Overview
Objective:
This chapter introduces the physical production relationship and cost relationship
in production. The examples are given to determine different product and cost
curves using production function.
Module 4904-420
content
Farm Level Modeling Physical production relationship
Cost relationship in production
Cost of production
Production function
Cost curves
Production responses
Cost related to production curves
Typical production function
Theory of Product curves
Stages of production
Production Economics
Elasticity of production
Effect of technological change
Reference: Casavant K.L et al., (1999): Agricultural Economics and
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Management.
Physical Production
Relationship
Combining goods and services (factors of production) to achieve maximum
efficiency in resource use – Production process
Behavioral assumptions:
3 core questions Maximize the Profits (Revenue – Cost)
How much to produce?
What to produce?
Firm behaves as the manage behaves
How to produce?
Decision of how much to produce – Physical production process
Production possibilities or capacity of firm – What and how much of
X Y
the product the firm capable of producing given its technology and available Resource Production
inputs
Input Output
Example: Wheat production by farmers
Factor Product
Based on Casavant et al., Ch 2 Based on Casavant et al., Ch 2
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Assumptions
1. Objective of the firm is to maximize the profits Inputs or Factors of production
2. The firm, or producer owns certain set of
resources, some of which are variable and
some are fixed
Fixed Variable
3. Producer makes decision under perfect
e.g. land, buildings, e.g. labor, seed, fertilizer,
certainty (price, cost and outcome) machinery etc irrigation water etc
Based on Casavant et al., Ch 2 Based on Casavant et al., Ch 2
Time period / Horizon Production Function
1. Immediate short-run
“ the technical relationship between inputs and output indicating the
No resource change can be made maximum amount of output that can be produced using
E.g. at the time of harvest amount of grains to be alternative amounts of variable inputs in combination with one
harvested is fixed or more fixed inputs under a given state of technology”
2. Intermediate short-run
Some factors are variable and some fixed Mathematical relationship
e.g. crop growing season – seed, fertilizer, water - variable and Y = f (X1, X2,……. Xn)
land, machinery - fixed
3. Long-run
All the factors are variable Y = f (X1| X2,……. Xn)
Based on Casavant et al., Ch 2 Based on Casavant et al., Ch 2
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Types of production
responses
Mathematical Production function
Y = 20 + 0.4X The amount of output produced depends
Production schedule upon the level of inputs used in the
production function
Amount of X Amount of Y
used kg produced
Linear production function Rate of change in output dependent on the
(fertilizer) (tons of technical relationship between inputs and
wheat) output
0 20
10 24 Four production response relationship
20 28 1. Constant return
30 32
2. Increasing return
40 36
3. Decreasing return
50 40 Figure reproduced from Casavant et al., (1999, ch. 2)
4. negative return
Production Responses Contd…
Constant Returns Decreasing returns
Increased Returns Negative returns
Figure reproduced from Casavant et al., (1999, ch. 2) Figure reproduced from Casavant et al., (1999, ch. 2)
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Typical production function Product curves
Physical correlation between inputs and output
1.Total physical product (TPP)
Used to examine the effects of changing input use level Max amount of output produced by each level of input
on output level
2. Average physical product (APP)
APP = TPP/X
Assumptions Productivity of the inputs
1. One product is produced, and there is only one
3. Marginal physical product (MPP)
means of producing it
MPP = ∆TPP/∆X
2. One input is variable and all others are fixed Slope of TPP
Based on Casavant et al., Ch 2 Based on Casavant et al., Ch 2
Production function and product
Exercise curves
X TPP (Y) APP MPP
(Y/X) (∆Y/∆X)
0 0
Production schedule (sandwich shop)
1 2 2.0 2
2 5 2.5 3
X TPP (Y) APP (Y/X) MPP (∆Y/∆X)
3 9 3.0 4
0 0 4 11 2.75 2
1 2 5 12 2.4 1
6 11 1.83 -1
2 5
3 9
4 11
5 12
6 11
Reference: Table 2.6 Casavant et al., ch 2 Reference: Table 2.6 Casavant et al., ch 2
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Relationship between product Production function
curves characteristics
Point of inflection
If we have information on any one curve, we can
derive the other two curves
X MPP Y APP
0
1 6
2 9
MPP > APP, APP
3 4
MPP = APP, APP maximum
MPP < APP, APP
Figure reproduced from Casavant et al., (1999, ch. 2)
Stages of production Stages of Production
We have to answer “How much to produce?”
Production function give information on
alternative level of input and output
We have to find which level of input and
corresponding level of output – maximizes the
profit
Product curves provide information to identify
the profitable range of production
Figure reproduced from Casavant et al., (1999, ch. 2)
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Effect of Technological
Elasticity of Production Change
Technology – specific method of producing product (e.g.
HYV seeds, machinery, drip irrigation method, etc)
% change in output for % change in input
Ep = % ∆ in output / % ∆ in input
= MPP/APP
Stage I, Ep > 1
Stage III, Ep < 0
Stage II, 0 < Ep < 1
Based on Casavant et al., Ch 2 Figure reproduced from Casavant et al., (1999, ch. 2)
Cost Relationship in
Production Assumptions
Production function examined the relationship between
inputs and output and identified a rational range of 1. One product, one production method
production
2. One variable input, others are fixed
For economic decision making and profit maximization –
information on cost is necessary 3. Firm seeks profit maximization and
Profit = Revenue – Cost
4. Firm is a “price taker”
Cost of Production – “How much does it cost to produce
a bushel or metric ton of wheat”
Based on Casavant et al., Ch 3 Based on Casavant et al., Ch 3
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Cost of production Cost curves
“ the payment that a firm must make to attract inputs and 3 curves based on total output produced
keep them from being used to produce other outputs” – 4 curves based on per unit of output
COP or economic cost
Cost based on total output
2 economic cost 1. Total fixed cost (TFC)
Implicit – cash e.g. seed, fertilizer Include explicit and implicit cost of fixed inputs
Explicit or opportunity cost – associated with inputs Do not change as output level changes
owned e.g. land, family labour 2. Total variable cost (TVC)
2 important COP based on time and inputs Changes as the level of output changes
Fixed cost TVC = Px x X
Variable cost 3. Total cost (TC)
TC = TFC + TVC
Based on Casavant et al., Ch 3 Based on Casavant et al., Ch 3
Exercise Total cost curves
Calculate the total cost curves if TFC =$10 and Px=$4
X Y TFC TVC TC TVC derived from production process, it
reflects the increasing/decreasing return
0 0 of TPP
1 2
TC curve shape identical to TVC,
2 5 because the TFC is same at each level of
3 9 output
4 11
5 12
6 11 Figure reproduced from Casavant et al., (1999, ch. 3)
Reference: Table 3.1 Casavant et al., ch 3 Based on Casavant et al., Ch 3
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Cost based on per unit of
output Exercise
Calculate the total cost curves if TFC =$10 and Px=$4
1. Average Fixed cost (AFC)
AFC = TFC / TPP or Y
X Y TFC TVC TC AFC AVC ATC MC
2. Average Variable cost (AVC)
0 0
AVC = TVC / Y
1 2
3. Average Total cost (ATC) 2 5
3 9
ATC = TC / Y or AFC + AVC
4 11
4. Marginal cost (MC) 5 12
MC = ∆TC / ∆Y or ∆TVC / ∆Y [∆TFC = 0] 6 11
Based on Casavant et al., Ch 3 Reference: Table 3.1 Casavant et al., ch 3
Cost related to production
Per-unit cost curves function
AFC – rectangular hyperbola
Mirror images of
ATC, ATV and MC – U shaped curves product curves
MC curves cross AVC and ATV from and cost curves
below and at minimum level
Figure reproduced from Casavant et al., (1999, ch. 3)
MC < AVC and ATC, both curves falling, because less is being
Figure reproduced from Casavant et al., (1999, ch. 3)
added to TC for each successive unit of output than average of all
pervious units
Based on Casavant et al., Ch 3 Based on Casavant et al., Ch 3
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Assignments
1. Using the production function information on crop yield response
to nitrogen, calculate product curves and cost curves if the price
of nitrogen is $0.20/lb and fixed cost is $ 80/acre.
2. Estimate elasticities of production for corn yield response to
nitrogen.
3. What will happen if the price of nitrogen increases to $0.50/lb
and decreased to $0.10/lb? show these changes both
numerically and graphically.
N rate (lb/ac) 0 25 50 75 100 125 150 172 200 225
Yield (bu/ac) 94 108 119 129 137 143 147 150 150 149
4. Prepare Casavant et al., (1999). Agricultural economics and
management, chapter 4.
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