH TO PRODUCE?
• WHEN TO BUY AND SELL?
• WHERE TO BUY AND SELL?
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 Three levels of agricultural production

level 1: Peasant farmer agriculture

➢Production is basically for own consumption with
marginal marketable surplus
➢Low output and productivity
➢Simple tools & traditional techniques of
production used
➢Lbr is the principal factor of production
➢Lbr is underemployed for most of the year except
during the planting, weeding & planting seasons
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 Peasant farmer agriculture contd....
➢Dependence on natural factors like rainfall which
makes it very risky
➢Household lbr is the main source of farm lbr.
➢Technological limitations, rigid social institutions,
fragmented markets & poor communication
networks discourage higher production levels.
➢Objective function of the farmer is survival not ∏
maxn. This makes the peasant farmer unwilling
to adopt new technologies that promise higher
yields but with greater risks of crop failure.
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level 2: Mixed and diversified farming
➢Staple crops no longer dominates farm output.
New crops are introduced plus simple husbandry
under the diversified farming system which even
reduces the risks of crop failure.
➢Simple lbr saving devices are used e.g. small
tractors, mechanical seeders, ox-ploughs etc.
➢High yielding seeds, fertilizers used.
➢A mktable surplus is realized which can be sold
to raise income and improve standard of living.

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level 3: Specialised Modern Commercial Farming
➢ Production is entirely for the mkt.
➢ Usually specialize in one crop or specific animal
husbandry.
➢ Specialised farms usually owned by multinational
corporations.
➢ Maximisation of o/p achieved thru use of irrigation,
fertilizers, hybrid seeds.
➢ Economic considerations ( e.g. FC & VC, investment &
rates of return, optimal factor combinations, market
prices) play a significant role in decision making.
➢ Capital formation; technological progress & scientific
research play a dominant role in augmenting o/p &
productivity.
➢ Sophisticated lbr-saving capital equipment used e.g.
combine harvesters.
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 Production functions (PF) commonly
used in agriculture
• Linear PF: Also known as 1st degree polynomial. It’s
algebraic form is given by: y = a + bx
where a is the intercept & b is the slope of the function.
It is not commonly used in research because it violates
the basic assumptions of characteristic functional
analysis.
•Quadratic PF: Also known as 2nd degree polynomial.
This type of PF allows both declining & negative marginal
productivity thus embracing the 2nd & 3rd stage of
production simultaneously. y = b0+ b1x + b2x2
➢ Such PFs are quite common in fertilizer response
studies.
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• Cobb-Douglas PF: It is also known as power PF. It is most
widely used PF.
It accounts for only our stage of production at a time &
cannot represent constant, increasing or decreasing marginal
productivity simultaneously.
Y = b0 x1b1
where b0 is efficiency parameters & b1 is elasticity of
production.
• Square root PF: It represents a compromise between C-D
& the quadratic PF.
Y= a0+ a1√x1+ a2 x2
This function gets rid of the limitations of field mix of inputs
for producing different levels of output inherent in the C-D PF
& that of linear isoclines in quadratic function.
Thus, this function allows both a diminishing TP in the same
way as QF does & for declining MPs at a diminishing rate as
the C-D function does.
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 Characteristics of Agricultural
Production Function
• weather conditions
- too much rainfall, flooding, drought
etc
• Seasonality
- dictates most farming activities
• Geographical dispersion
-type of pdts, technology
• Risk and uncertainty
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• Perishability of the products.
• Joint products
• Bulkness of the products
-transport
-storage.
• Price fluctuactions
• Nature of demand
“-necessity of life”

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Agricultural Production and Farm
Management(Eco 2115)
2nd Handout
August 2024

1
BASIC PRODUCTION RELATIONSHIPS

Major production relationships are:

1. Factor -Product relationship
2. Factor -Factor relationship
3. Product-Product relationship

2
 Factor-Product relationship
➢ Deals with the production efficiency of resources.

➢ Deals with the rate at which the factors are transformed into
products.

➢ Optimization of production.

➢ Guides the producer in making the decision ‘how much to

produce?

➢ Helps the producer in the determination of optimum input to

use & optimum output to produce.
3
• Price ratio is the choice indicator.

• This relationship is explained by the law of

diminishing returns.

• Algebraically, this relationship can be expressed

as;
• Y = f (X1 / X2,X3………………Xn)

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 Review of basic concepts of
production
TP: -Amount of product which results from different qtties of variable input.

AP: TP/X ( x being the input)

MP: Change in TP / Change in input level (∆Y/∆X)

TPP: TP expressed in terms of physical units like kgs, tonnes.

APP: AP expressed in terms of physical units like kgs, tonnes.

MPP: MP expressed in terms of physical units like kgs, tonnes.

TVP: TPP. Py or Y. Py

AVP: APP. Py

MVP: MPP.Py

5
 Three regions of production function
• Region I : MP>AP
• Region II : Both MP & AP are falling but +ve
• Region III: MPx is negative. Additional units of
fertilizer reduce total product. The fixed inputs are
overloaded.

Optimal position in terms of the variable input is in

stage II

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Y Bliss point

output TPP
I II III

point of max APP

point of
inflexion

APP
MPP X
input

7
Stage-I occurs when MPP > APP. APP is increasing
throughout this stage, indicating that the average rate at
which X is transformed into Y, increases until APP reaches its
maximum.
Stage-II occurs when MPP is decreasing & is less than APP but
greater than zero. The physical efficiency of the variable input
reaches a peak at the beginning of Stage–II. On the other
hand physical efficiency of fixed input is greatest at the end of
Stage-II. This is because the nos of fixed input is constant &
therefore the output/ unit of fixed input must be largest
when total output from the production process is maximum.
Stage-III occurs when MPP is negative. Stage III occurs when
excessive quantities of variable input are combined with the
fixed input, so much, that TPP begins to decrease.

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 Three Regions of Production-
Economic decisions
Region 1/zone 1
➢ It is called irrational zone of production.
➢ Any level of resource use falling in this region is
uneconomical.
➢ Technical efficiency of variable resource is increasing
throughout the zone (APP is increasing).
➢ Thus, it is not reasonable to stop using an input
when its efficiency is increasing.
➢ In this zone, more products can be obtained from the
same resource by reorganizing the combination of
fixed & variable inputs. For this reason, it is called
irrational zone of production. 9
 Zone 1 contd…….

➢The first stage of production starts from the

origin i.e., zero input level.
➢In this zone, MPP>APP
➢Product and hence APP increases throughout this
zone.
➢MPP is increasing up to the point of inflection &
then declines.
➢Since MPP increases up to the point of inflection,
TPP increases at increasing rate.

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 Zone 1 contd……

➢ After the point of inflection, TPP increases at decreasing rate.

➢ Ep >1 up to maximum APP.
➢ Ep= 1 at the end of the zone (MPP = APP).
➢ In this zone fixed r’ces are in abundancy relative to variable
r’ces.
➢ Technical efficiency of variable r’ces is increasing throughout
this zone as indicated by APP.
➢ Technical efficiency of fixed r’ces is also increasing as reflected
by the increasing TPP.
➢ MVP >MFC
➢ MR > MC)
➢ This is irrational or sub-optimal zone of production.
➢ This zone ends at the point where MPP=APP or where APP is
Maximum

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Region/Zone II
➢ It is rational zone of production.
➢ Within the boundaries of this region is the area of
economic relevance. Optimum point must be somewhere
in this rational zone.
➢ It can, however, be located only when input & output
prices are known.
➢ The second zone starts from where the technical efficiency
of variable resource is maximum i.e., APP is Maximum
(MPP=APP)
➢ In this zone, MPP<APP & APP is decreasing. Therefore, APP
decreases throughout this zone.
➢ MPP is decreasing throughout this zone.
➢ As the MPP declines,TPP increases but at decreasing rate.
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 Region II contd….
➢ Ep <1 between maximum APP & maximum TPP.
➢ Ep=0 at the end of this zone.
➢ In this zone variable r’ces more relative to fixed r’ces.
➢ Technical efficiency of variable r’ces is declining as
indicated by declining APP.
➢ Technical efficiency of fixed r’ces is increasing as
reflected by increasing TPP.
➢ MVP=MFC.
➢ MR= MC
➢ This is rational zone of production in which the
producer shd operate to attain his objective of profit
maximization.
➢ This zone ends at the point where TPP is maximum or
MPP is zero.
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III Region or Zone III:
➢ It is also an area of irrational production.
➢ TPP is decreasing at increasing rate & MPP is negative.
➢ Since the additional qtties of r’ce reduces total o/p, it
is not profitable zone even if the additional qtties of
r’ces are available at free of cost.
➢ In case if a farmer operates in this zone, he will incur
double loss. i.e., Reduced Production & Unnecessary
additional Cost of inputs.
➢ This zone starts from where the technical efficiency of
fixed resource is maximum (TPP is Max).
➢ APP is declining but remains positive.
•
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 Region III contd…..

➢ MPP becomes negative.

➢ TPP declines at faster rate since MPP is -ve.
➢ Ep < 0
➢ In this zone variable r’ce is in excess capacity.
➢ Technical efficiency of variable r’ce is decreasing as
reflected by declining APP.
➢ Technical efficiency of fixed r’ce is also decreasing as
indicated by declining TPP.
➢ MVP < MFC
➢ MR < MC
➢ This zone is irrational or supra-optimal zone.
➢ Producer shd never operate in this zone even if the r’ces
are available at free of cost.
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Relationship btn Total Product (TP) &
Marginal Product (MP):
• When TP is increasing, MP is +ve.
• When TP remains constant, MP=0.
• When TP decreases, MP is -ve.
• As long as MP increases, TP increases at
increases at increasing rate.
• When MP remains constant, TP increases at
constant rate.
• When MP declines, TP increases at decreasing
rate.
• When MP is zero, TP is maximum.
• When MP <0 (negative), TP declines at increasing
rate.
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Relationship btn Marginal and Average Product

• When MP > AP, AP increases.

• When MP=AP, AP is at Maximum.
• When MP <AP, AP decreases.

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Elasticity of Production (Ep):
➢Ep = 1 ,Constant Returns. Ep is one at MPP = APP
(At the end of I stage)
➢Ep > 1 , Increasing Returns (I Stage of Production)
➢Ep < 1 , Diminishing returns (II Stage of Production)
➢Ep = 0 , When MPP is zero or TPP is Maximum (At
the end of II stage)

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 Y
Ep<1
TPP
Ep>1 Ep<0
Inflexion point
APP input congestion
MPP X

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• Region 1 indicates that the average rate at which
X is transformed into Y, increases until APP
reaches its maximum at the end of Stage-I.
• Region II: output/ unit of fixed input must be the
largest when the total output from the
production process is maximum.
• Region III: excessive quantities of variable input
are combined with the fixed input, so much, that
TPP begins to decrease

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Example
Units of land labor TP AP MP
Fertilizer 0 0 0 0 -
1 1 1 44.9 44.9 44.9
2 1 1 83.6 41.8 38.7
3 1 1 110.1 36.7 26.5
4 1 1 127.3 31.8 17.2
5 1 1 136.9 27.4 9.6
6 1 1 139.9 23.3 3.0
7 1 1 137.1 19.6 -2.8
8 1 1 129.2 16.2 -7.9

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Total product relationships in Peasant
Agriculture
The surplus labour case
TP

TP
a

0 L1 labour input

22
 . AP
The surplus labour case: MP,

MP
AP

AP
a
MP
0 L1 labour input

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• Oa-subsistence wage
• As the labour usage increases, total output soon
reaches its maximum & MP of labour falls to zero.
• As labor input increases, AP approaches
subsistence wage.
• Average income=subsistence wage.
• Implication is that when workers are withdrawn
from the agricultural sector, the remaining
workers will be willing to work longer

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Hard working peasant farmer
TP
TP

0 L1 labor input

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• TP is a straight line from origin, with a slope which
implies that ↑sed lbr input provides only basic
subsistence o/p.
• MP = AP, just equal to subsistence wage.
• No surplus o/p will be forthcoming.
• Once the maximum o/p is reached, the farm can’t
support further increases in lbr & additional lbr will
reduce TP, leading to fall in AP, & MP will be -ve.
• Beyond L1, alternative employment outside the
farm must be sought by the surplus lbr.

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a AP=MP
AP
0 L1 labor input
MP
27
 The objective of factor-product
relationship
➢ To determine the optimum qtty of the variable input that
will be used in combination with fixed inputs in order to
produce optimal level of output.
➢ Further questions such as, how much fertilizer to be applied
per acre? how much irrigation to be given?

There can be three types of input-output relationships in

producing a commodity where one input is varied and the
quantities of other inputs are fixed. i) Constant Marginal
Rate of Returns or Law of Constant Returns.
ii) Increasing Marginal Rate of Returns or Law of Increasing
Returns.
iii) Decreasing Marginal Rate of Returns or Law of Decreasing
Returns
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 Laws of return
Law of increasing returns (Increasing marginal productivity)
Each successive unit of variable input when applied to the fixed factor adds more &
more to TP than the previous unit.

MPP is increasing & hence known as law of increasing returns. Increasing returns
means lower costs per unit of o/p. Thus the law of increasing returns signifies
that cost per unit of additional product falls as more & more output is produced.
Hence law of increasing returns also called law of decreasing costs.

Input(X) Output(Y) ∆X ∆Y ∆Y/∆X=MPP

1 2 1 2 2/1=2
2 6 1 4 4/1=4
3 12 1 6 6/1=6
4 20 1 8 8/1=8
5 30 1 10 10/1=10

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 Graphical representation
Y

X
∆ Y1/ ∆X1 < ∆Y2/∆X2 < ………… < ∆Yn/∆Xn

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 Law of constant returns (constant
marginal productivity)
➢ Each additional unit of variable input when applied to
fixed factors produces an equal amount of additional pdt.
➢ TPP increases by the same magnitude for each additional
unit of input.
➢ MPP remains the same for each additional unit of input &
hence it is called law of constant marginal productivity.
➢ Regardless of the scale of prodn, cost of additional unit of
product remains the same & hence it is also called law of
constant costs.

NB: linear production function or constant returns is not a

common relationship in agriculture.

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Input(X) Output(Y) ∆X ∆Y ∆Y/∆X=MPP
1 10 1 10 10/1=10
2 20 1 10 10/1=10
3 30 1 10 10/1=10
4 40 1 10 10/1=10
5 50 1 10 10/1=10

As shown in the table, each unit of input adds 10 units.

The shape of the total product curve is linear. Linear
production indicates constant returns.

Algebraically constant returns is expressed as

∆Y1/∆X1 = ∆Y2/∆X2 = ………… = ∆Yn/∆Xn
32
Law of Decreasing returns (Decreasing marginal productivity)
Each additional unit of variable input when applied to the fixed
factors adds less & less to total product than the previous
unit.
MPP is declining, hence the name law of decreasing returns.

Input(X) Output(Y) ∆X ∆Y ∆Y/∆X=MPP

1 25 1 25 25/1=25
2 45 1 20 20/1=20
3 60 1 15 15/1=15
4 70 1 10 10/1=10
5 75 1 5 5/1=5

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➢The production function which exhibits
diminishing returns is concave to the origin.
➢Law of diminishing returns is very common in
agriculture.
➢Cost of each additional unit of o/p increases as
we produce more & more o/p & hence it is
called Law of increasing costs.
➢Algebraically, it can be expressed as
∆Y1/∆X1 > ∆Y2/∆X2>= ………… > ∆Yn/∆Xn

34
 Law of diminishing returns contd….

➢This law explains how the amount of product

obtained changes as the amount of one of the
resources is varied while the amount of other
resources is fixed.
➢It is also known as law of variable proportions or
principle of added costs & added returns.

35
Why the law of diminishing returns operates in
agriculture.
➢Excessive dependence on weather.
➢ Limited scope for mechanization.
➢ Limited scope for division of labour.
➢ Agriculture uses larger proportion of land resource.
➢ Soil gets exhausted due to continuous cultivation.
➢ Cultivation is extended to inferior lands.

36
Limitations of the law in Agriculture.
➢ Improved methods of cultivation
➢ New soils and
➢ Insufficient capital.

Question
List and explain the three types of returns in
production relationships

37
Economic Recommendations from F-P relationship

• If the product has any value at all, input use once

begun, it shd be continued until zone II is reached.
That is b’se physical efficiency of variable resources,
measured by APP, ↑ses throughout zone 1.
• Even if input is free, it will not be used in zone III.
Maxm o/p occurs when zone II closes. It is of no use
applying variable i/p when TPP starts coming down.
• Zone II defines the area of econ relevance. Variable
i/p use must be somewhere in zone II, but exact input
amnt can be determined when choice indicators
(input & o/p prices) are known.

38
Algebraic Example

TP : Y = ( X − 2 1
30
3
X )
Y
AP = = X − 30 X
1 2

X
Y Y
MP = = = 2 X − 10 X
1 2

X X

39
Interpretation
At the max TP, MP=0
=>
20 X − X = 0
2

X (20 − X ) = 0
X = 20
TP = 20 − * 20 = 400 − 266.7
2 1
30
3

= 133.3
40
MP meets AP at its maximum
=>
AP
= 1 − 151 X = 0
X
X = 15
TP = 15 − 15 = 225 − 112.5
2 1
30
3

= 112.5
41
• MP at the maximum when MP
=0
X

2 − 15 X = 0
X = 10
TP = 10 − 10 = 100 − 33.3
2 1
30
3

= 66.7
42
Cost of production
TC=TFC+TVC= TFC +PxX
Given a prod fn, Y=f(X)
-1
Inverse prod fn: X=f (Y)
ΔTC PX. Δ𝑋 PX 𝑃𝑋
𝑀𝐶 = = = =
ΔY Δ𝑌 Δ𝑌 𝑀𝑃𝑃
ΔX
NB:MC curve reaches its minimum when MPP is at
maximum and it increases as MPP declines

43
Example
Y = 8X − 2 X
1 2

Y
AP = = 8 − 12 X
X
MP = dY = 8− X
dX
TPMax = 32

44
Inverse production function=
− 1
2X + 8X − Y = 0
2

−b  b 2 − 4 ac
Using the formula 2a

X = 8 − 64 − 2Y ;0  Y  32
TVC = Px X = Px (8 − 64 − 2Y )
dTVC Px
MC = = ;0  Y  32
dY 64 − 2Y 45
 Most Profitable level of production
(a) Optimum input to use
➢ Determining how much of the variable input to
use.
Given a goal of maximizing profit, the farmer must
select from all possible input levels, the one which
will result in the greatest profit.
➢ Use the concept of MVP vs MFC.

46
π = PyY - PxX – F
Profit is maximized when marginal profit = O
Therefore
Δπ = Py . ΔY/ ΔX - Px = 0
Py (ΔY/ ΔX) = Px (MVP = MFC)
and
ΔY/ ΔX = Px/Py = (MP = Input-output price ratio)

47
MVP refers to additional income received from
using an additional unit of input.
• change in the total value product with respect
to change in input level.

Y .Py
MVP =
X

48
 Marginal Input Cost (MIC) or Marginal Factor Cost
(MFC): It is defined as the additional cost associated
with the use of an additional unit of input.
– Change in the total input cost by using an additional unit
of input.
– Price per unit of input

Marginal Factor Cost = ∆ Total Input Cost/∆ Input level

MFC or MIC = ∆X. Px/∆X = Px
X= input Quantity
Px= Price per unit of input

MFC is constant & equal to the price per unit of input. This conclusion holds
provided the input price does not change with the quantity of input
purchased
Decision Rules:
1. If MVP is greater than MIC, additional profit can
be made by using more input.
2. If MVP is less than MIC, more profit can be made
by using less input.
3. Profit maximizing or optimum input level is at the
point where MVP=MFC
(∆Y/∆X) . Py = Px ∆Y/∆X = Px/ Py
Determination of optimum input level – Example
Input price: Shs.12 per unit, Output price: Shs 2 per unit
Input level TPP MPP TVP ( shs) MVP (shs) MIC (shs) px/py
0 0 -- -- -- --
1 12 12 24 24 12 6
2 30 18 60 36 12 6
3 44 14 88 28 12 6
4 54 10 108 20 12 6
5 62 8 124 16 12 6
6 68 6 136 12 12 6
7 72 4 144 8 12 6
8 74 2 148 4 12 6
9 72 -2 144 -4 12 6
10 68 -4 136 -8 12 6
Using less than 6 units of input causes MVP to be
greater than MFC. These relationships exist until
the input level reaches 6 units. At this input level
MVP=MFC.

Using more than 6 units of input causes MVP to

be less than MFC which causes profit to decline as
more input is used.
How much output to produce (Optimum output): The determination of optimum
output to produce. To answer this question, requires the introduction of two new
marginal concepts.

Marginal Revenue (MR): It is defined as the additional income from selling

additional unit of output. It is calculated from the following equation;

Marginal Revenue = Change in total revenue / Change in Total Physical Product

MR = ∆TR / ∆Y = Py ∆Y / ∆Y = Py ( TR= Py Y}
Y = output
Py = price per unit of output
Total Revenue is same as Total Value Product. MR is constant and equal to the price
per unit of output.

Marginal Cost (MC): It is defined as the additional cost incurred from producing an
additional unit of output. It is computed from the following equation;
Marginal Cost=Change in Total Cost / Change in Total Physical Product
MC = Px .∆X/∆Y
X= Quantity of input
Px= Price per unit of input.
Decision Rules:
1. If Marginal Revenue is greater than Marginal Cost,
additional profit can be made by producing more output.
2. If Marginal Revenue is less than Marginal Cost, more
profits can be made by producing less output.
3. The profit maximizing output level is at the point
where MR=MC
From: ΔY/ ΔX = Px/Py
∆Y. Py=∆X. Px
Diving by ∆Y both sides:-
Py= Px .∆X/∆Y (MR=MC)
or
Py= Px / ∆Y/∆X = Px / MPP
Determination of Optimum output to produce: (An example)
Input Price Shs 12 per unit, output price Shs 2 per unit
Input level TPP MPP TR (shs) MR (shs)(py) MC (shs)(Px/MPP
0 0 - - -- --
1 12 12 24 2.00 1.00
2 30 18 60 2.00 0.67
3 44 14 88 2.00 0.86
4 54 10 108 2.00 1.20
5 62 8 124 2.00 1.50
6 68 6 136 2.00 2.00
7 72 4 144 2.00 3.00
8 74 2 148 2.00 6.00
9 72 -2 144 2.00
10 68 -4 136 2.00
In the above table, it is clear that MR is greater than
MC up to the output level 62 units. At the output
level of 68 units, the MR=MC. This is the optimum
output to be produced. If we produce 72 units of
output, additional revenue from additional output is
less than the additional cost of producing output.
Therefore profit decline.
COST PRINCIPLE OR MINIMUM LOSS PRINCIPLE:
This principle guides the producers in the minimization of losses. Costs are divided
into fixed and variable costs. VC are important in determining whether to produce
or not. FCs are important in making decisions on different practices and different
amounts of production.

In S-R, the gross returns or total revenue must cover TVC. To state in a different
way that selling price must cover AVC to continue production in the short run.

In the long run, gross returns or total revenue must cover TC. Alternatively stated,
that the selling price must cover cost of production (ATC).

In the short run MR = MC point may be at a level of output which may involve loss
instead of profit. The situation of operating the farms when the price of product
(MR) is less than ATC but greater than AVC) is common in agriculture.
This explains why the farmers keep farming even when they run into losses.
PROFIT OR DECISION RULES
SHORT RUN:
1. If expected selling price is greater than minimum ATC, profit is expected
and is maximized by producing where MR = MC.
2. If expected selling price is less than minimum ATC but greater than
minimum cost AVC, a loss is expected but the loss is less than TFC and is
minimized by producing where MR = MC.
3. If expected selling price is less than minimum AVC, a loss is expected but
can be minimized by not producing anything. The loss will be equal to TFC.

LONG RUN
1. Production should continue in the long run when the expected selling
price is greater than minimum ATC.
2. Expected selling price which is less than minimum ATC result in
continuous losses. In this case, the fixed assets should be sold and money
invested in more profitable alternative.
The following example illustrates the operation of cost principle.
Cost of cultivation of groundnut (Ushs/ha)
Total variable costs 2621
Total fixed costs 707
Total costs 3328
Yield (tonnes) 9
Average variable cost 291
Average total cost 369.77
Selling price 430
Gross returns 3870
Net returns 542
Suppose the price declines to 350
Gross returns 3150
Net income -178

If the price of groundnut per kg is Ushs 430, for 9kgs, farmer gets Ushs. 3870 as gross income. The net income
is Ushs 542 (3870 – 3328). Suppose the price decline to Ushs 350 per kg, the net income would be Ushs -178
(3150 – 3870).

Now the question is whether the farmer should continue the production or not at the price of Ushs 350.

If the farmer does not operate the farm the loss would be Ushs 707 in the form of fixed costs. If farm is
operated, gross income of Ushs 3150 exceeds the variable costs (Ushs 2621) by Ushs 529. By this amount the
loss of Ushs 707 on account of fixed costs gets reduced i.e., (Ushs 707-529 = 178). The loss would be reduced to
Ushs 178 by operating the farm.
1
Introd
 This relationship deals with resource combination &
resource substitution.
 Choosing optimal proportion of inputs in order to
efficiently produce output.
 The goal of factor-factor relshp is Cost minimization
 It is concerned with the determination of least cost
combination of resources.

2
 Output is kept constant, input is varied in quantity.
 Guides the producer in deciding ‘How to produce’.
 This relationship is explained by the principle of
factor substitution or principle of substitution btn
inputs.
 The choice indicators are substitution ratio & price
ratio.

3
 Objectives of factor-factor
relationship
➢Minimization of cost at a given level of output.
➢Optimization of output to the fixed factors thru
alternative resources combinations.

4
 Isoquant (Iso-product curve):
All possible combinations of two resources to produce a
given level of output.
 Characteristics of Isoquants
✓ Slope downwards from left to right or -vely sloped.
✓ Convex to the origin.
✓ Nonintersecting
✓ Isoquants lying above & to the right of another
represents higher level of output.
✓ The slope of isoquant denotes MRTS.

5
 MRTS defined:
The amount by which one resource is reduced as another
resource is increased by one unit.

MRTS X1X2 = ∆X2/∆X1

MRTSX2X1 = ∆X1/ ∆X2

6
 Substitutes:- MRTS <0, increase in =>reduce the other.
 Perfect subsitutes: MRTS –constant, isoquant a line,
negatively sloped.
 Complements: MRTS=0, used together.
 Perfect complements: used together in fixed propon

7
 Types of factor-factor relshp.
 Fixed proportion combination of inputs,
-no substitution
- Perfect complementarity
- Isoquants L-shaped(leontif )

 Constant rate of substitution.

- Linear isoquants.
- MRTS constant
 Varying rates of substitution( increasing or decreasing
- For decreasing:- ΔX21/ΔX11> ΔX22/ΔX12> ----- >ΔX2n/ΔX1
8
 MRTS12= ΔX2/ΔX1 = For (replaced)/ of (added)=
MP1/MP2
Proof:
➢ Y=F(X1, X2)
➢ dY= ΔY/ΔX1 dX1+ ΔY/ΔX2 dX2
➢ Output constant => dy=0
➢ dX2/ dX1 =- ΔY/ΔX1/ ΔY/ΔX2= MP1/MP2

9
 Isocost
C=P1X1+P2X2

Slope of isocost = price ratios : ΔX2/ΔX1=P1/P2.

 The characteristic features of Isocost lines are:

i. When the total outlay increase, the Isocost line shift away
from the origin i.e shift upward from the left to the
right.
ii. The slope of Isocost line shows the inverse price ratio of
the two variable inputs i.e only changes in the unit price
of either input factors or both can change the slope of the
Isocost line.

10
Least Cost Combination
In a factor- factor relationships there are various possible
combinations of input factors that can produce a given
level of output.

The major concern here is to determine the particular

combination that will require the least cost i.e. the point
of minimum cost.

11
Least Cost Combination

The following methods can be used to determine the least

cost combination of resources:
i. Tabular method
ii. Graphical method
iii. Algebraic method

MRTS =PR

12
 Tabular method
➢ This method involved the computation of the total
amount of fund when the various units of resources &
their unit prices are given.
➢ However, this method can only be used if few
combinations are involved.
➢ When the total costs are computed for the various costs
combinations, we can then select the least cost
combination.
i.e Calculate total costs-> choose lowest costs

13
 Example
units of units of cost of X1 cost of X2 Total cost
X1 X2 @shs 3 @ shs2
10 3 30 6 36
7 4 21 8 29
5 6 15 12 27
3 8 9 16 25
2 12 6 24 30

From the table, it is advisable to choose the combination of 3

units of X1 and 8 units of X2 which gives the least cost
combination of 25.
14
 Exercise
(i)Use the profit function Π = PyY - Px1X1 - Px2X2 - F to
proof that VMPx1/Px1 = VMPx2/Px2 = 1
ii. Determine the minimum cost combination of inputs X1
and X2 for an output level of 250 units in the table below
(Price of input X1 shs50 and that of X2 = shs 100):
Units x1 Units x2
1 30
2 25
3 20
4 15
5 10
6 5
15
Graphical method
➢ The least cost combination occurs where MRTS equals the
input price ratio.
➢ This point is met at the point of tangency of isoquant
curve and iso-cost line.
➢ At this point MRTS is equated with the price ratio.
X2
isoquant
least cost combination

isocost
x1
16
Algebraic method
➢ Compute the MRTS
MRTS X1X2= ∆X2/∆X1 (when we substitute X1 for X2)
or
MRTSX2X1 = ∆X1/∆X2 (when we substitute X2 for X1)
➢ Compute the inverse price ratio (PR) of the inputs.
PR = Px1/ Px2 when we substitute X1 for X2
PR = Px2/ Px1 when we substitute X2 for X1

➢ MRTS= PR
∆X2/∆X1= PX1/PX2 for MRTSX1X2
∆X1/∆X2 = PX2/ PX1 for MRTSX2X1
17
Isocline
Isocline is defined as a line which connects points of equal slope on a
production surface. This definition implies that isoclines pass through
points of equal MRTS on an isoquant map. This also means that it is
possible to have more than one isocline on a production surface as there
are different MRTS on an isoquant. However, the isoclines for each MRS
is constant.

Input Expansion Path

Expansion path can be described as an isocline that connects the points
of least cost combination for different values of output. Expansion path
is a line or curve on which the slope of isoquant (MRTS) equals the
slope of iso-cost line (price ratio). The expansion path indicates the best
way of producing different levels of output given the prices of inputs.

18
Ridgeline
Ridgeline is a line which connects points of zero slope on
the successive isoquants.
Ridgeline shows boundaries for the stages of production
function in factor-factor relationship where MPP & MRTS
for each input = 0.
It marks the limit of the efficiency of resource use.
Ridge line represents the point of maximum output for
each input given a fixed quantity of other inputs.
Ridge line represents the limit of input substitution.
Beyond the line, it is not possible to substitute inputs

19
X2
Ridge line for x2

Ridge line for x1

X1

20
Questions
1. Explain the significance of the following economic terms in agricultural
production and farm management:- Isoquant; Isocost line; Expansion path;
and Marginal Rate of Technical Substitution.
2. Determine the minimum cost combination of inputs X1 & X2
for an output level of 200 units given the following table:
Units of X1 Units of X2
4 24
6 18
8 16
10 15
12 17
14 14
16 10
18 12
20 14
Px1=shs 50 and Px2 =shs 100

21
Economic Optimum
 Profit maximisation(cost minimisation)
➢ Proft function
Π= TR-TC
➢ FOC=> 1st partial derivatives
➢

22
Y = f (X1X 2 )
Pr ofit = Py Y − P1 X 1 − P2 X 2 − TFC

 Y Y
= Py − P1 = 0 = Py = P1
X 1 X X 1
 Y Y
= Py − P2 = 0 = Py = P2
X 2 X X 2

23
Example 1
➢ Y= 18X1-X12+14X2- X22
Revenue maximised when the MPs=0

ie When X1=9 and X2= 7, Y= 130.

NB: Revenue Maximisation not the same as profit

maximisation. For profit maximization, we need the
input and output prices

24
Example 2:
The farmer is faced with the following production function;
the price of out is $0.65, Px1=9 and Px2=7. Find the profit
maximization point of the farmer.

Y = 18 X 1 − X + 14 X 2 − X + X 1 X 2
1
2 2
2

Y
= MP1 = 18 − 2 X 1 + X 2
X 1
Y
= MP2 = 14 − 2 X 2 + X 1
X 2

25
Equating MPs to zero

2 X 1 − X 2 = 18
− X 1 + 2 X 2 = 14 − 2 X 1 + X 2 = −18
X 1 − 2 X 2 = −14
3 X 2 = 46  X 2 = 46
3

3 X 2 = 46  X 2 = 46
3 X 1 = 50  X 1 = 50
3
Ymax = 257.3

3
3 X 1 = 50  X 1 = 50
3
Ymax = 257.3 26
 Profits are maximised when,
VMPxi = Pxi
0.65(18 − 2 X 2 + X 1 ) = 9
0.65(14 − 2 X 1 + X 2 ) = 7

11.7 − 1.3 X 2 + .65 X 1 = 9

9.1 − 1.3 X 1 + .65 = 7

X 1 = 3.85; X 2 = 354
Y = ???, = ????? 27
 Example 3

Y = X1 X 25
1 3
5

P1 = $3; P2 = $1; Py = $10

3X1 1
=  X 2 = 9 X1
X2 3
 = 10Y − 3 X 1 − X 2 − TFC
= 10 X 1 5 (9 X 1 ) 5 − 12 X 1 − TFC
1 3

28
Example 3
Assume a Cobb-Douglas production
function
Y = X 1 X 25
1 3
5

P1 = $3; P2 = $1; Py = $10

Find the profit maximising level of inputs and
output.

29
Y −2
X 2
1
3
X 2 X1 5
5
3X 1
= 5
=
Y 1 −4
X 1 X 25
5
3
X2
X 1 5

3X 1 1
=
X2 3
X 2 = 9X1

30
 = Py Y − P1 X 1 − P2 X 2 − TFC
= 10Y − 3 X 1 − X 2 − TFC
But

X 2 = 9X1
Thus

 = 10Y − 12 X 1 − TFC
= 10 X 1 (9 X 1 ) − 12 X 1 − TFC
1 3 5
5

31
d 4 3 5 −1
= 5 (10)9 X 1 − 12 = 0
5
dX 1
3 3
89 5
89 5 5
2 9
3

1
= 12; X 15
1 = = X 1 = 5 = 96
X1 5 12 3
3 4
X 2 = 9 X 1 = 9 * 96 = 864; Y = 9 5 * 96 5 = 144

32
Using the Cost Minimisation Theory -Duality

➢ Cost function as a function of input prices and given level

of production.
➢ The farmer will mininise costs at a point where MC =Py

➢ Using the example above;

➢ TVC= P1X1 +P2X2= 12X1

33
 But
3 4
Y = 9 5 X1 5
5 5
4 4
Y 12Y
X1 = 3
; TVC = 3
4 4
9 9
1
4
dTVC 15Y
MC = = 3
dY 9 4

34
 Thus at the optimum
1
4
15Y
3
= 10
4
9
4
3
 2*9 3
 4 3
=  =
4 4
1 10 * 9 2 * 9
Y 4
= = 144
15  3  3 4
 

35
PRINCIPLE OF FACTOR SUBSTITUTION
States that go on adding a resource so long as the cost of
resource being added is less than the saving in cost from the
resource being replaced.
Thus,
➢ If input X1 is being increased, and input X2 is being
replaced, increase the use of X1 so long as.
Decrease in cost > Increase in cost
➢ It guides in the determination of least cost combination of
resources.
➢ It helps in making a management in making decision of
how to produce.

36
➢ Substitution of one input for another input occurs frequently in
agricultural production.

➢ For example, one grain can be substituted for another or forage

for grain in livestock ration, chemical fertilizers can be
substituted for organic manure, machinery for labour,
herbicides for mechanical cultivation etc.

➢ The farmer must select that combination of inputs or practices

which will produce a given amount of output for the least cost.

➢ In other words, the problem is to find the least cost

combination of resources, as this will maximize profit from
producing a given amount of output

37
Decision rule under the principle of
factor substitution
If Marginal rate of substitution (MRS) is greater than
price ratio (PR), costs can be reduced by using more of
added resource.

𝚫𝑿𝟐 𝑷𝟏
 If >𝐏 , increase the use of X1
𝚫𝒙𝟏 𝟐

𝚫𝑿𝟐 𝑷𝟏
 If <𝐏 , increase the use of X2
𝚫𝒙𝟏 𝟐

38
If Marginal rate of substitution (MRS ) is less than price
ratio (PR), costs can be reduced by using more replaced
resource.
𝚫𝑿𝟐 𝑷𝟏
 If <𝐏 , increase the use of X2
𝚫𝒙𝟏 𝟐

𝚫𝑿𝟐 𝑷𝟏
 If >𝐏 , increase the use of X1
𝚫𝒙𝟏 𝟐
 The least cost combination of resources will be at that
point where MRS=PR.

39
Example : Selecting a Least-cost feed ratio : (Price of grain: Shs.4.40
per kg , price of hay : Shs.3/- per kg)
The least cost combination of grain and hay is a combination of 1200 kgs
of grain and 520 kgs of hay, as the substitution ratio equals price ratio.
Grains in kg(X1) Hay in Kgs( ∆X1 ∆X2 MRS(∆X2/∆X1 PR(Px1/Px2 )
X2)

825 1350 - -

900 1130 75 220 2.93 1.47

975 935 75 195 2.6 1.47

1050 770 75 165 2.2 1.47

1125 630 75 140 1.87 1.47

1200 520 75 110 1.47 1.47

1275 440 75 80 1.07 1.47

40
 Product- Product Relationship
 Deals with resource allocation among
competing enterprises.
 Choosing the optimal combination of
products to produce given fixed amounts of
land, labor, capital and management.
 Inputs are kept constant while products
(outputs) are varied.
41
 Goal of Product-Product relationship is profit
maximization.
 Guides the producer in deciding “What to produce”
 This relationship is explained by the principle of
product substitution and law of equi marginal returns.
 Determination of optimum combination of products
(enterprises).
 Choice indicators are substitution ratio & price ratio

42
➢ Production Possibility Curve .
➢ Opportunity Curve
➢ Isoresouce Curve
➢ Iso factor curve
➢ Transformation curve

43
 Production Possibilities - The full range of
products a farm can produce given the set of
resources in the farm's control.

peas

beans
44
Marginal rate of product substitution
(MRPS).
Measures the rate at which one product is
substituted for the other on the PPC.
MRPS= No. units of replaced product / No. of
units of added product

MRPS Y1 Y2 = ΔY2 / ΔY1

45
X=g[Y1,Y2]
dX/dY1=
dX/dY2=
dY2/dY1= MPPy2,x/MPPy1,x= slope of the PPC

46
Types of PP relations
 Joint products- single production process eg beef and
hides.
 Complementary products-change in same direction.
 Supplementary products-don’t compete for resources
 Competitive products-increase in one leads to
decrease in the other.
 Antagonistic products.

47
 Types of Product Substitution
 Constant rate of Substitution.
PPC is linear , negatively sloped.

Constant rate of substitution occurs when :-

One of the production function has an elasticity greater than
one (increasing returns), the other has an elasticity of less than
one (decreasing returns)
Or
Both the production functions have stages of increasing and
decreasing returns.

If two products substitute at constant rate, only one of the

products will be economical to produce depending on their
relative prices-specialization.

48
Y1 Y2 ∆Y1 ∆Y2 MRPS
0 40 -- -- --
10 30 10 10 10/10=1
20 20 10 10 10/10=1
30 10 10 10 10/10=1
40 0 10 10 10/10=1

49
 Increasing rate of product substitution:
➢Each unit increase in the output of one product is
accompanied by larger & larger sacrifice (decrease) in
the level of production of other product.
➢Increasing rates of substitution holds true when the
production for each independent commodity is one of
decreasing resource productivity (decreasing returns) &
non-homogeneity in quality of limited resource.
➢ PPC Curve is concave to the origin when product
substitutes at the increasing rate-common to agric pdn.
➢ general pattern of production is diversification i.e.,
profits are maximized by producing both the products

50
Y1 Y2 ∆Y1 ∆Y2 MRSY1Y2
0 60 -- -- --
8 48 8 12 1.50
15 36 7 12 1.71
21 24 6 12 2.00
26 12 5 12 2.40
30 0 4 12 3.00

51
 Decreasing rate of Product Substitution
➢ Each unit increase in output of one product is
accompanied by lesser & lesser decrease in production of
another product.
➢ This type of product substitution holds good under
conditions of increasing returns.
➢ PPC is convex to the origin when products substitute at
decreasing rate.

52
Y1 Y2 ∆Y1 ∆Y2 MRSY1Y2
1 18 -- -- --
2 13 1 5 5
3 9 1 4 4
4 6 1 3 3
5 4 1 2 2

53
 Iso-revenue
Represents all possible combination of two products which
would yield an equal (same) revenue or income.
R=P1Y1 +P2Y2

Characteristics:
 It is a straight line b’se product prices do not change with
qty sold.
 As total revenue increases, the isorevenue line moves
away from the origin since the total revenue determines
the distance from the origin.
 The slope indicates ratio of product prices.
54
Objective function of the producer
 Revenue maximisation subject to the production
function.

55
Determination of optimal
combination of products
1- Algebraic Method:
➢ Compute Marginal Rate of Product Substitution
➢ Workout price ratio (PR)
➢ Optimum combination of enterprises is at where
MRPS=PR

56
2) Graphic Method.

3) Tabular Method
Compute total revenue for each possible output
combination and then select that combination of outputs
which yields maximum total revenue.

57
 example
Y1 Y2 Py1@ shs 50 Py2@shs 80 Total revenue
8 2 400 160 560
5 3 350 240 490
6 4 300 320 620
4 5 200 400 600
3 7 150 560 710

58
Let us consider our production possibility data where the price of
maize (Y1)=shs 2.0 and the price of cowpea (Y2)=shs 5.0 Determine
the optimal combination of maize and cowpeas, and the maximum
income of the farm.

Maize cowpea
Y1 Y2
0 44
13 40
20 34
26 26
31 16
35 0

59
 LAW OF EQUI-MARGINAL RETURNS
➢ A limited input should be allocated among alternative
uses in such a way that MVPs of the last unit are equal
in all its uses.
-deciding on the best allocation of inputs between
different enterprises.
-Each successive input allocated to product which has
highest MVP remaining after previous allocation.

60
Example
A farmer with 3,000/- to spend on 3 crops with MVPs
as follows
Amounts (Ushs) Sugar canes Wheat Cotton
500 800(1) 750(2) 650(6)
1000 700(3) 650(5) 560
1500 650(4) 580 550
2000 640 540 510
2500 630 520 505
3000 605 510 500
1,500 1,000 500
61
 Opportunity cost.
- Amount forgone for the next best alternative

62
Principal of product substitution
 Guides on what to produce.
 It is economical to substitute one product for another,
if decrease in returns from the product being replaced
is less than increase in returns from the one being
added.
 if ΔY2/ΔY1 < P1/P2 , increase Y1
 if ΔY2/ΔY1 > P1/P2 , increase Y2

63
Example: select optimum combination , given
Py1=280/= , Py2=400/=,
Y1 Y2 ΔY1 ΔY2 MRS Y1, Y2 PR decrease increase
0 60 - - - .7 - -
20 56 20 4 .2 .7 1600 5600
40 50 20 6 .3 .7 2400 5600
60 41 20 9 .45 .7 3600 5600
80 30 20 11 .55 .7 4400 5600
100 16 20 14 .7 .7 5600 5600
120 0 20 16 .8 .7 6400 5600

64
Economic Optimum-Examples
Miximisation of revenue will occur when;

Y2 P1
=−
Y1 P2
or
− PY 1 Y1 = PY 2 Y2
Y1 Y2
PY 1 = PY 2
X X
PY 1 MPXY 1 = PY 2 MPXY 2

65
Example

Y1 = 100 − 0.0065Y22

The maximum amount of Y1 =100.

The above suggest that Y1 and Y2 are competitive for the limited input.
Increase in one product requires a decrease in the other.

dY1
= −0.013Y2
dY2

66
Assume the price of Y1 and Y2 are $5 and $6 respectively, then

dY1 PY 2
=−
dY2 PY 1
6
− 0.013Y2 = −
5
Y2 = 92.3
Y1 = 100 − 0.0065(92.3) 2 = 44.6

67
Opportunity Cost Principle:
When resources are limited and there are more than one
enterprise where farmer can invest.
When recourses are used in one product some alternative is
always forgone.
The opportunity cost is the value of next best alternative
forgone.
The value of one enterprises sacrificed is the cost of
producing another enterprise.
This principle thus refers to the advantages (returns) which
might have been obtained from any factor if it had net been
used in producing that commodity.
1
Time Comparison Principle
There are two types of investments:
(1) Investments on operating inputs
(2) Investment on capital assets (land, farm building,
machinery, equipment, etc).
Analysis of these investments involves not only the
comparison of costs and returns associated with it, but also
the timings of occurrence of costs & returns.
The costs & returns from investments in operating
resources occur with a production period of a year or less.

2
The marginal principles are used to determine the optimum
level of operating resources & there is no need to bring in
time element here.
But in case of capital assets where the costs & returns are in
different time periods and also capital expenditure involves
costs & returns over time (orchards).
Some expenditure may be recurring & some non- recurring.

3
To examine the profitability of these investments it requires
the recognition of time value of money.
➢ Money has time value for the following reasons.
(1) Earning power of money: represented by opportunity
cost of money (rate of interest )
(2) Inflation – purchasing power of money varies
inversely with the price level. A rupee earned a year
from now is less valuable than a rupee earned today.
(3) Uncertainty: Investment deals with future & future is
uncertain.

4
Investments are made with the expectation of receiving a stream of
benefits in the future.
Thus, Agric prod & farm management involves dynamic adjustments
in the organization & operation of farm business by taking into
account the time element in the valuation of present value of future
incomes by discounting future returns.
For discounting one needs to know the future & the capital position of
the farmer. This implies the exact future income / cost should be
known.
Capital position of the farmer affects the interest rate to be used for
discounting and the risks & uncertainties in farm operations over
time (natural calamities, price fluctuations, technical changes.
Two aspects of the problem are considered under such situations:
(a) Growth of a cash outlay over time i.e. compounding
(b) Discounting of future income
5
 Compounding: Compounding is the procedure to find the
future value of a present sum, given the earning power
(interest rate) of money & the frequency of compounding.
For example
Shs 100 at 10% interest rate after 4 years.
1st year = 100+10 =110; 2nd = 110 at 10% = 110+11=121;
3rd year = 121 at 10% = 121+12.10 = 133.10;
4th year = 133.10 at 10% = 133.10+13.31 = 146.41

S=P 1 + 𝑖 𝑛 = 100 1 + 0.1 4 =100*1.4464=146.4

6
Discounting: is the procedure where the present value of
the future income is determined.
𝑃
PV= 𝑛 ; P is the amount to be received in future, PV is
1+𝑖
the present value e.g. shs 5000 to be received after 3 years
i = 10%

5,000 5,000
PV= = = 3,756.57
1+.10 3 1.331

7
Example: Analysis of time value of money in purchasing a tractor:
A farmer wants to purchase a tractor & he has two options:-
(1) purchase a new tractor 2,500,000 that will last 10 years or
(2) purchase an old tractor worth 1,500,000 & replace it after 5 years with
another old tractor worth 1,500,000.
(A) Farmer with unlimited capital : Has the opportunity of lending money at 5%
1,500,000
PV= = 1,176,000
1+.05 5
so 2,500,000 vs 1,500,000 + 1,176,000 = 2, 676,000

(B) With limited capital: Has on opportunity of investing in poultry & earning
15% a year. The opportunity cost of not using money for poultry is:-
1,500,000
PV= =745, 500
1+.15 5

So his compromise is 1,500,000 + 745,500 =2,245,500

New tractor: 2, 50,000