Chapter 6: Agricultural Production Economics
Production with One Input and One Output
A Production Function:
Transformation of
input into output
A technical relationship
(not behavioral)
Output:
CornTobaccoWheatBeefMilk
Input:
SeedFertilizerFeedMachinery
FERTILIZER
11-48-0
P205 N K20
JOHN DEERE
Fixed versus Variable InputsFixed--
Farmer does not expectto vary
Over the planning horizon
Variable--
Farmer expects to vary
Over the planning horizon
???
??
?
Length of Planning Horizon:in the mind of the farmer6 months?The Growing Season?2 years?10 years (for Christmas trees)?Only the farmer knows for sure
6 months ?
2 years ? 50 years ?
Old idea--
Inputs could be categorizedLand--fixedLabor--variableMachinery--fixed (sort of!)
Not a correct idea
JOHN DEERE
Correct idea:Planning horizon determines whether inputs
Short Run--All inputs fixedIntermediate Run--Some fixed,
some variableLong Run--All inputs variable
are fixed or variable
Inputs:Traditional list
LandLabor
CapitalManagement
With capital you can purchaseland and laborIs management an input??
A Production Function:
Y = f(X)Y = output such as bu. of corn
X = input such as fertilizer
f(x) = rule for transforming X into Y
such as:
Y = 3X
Y = X
Y = .3X + .05X - .002X
Each of theseare production functions
0.5
2 3
Y = f(X | X X X )
The Variable inputThe output
Inputs treated as fixed
Y
X | X X X3
Y or TPP
TPP = TotalPhysical
Product
1 2 3 4
1 2 3 4
Y
X | X X X
Y or TPP
Y'
Y''
Y'''
X' X'' X'''
Specific amount of output froma specific amount of input
1 2 3 4 1 1 1
Marginal ProductThe incremental change in output
associated with a1 unit change
in the use of the input
Marginal Product of input x:
x = change in x
y = change in y
y = change in y
x = change in x= Marginal Product
Also called Marginal Physical Product
or MPP for short
Diminishing,
Constant
and Increasing
Marginal Product
ConstantMarginal Product
Case 1:
Output
Input (x)0 1 2 3 4
2
4
6
8
(y)
Constant slope
y
Constant Marginal Product
Output
Input (x)1 2 3 4
2
4
6
8
(y)
0
Constant slope
y
Triangles all thesame size and slope
= 2x
2
1
1 unit across2 units up2
2
2
1
1
1
Constant Marginal Product
Output
Input (x)1 2 3 4
2
4
6
8
(y)
0
Constant slope
y = 2x
2
1
2
2
2
1
1
1Each additionalunit of Xproduces twoadditional unitsof Y
Constant Marginal Product
Input (x)1 2 3 4Constant Marginal Product of b
Output (y)
0
Constant slope of by
1
1
1
1
b
b
b
b
b
b
b
b
=bx
Each additionalunit of x
additional Unitsof y
produces b
The MarginalProduct of anadditional unitof x is b
Constant Marginal Product
x x y y y/ xMPP
Constant Marginal Product
x x y y
0 0
1 2
2 4
4 8
5 10
3 6
y / xMPP
Constant Marginal Product
x x y y
0 0
1 2
2 4
4 8
5 10
3 6
1
1
1
1
1
y /MPP
x
Constant Marginal Product
x x y y
0 0
1 2
2 4
4 8
5 10
3 6
1
1
1
1
1
Y /MPP
2
2
2
2
2
x
Constant Marginal Product
x x y y
0 0
1 2
2 4
4 8
5 10
3 6
1
1
1
1
1
Y /MPP
2
2
2
2
2
2/1
2/1
2/1
2/1
2/1
MPP = 2 everywhere
x
Constant MPP
x
y = b
x
y
b
y = bx
b = MarginalProduct of anAdditionalUnit of x
Marginal Product
Case 2:Increasing
Output (y)
Input (x)0 1 2 3 4 5
0.72
3.5
0.7 1.3
4.5
Increasingmarginalreturnsto the
variableinput
Increasing Marginal Product
3
6.5
11
1.5
x x y y
0 0
Y / xMPP
1 0.7
2 2.0
3 3.5
4 6.5
Increasing Marginal Product
5 11.0
x x y y
0 01
1
1
1
1
Y / xMPP
1 0.7
2 2.0
3 3.5
4 6.5
Increasing Marginal Product
5 11.0
x x y y
0 01
1
1
1
1
Y / xMPP
.7
1.3
1.5
3.
4.5
1 0.7
2 2.0
3 3.5
4 6.5
Increasing Marginal Product
5
MPP increases as x increases
11.0
x x y y
0 01
1
1
1
1
Y / xMPP
.7
1.3
1.5
3.
4.5
1 0.7
2 2.0
3 3.5
4 6.5
.7/1
1.3/1
1.5/1
3.0/1
4.5/1
Increasing Marginal Product
5
MPP increases as x increases
11.0
Case 3:
Decreasing(Diminishing)MarginalProduct
Output (y)
Input (x)0 1 2 3 4 5
y = f(x)
5
2
1
.5
.3
1
1
1
1
1
5
7
88.58.8
Slope increasesbut at adecreasing rateAdditional unitsof x produceless and lessadditional y
Decreasing (Diminishing) Marginal Product
x x y y y / x MPP
Decreasing Marginal Product
x x y y y / x MPP
0 0
1 5
2 7
3 8
4 8.5
5 8.8
Decreasing Marginal Product
x x y y y / x MPP
0 0
1 5
2 7
3 8
4 8.5
5 8.8
1
1
1
1
1
Decreasing Marginal Product
x x y y y / x MPP
0 0
1 5
2 7
3 8
4 8.5
5 8.8
1
1
1
1
1
5
2
1
0.5
Decreasing Marginal Product
0.3
x x y y y / x MPP
0 0
1 5
2 7
3 8
4 8.5
5 8.8
1
1
1
1
1
5
2
1
0.5
5/1
2/1
1/1
.5/1
.3/1
Decreasing Marginal Product
As the use of x increases, MPP decreases
0.3
A Neoclassical ProductionFunction
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
Increasing MPP(and TPP)
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
Increasing MPP(and TPP)
InflectionPoint
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
Increasing MPP(and TPP)
InflectionPoint
Decreasing MPPIncreasing TPP
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
Increasing MPP(and TPP)
InflectionPoint
Decreasing MPPIncreasing TPP
Maximum TPP0 MPP
X | X X X X 1 2 3 4 5
A Neoclassical ProductionFunction
Y
Increasing MPP(and TPP)
InflectionPoint
Decreasing MPPIncreasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
X | X X X X 1 2 3 4 5
Law of Diminishing
(Marginal) ReturnsAs units of the variable input (X )are added to units
of the fixed inputs ( X , X , X , X )we eventually reach a pointwhere each ADDITIONAL unitof the variable input (X )produces Less and Less ADDITIONAL output!
1
2 3 4 5
1
Y
Increasing MPP(and TPP)
InflectionPoint
Decreasing MPP Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
Law of DiminishingReturns holdsStarting Here
X | X X X X 1 2 3 4 5
Y
Increasing MPP
(and TPP)
InflectionPoint
Decreasing MPP
Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
X | X X X X 1 2 3 4 5
Y
Increasing MPP
(and TPP)
InflectionPoint
Decreasing MPP
Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
MPP
0
X | X X X X 1 2 3 4 5
Y
Increasing MPP
(and TPP)
InflectionPoint
Decreasing MPP
Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
MPP
0
X | X X X X 1 2 3 4 5
MPP
X | X X X X 1 2 3 4 5
Y
Increasing MPP
(and TPP)
InflectionPoint
Decreasing MPP
Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
MPP
0
X | X X X X 1 2 3 4 5
MPP
X | X X X X 1 2 3 4 5
Y
Increasing MPP
(and TPP)
InflectionPoint
Decreasing MPP
Increasing TPP
Maximum TPP0 MPP
Negative MPPDeclining TPP
MPP
0
X | X X X X 1 2 3 4 5
MPP
X | X X X X 1 2 3 4 5
AveragePhysical
ProductThe ratio of output to variable input
Y/XY/X | X X X X
Average productof ALL units of X used(not the incremental unit)
1 2 3 4 5
X Y Y/X
2 16 83 21 74 24 65 25 56 18 3
0 0 undefined1 7 7
Input Output (TPP) APP
TPP and APP
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
TPP
APP
PointInflection
X
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
Line out of Origin
TPP
APP
PointInflection
X
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
Line out of Origin
Point of Tangency
TPP
APP
PointInflection
X
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
Maximum APP
Line out of Origin
Point of Tangency
TPP
APP
PointInflection
X
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
Maximum APP
Line out of Origin
Point of Tangency
TPP
APP
PointInflection
X
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
XY (Scatter) 1 XY (Scatter) 2
Y
Line out of Origin
Ratio Y/X
= Slope of Line
From OriginTPP
APP
APP = Y/X
Y
X
X
YAPP MAXIMUM
InflectionPoint
X
X
APPAPP,MPP
0
APP:Never Negative
YAPP MAXIMUM
InflectionPoint
MPP = 0
MPP MAXIMUM X
X
MPP=APP
MPP = APP
APP
MPP
APP,MPP
0
Do They have a Relationship???
MPP
APP
Marginal Physical ProductAverage Physical ProductMPP
X X
MPP APP
APP
0X | X X X X 1 2 3 4 5
MPP,
APP
APP
0X | X X X X 1 2 3 4 5
and Increasng APP
Positive
APP
MPP,
APP
APP
0X | X X X X 1 2 3 4 5
and Increasng APP
Positive
MPP,
APP
Maximum
APP
APP
0X | X X X X 1 2 3 4 5
and Increasng APP
Positive but Decreasing APP
Positive
MaximumAPP
MPP,
APP
APP
0X | X X X X 1 2 3 4 5
and Increasng APP
Positive but Decreasing APP
Positive
MaximumAPP
MPP,
APP
APP
0X | X X X X 1 2 3 4 5
and Increasng APP
InflectionPoint of
TPPMaximum
MPP
Positive but Decreasing APP
Positive
MaximumAPP
MPP,
APP
APP
0X | X X X X 1 2 3 4 5
IncreasingMPP
DecreasingMPP
0 MPPMaximum TPP
Positive
and Increasng APP
InflectionPoint of
TPPMaximum
MPP
Positive
but
Positive but Decreasing APP
Positive
MaximumAPP
MPP=APP
MPP,
APP
APP
MPP
0X | X X X X 1 2 3 4 5
IncreasingMPP
DecreasingMPP
0 MPPMaximum TPP
Positive
Negative andDecreasing MPP
and Increasng APP
InflectionPoint of
TPPMaximum
MPP
Positive
but
Positive but Decreasing APP
Positive
MaximumAPP
MPP=APP
MPP,
APP
measures:responsiveness of outputto changes in the useof Inputs
Elasticity of Production
A pure number(has no units)
Elasticity of Production% Change in output (Y)
divided by% Change in input (X)
% in output Y% in input X
=
Elasticity of Production
% in output Y% in input X
Y/YX/X
=
YX
XY
.
MPP 1/APP
= = MPP/APP
% in output Y% in input X
= MPP/APP
The Elasticity of Production (Ep)is the Ratio
of MPP to APP
AVP
Ep = 0
$
MVP
Ep = 1
0X | X X X X 1 2 3 4 5
Ep > 1(MPP>APP)
0<Ep<1 Ep < 0
IncreasingMPP
DecreasingMPP
0 MPPMaximum TPP
Positive
Negative andDecreasing MPP
and Increasng APP
When the elasticity of production is greaterthan one, MPP lies above APP, APP is increasing,but MPP may be either increasing or decreasing.
When the elasticity of production is betweenzero and 1, both MPP and APP are decreasing.However, MPP is positive here.
Wnen the elasticity of production is negative,MPP is negative, and TPP is falling. However,
APP still remains positive.
Profit Maximixation:
and 1 output (Y)
1 input (X)
Assumptions:
1. Constant Input Price
The producer can purchaseas much or as littleof the needed input
at the going market price.
No producer canaffect input prices
by the amount of the purchase.
2. Constant Output PriceNo producer can affectthe price of the output (Y)because of theindividual production decision.
The price of the input is V.The price of the output is P.
3. Production Function Known
with CertaintyThis is an unrealistic assumption for agriculture!
Profit =Total Revenue - Total Cost
= TR - TC
= PY –V X. but Y = f(X)
so= Pf(X) – V X.
Total Value of Product Total Factor Cost
.
.
P f(X) - V X
Total Value of Product Total Factor Cost
Maximizing Profit:Maximize the difference
between
TVP and TFC
TVP TFC
. .
What is the appearance of a
TVP CURVE?
The TVP curve is a production function
with the vertical axis measured in dollar value
of output, not physical units
TVP = P TPP.
such as bushels or pounds.
TPPY
Production Function
TPP P .$
TPP P.
=TVP
TVP Curve
XX
TPP
What is the appearance of a
Total Factor Cost (TFC)Curve?
Total Factor Cost (TFC) Curve
TFC = V X
TFC
.
$
V
1
x
TFC = V X
TFC TVP
TPP and TVP max
.
$
V
1
x
Now Superimpose TVP Curve
TFC = V X
TFC TVP
Tangent
Tangent
TPP and TVP max
.
$
V
1
x
TFC = V X
TFC TVP
Tangent
Tangent
TPP and TVP max
.
$
V
1
x
Right of APP maxLeft of TPP Max
APP Max
TFC = V X
TFC TVP
Tangent
Tangent
TPP and TVP max
.
$
Maximum Vertical Distance= Maximum Profit
Maximum Vertical Distance= Maximum Loss
V
1
x
TFC = V X
TFC
1
V
TVP
Tangent
Tangent
TPP max
.
$
Profit is maximumwhere slope of TVP= Slope of TFC
X
Slope of TVP = Slope of TPP P .
= MPP P.
= MVP
= Marginal Value of the Product
So profits are maximum where:Slope of TVP = Slope of TFCMVP = MFCMVP = VMVP = the input price,assuming constant input and output prices
$MVP
0
MVP= MPP P
MFC = V
Profit MaxMVP=MFC=V
Profit Min
AVP=APP P
TFC = V X
TFC
1
V
TVP
Tangent
Tangent
TPP max
.
$
MVP=MFC=V
AVP Max
X
X
Stagesof
Production
Stage I
0 units of Xto level of X whichMaximizes AVP
Stage II
Level of X that Maximizes AVP
toLevel of X that Maximizes TPP
(0 MVP and 0 MPP)
Stage III
Level of X that Maximizes TPP (0 MPP)
and Beyond ......
Y
Stage III
X
The Rational Producer...1. Never produces beyond
the point of maximum TPP(input prices are never negative)
2. Produces at the point of maximum TPPonly if the input is free!
3. Does not normally producein stage I of Production
Stage II is theRational Stage of Production
Where the profit maximizing pointis found
$AVP
AVP=APP P.
Why not stage I?
Pick any point on the AVP curve.Draw an AVP curve.
Average Value of the Product= Average Physical Producttimes the product price
0X
$AVP
AVP=APP P.
X'
Area enclosed by rectangleis total revenue
from the use of X' units of X
X0
$
X
AVP=APP P.
MVP= MPP P.
Now add MVP curve
Marginal Value Product
= Marginal Physical Product
times the product price
0
$
MVP
Maximum ProfitTotal Factor Cost
of Input X
at profit max
Now add MFC curve (MFC = V)
Marginal Factor Cost= the price (V) of the input (X)
AVP=APP P
0X
MFC=V
$
AVP=APP P.
MVP
Maximum Profit
Total Revenuefrom sale of the product
using profit maximizinglevel of X
MFC=V
X0
$
X
AVP=APP P.
MVP
Maximum ProfitTotal Factor Costof Input X
at Profit MaxCost of X
Revenue-Cost=Profit
MFC=V
MFC=V
0
$
X
MVP
AVP
But if MFC > Maximum AVPCosts > RevenueLose money where MVP=MFC, andshut down instead!
Revenue
MFC= V
0
$
X
MVP
AVPRevenueCost of X
MFC= V
0
$
X
MVP
AVPRevenue
MFC= V
Revenue fails to cover costsresulting in a loss as indicated
Revenue
Loss
0
Stages of Productionand Elasticities of Production
Stage I Ep > 1Stage II 0 <Ep < 1
Stage III Ep < 0Rational Stage where0 <Ep < 1
AVP
Ep = 0
Stage I Stage II Stage III
$
MVP
Ep = 1
0X | X X X X 1 2 3 4 5
Ep > 1(MPP>APP)
0<Ep<1 Ep < 0
IncreasingMPP
DecreasingMPP
0 MPPMaximum TPP
Positive
Negative andDecreasing MPP
and Increasng APP
AVP
Ep = 0
Stage I Stage II Stage III
Demand Curve for input X$
MVP
Ep = 1
0X | X X X X 1 2 3 4 5
Ep > 1(MPP>APP)
0<Ep<1 Ep < 0
The Demand Curve for a Singe Input
All Points of Intersection BetweenMFC and MVP that liein Stage II of Production
The Quantity of Input the ProducerWould Use to Maximize Profitsat Each Possible Input Price