Transcript Production
Chapter 6
Production and Costs
The Case of One Variable Input
in the Short-Run
Steven Landsburg,
University of
Rochester
Copyright ©2008 by Thomson South-Western, a part of the Thomson Corporation. All rights
reserved.
Production Relationships
Definition: The technical relationship between
inputs & output indicating the maximum
amount of output that can be produced using
alternative amounts of variable inputs in
combination with one or more fixed inputs
under a given state of technology.
Or, simply speaking, it is the technical
relationship between inputs & output
Factors of Production
Inputs
Fixed Inputs - factors must be maintained (i.e. paid
for, kept up, etc.) whether production occurs or not
(ex. - land, buildings, heavy machinery, etc.)
Variable inputs - factors that vary as the output
level changes (ex. - labor, fertilizer, seed, etc.)
Assumption
For this section, assume that only one variable
input (e.g., labor) is required to produce a good.
Production Relationship
The Case of One Variable Input
Total Product (TP) - illustrates
the technological or physical
relationship that exists between
output and one variable input,
ceteris paribus
Y
Starts increasing at an
increasing rate.
Continues to increase but at a
decreasing rate
TP
X
TPP=Y
0.00
0.00
1.00
10.00
2.00
25.00
3.00
50.00
4.00
70.00
5.00
85.00
6.00
95.00
7.00
100.00
8.00
101.00
9.00
95.00
10.00
85.00
Reaches the maximum, then
decreases
The functional form of a production function is given by:
Y = f (X), where Y is the quantity of output and X is the quantity of input
X
Product Curves
The point where TP
changes from increasing at
an increasing rate to
increasing at a decreasing
rate is called the Inflection
Point.
Y
Maximum Point
Y3
C
Y2
B
TP
Inflection Point
Points A, B, and C Indicate
total amount of output
produced at each level of
input use
Y1
A
X1
X2
X3
X
Product Curves (Cont.)
Average Product (AP) - shows how much production, on average, can
be obtained per unit of the variable input with fixed amounts of other
inputs
Indicates average productivity of the inputs being used how productive is each input level on average
AP = Y / X
Drawing a line from the origin which is tangent to the TP
curve gives maximum AP
Marginal Product (MP) - represents the amount of additional (i.e.,
marginal) output obtained from using an additional unit of the variable
input (X).
MP = ΔY / ΔX = ∂Y/∂X, or the slope of the TP curve. Thus, MP
represents the rate of change in output resulting from adding one
more unit of input
Since MP is the slope of TP, it reaches a maximum at inflection point
It reaches zero at the maximum point of TP
Product Curves (Cont.)
X
Y = TP
AP=Y/X
0
0
0
1
10
10.0
2
25
12.5
3
50
16.7
4
70
17.5
5
85
17.0
6
95
15.8
7
100
14.3
8
101
12.6
9
95
10.6
10
85
8.5
Y
TP
Y
X
AP
X
Product Curves (Cont.)
MP=∂Y/∂X
X
Y = TP
AP=Y/X
0
0
0
1
10
10.0
10
2
25
12.5
15
3
50
16.7
25
4
70
17.5
20
5
85
17.0
15
6
95
15.8
10
7
100
14.3
5
8
101
12.6
1
9
95
10.6
-6
10
85
8.5
-10
Y
TP
X
Y
AP
MPP
X
Product Curves
MP=∂Y/∂X
X
Y = TP
AP=Y/X
0
0
0
1
10
10.0
10
2
25
12.5
15
3
50
16.7
25
4
70
17.5
20
5
85
17.0
15
6
95
15.8
10
7
100
14.3
5
8
101
12.6
1
9
95
10.6
-6
10
85
8.5
-10
Y
TP
X
Y
AP
MPP is negative
MP
X
Relationships between
Product Curves
MP reaches a maximum at inflection
point
MP = 0 occurs when TP is maximum
MP is negative beyond TP max
Y
TP
Drawing a line from the origin which is
tangent to the TP curve gives AP max
At point where AP is max, MP crosses AP
(MP=AP)
Y
X
When MP > AP, AP is increasing
When MP = AP, AP is at a max
When MP < AP, AP is decreasing
The relationship between TP, AP, & MP is
very specific. If we have COMPLETE
information about one curve, the other two
curves can be derived.
AP
MPP is negative
MP
X
Law of Diminishing Marginal
Physical Product
Law of Diminishing Marginal Product: As
additional units of one input are combined with
a fixed amount of other inputs, a point is always
reached where the additional product received
from the last unit of added input (MP) will
decline
This occurs at the inflection point
Stages of Production:
Rational & Irrational
The stage I of the production
function is between 0 and X1
units of X.
In stage I:
TP is increasing
AP is increasing
MP increases, reaches a
maximum & decreases to
AP
Y
I
TP
X
Y
AP
Stage I is an irrational stage
because AP is still increasing
0
X1
MP
X
Stages of Production:
Rational & Irrational
The stage II of the production
function is between X1 and
X2 units of X.
In Stage II:
TP is increasing
AP is decreasing
MP is decreasing and less
than AP, but still positive
Rational stage, because
TP is still increasing
Y
I
TP
II
X
Y
AP
0
X1
X2
MP
X
Stages of Production:
Rational & Irrational
Stage III of the production
function is beyond X2 level
Y
I
TP
II
In Stage III:
TP is decreasing
AP is decreasing
MP is decreasing and
negative
Stage III is a irrational
stage because TP is
declining
III
X
Y
AP
0
X1
X2
MP
X
A Hypothetical Production Function
Schedule
Total Physical Product Curve
Input
(X)
TP
(Y)
AP
(Y/X)
0
0
0
1
10
10
10
2
25
12.5
15
3
50
16.67
25
4
70
17.5
20
5
85
17
15
6
95
15.83
10
7
100
14.29
5
8
101
12.63
1
9
95
10.55
-5
MP
(ΔY/ ΔX)
Output
Stage I
Stage II
Stage III
Input
APP/MPP
APP and MPP
0
1
2
3
4
5
Input
10
85
8.5
-10
6
7
8
9
10
Effects of Technological Change
We know that the PF gives
the max amount of output
that can be produced by a
firm using a given
technology.
Y
TP’
TP
The PF can shift over time as
a result of a technological
change
X
Technological change refers
to the introduction of new
technology that increases
output with the same amount
of resources.