Agricultural Production Economics
THE ART OF PRODUCTION THEORY
DAVID L. DEBERTIN
University of Kentucky
This is a book of full-color illustrations intended for use as a
companion to 428-page Agricultural Production Economics,
Second Edition. Each of the 98 pages of illustrations is a large,
full-color version of the corresponding numbered figure in the
book Agricultural Production Economics, Second Edition. The
illustrations are each a labor of love by the author representing a
combination of science and art. They combine modern computer
graphics technologies with the author’s skills as both as a
production economist and as a technical graphics artist.
Technologies used in making the illustrations trace the evolution
of computer graphics over the past 30 years. Many of the handdrawn illustrations were initially drawn using the Draw Partner
routines from Harvard Graphics®. Wire-grid 3-D illustrations
were created using SAS Graph®. Some illustrations combine
hand-drawn lines using Draw Partner and the draw features of
Microsoft PowerPoint® with computer-generated graphics from
SAS®. As a companion text to Agricultural Production
Economics, Second Edition, these color figures display the full
vibrancy of the modern production theory of economics.
© 2012 David L. Debertin
Second Printing, December, 2012
David L. Debertin
University of Kentucky,
Department of Agricultural Economics
400 C.E.B. Bldg.
Lexington, KY 40546-0276
All rights reserved. No part of this book may be reproduced
or transmitted in any form or by any means, without permission
from the author.
Debertin, David L.
Agricultural Production Economics
The Art of Production Theory
1. Agricultural production economics
2. Agriculture–Economic aspects–Econometric models
ISBN- 13: 978-1470129262 2
ISBN- 10: 1470129264
BISAC: Business and Economics/Economics/Microeconomics
Price
Supply
p1
Demand
(New Income)
p2
Demand
(Old Income)
q1
q2
Quantity
Figure 1.1 Supply and Demand
y
y = 2x
A
y =x 2
y
x
B
y
x
Figure 2.1 Three Production Functions
y=x
0.5
x
C
1
y
C
y = f(x)
D
y
x
B
A
Figure 2.2 Approximate and Exact MPP
2
x
y
or
TPP
Slope
Equals
Zero
Slope Equals
MPP Equals
Maximum
Maximum
TPP
Maximum
APP
APP
TPP
y = f(x1)
Slope
Equals
APP
Inflection
Point
x o1
MPP
or
APP
Maximum
MPP
x 1*
x1
A
Maximum
APP
B
APP
0 MPP
x1
MPP
Figure 2.3 A Neoclassical Production Function
3
y = 136.96
140
TPP
TPP Maximum
120
100
TPP
y = 85.98
80
APP Maximum
y = 56.03
60
MPP Maximum
Inflection Point
40
20
60.87
181.60
91.30
0
0
50
100
150
x
200
1.2
1.01
1.1
MPP
APP
0.94 MPP = APP
1
0.9
0.8
APP
0.7
0.6
0.5
0.4
0.3
0.2
0 MPP
0.1
0
-0.1
MPP
-0.2
-0.3
0
50
100
150
200
Figure 2.4 TPP, MPP and APP for Corn (y) Response to
Nitrogen (x) Based on Table 2.5 Data
4
x
+
(a)
MPP
MPP
+
f1 > 0
f2 > 0
f3 > 0
MPP
0
+
(e) f1 > 0
f2 < 0
f3 > 0
(h)
MPP
f1 < 0
f2 < 0
f3 < 0
MPP
MPP
(i) f1 < 0
f2 < 0
f3 = 0
MPP
(l)
f1 < 0
f2 > 0
f3 > 0
+
MPP
+
f1 > 0
f2 < 0
f3 = 0 MPP
+
MPP
MPP
MPP
(m) f1 < 0
f2 > 0
f3 = 0
+
MPP
(d) f1 > 0
f2 = 0
MPP
0
(g) f1 > 0
f2 < 0
f3 < 0
MPP
+
(j) f1 < 0
f2 < 0
f3 > 0
MPP
0
(k)
f1 < 0
f2 = 0
0
MPP
MPP
-
(n) f1 < 0
f2 > 0
f3 < 0
0
MPP
MPP
-
f1 > 0
f2 > 0
f3 < 0
0
0
MPP
+
MPP
(c)
0
0
0
-
MPP
MPP
0
+
0
+
(f)
MPP
MPP
0
+
+
MPP
f1 > 0
f2 > 0
f3 = 0
MPP
0
+
(b)
-
Figure 2.5 MPP’s for the Production Function y = f(x)
5
y,
MPP
or
APP
Ep > 1
0 < Ep < 1
Ep > 1
Ep < 0
B
A
E p =1
APP
C
0
x
MPP
-
Figure 2.6 MPP, APP and the Elasticity of Production
6
TVP
$
py
or
pTPP
TVP
Inflection
Point
x
$
VMP =
pMPP
AVP =
pAPP
MFC
MFC
AVP
0
x
VMP
Figure 3.1 The Relationship Between TVP, VMP, AVP, and MFC
7
Zero
Profit
$
TVP
TFC
TFC
Zero
Slope
Maximum
Profit
TVP
Maximum
Parallel
TVP
Maximum
AVP
Zero
Profit
Maximum
VMP
Inflection
Parallel
Point
Minimum
Profit
x
x*
VMP
AVP
MFC
$
v
Maximum
Profit
o
Minimum
Profit
VMP =
MFC
Maximum
VMP
VMP =
MFC
MFC = v o
AVP =
p o APP
0
Maximum
Profit
Profit
$
Zero
VMP
x
VMP
0
Zero
Profit
x*
Zero
Profit
Minimum
Profit
8
Figure 3.2 TVP, TFC, VMP, MFC and Profit
x
Profit
600
$
547.69
547.86
500
520.79
520.62
TVP
400
Profit
300
200
100
179.322
181.595
160
200
TFC
0
0
40
80
120
x
240
600
$
546.28
500
467.69
547.86
466.14
TVP
400
300
Profit
200
TFC
100
174.642
181.595
0
0
40
80
120
160
200
240
x
Figure 3.3 TVP, TFC and Profit (Top and Second Panel)
9
600
547.86
541.26
$
500
390.75
400
384.42
300
200
100
167.236
181.595
0
0
40
80
120
160
200
x
Figure 3.3 TVP, TFC and Profit (Third Panel)
4.02
240
3.77
4
$3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
AVP
MFC 0.90
MFC 0.45
MFC 0.15
VMP
0
40
60.870
80
91.304
120
167.236
160
174.642
200
179.322
181.595
240
x
Figure 3.3 Profit Maximization under Varying
Assumptions with Respect to Input Prices (Bottom Panel)
10
y
TPP
Stage II
Stage I
A
y
B
Stage III
C
x
APP
0
x
MPP
Figure 3.4 Stages of Production and the Neoclassical Production Function
11
$
C
D
E
MFC
Loss
B
Cost
Per
Unit
Revenue
Per
Unit
AVP
0
A x*
x
VMP
Figure 3.5 If VMP is Greater than AVP, the Farmer Will Not Operate
$
VMP
MFC
MFC
0
x
VMP
Figure 3.6 The Relationship Between VMP and MFC Illustrating the
12
Imputed Value of an Input
$
SRAC5
SRMC1
SRMC5
SRAC2
SRAC1
SRMC2
LRAC
SRAC4
SRAC3
SRMC3
SRMC4
y
Figure 4.1 Short and Long Run Average and Marginal Cost
with Envelope Long Run Average Cost
13
TC
VC or
TVC
$
Minimum
slope of
TC
Minimum
slope of
TVC
Inflection
Point
FC
y
AC*
$
MC
AVC*
B
AC
AVC
A
AFC*
FC = k
AFC
y
Figure 4.2 Cost Functions on the Output Side
14
$
∞
+
AFC AC
AC
AVC AFC
AVC
AFC
MC
Stage III
Stage II
AFC
AFC
AFC
0
y*
y
MC
-
-
∞
Figure 4.3 Behavior of Cost Curves as Output
Approaches a Technical Maximum y*
15
TC
TR
TVC
$
p
Parallel
y
Parallel
FC
y
$
MC
MR = p
AC
AVC
AFC
Maximum Profit
$
+
Zero
Profit
0
y
Profit
y
Minimum Profit
Figure 4.4 Cost Functions and Profit Functions
16
600
TR
$
500
TC
400
VC
300
200
Maximum Profit
Profit
FC
100
0
Zero Profit
y = ~ 115
-100
0
20
40
60
80
100
120
140
y
7
$
MC
6
5
4
MR
3
AC
AVC
2
1
AFC
y
0
0
20
40
60
80
100
120
Figure 4.5 The Profit-Maximizing Output Level
Based on Data Contained in Table 4.1
140
17
Maximum
TPP
Y
45
Y
Maximum
APP
TPP
Maximum
MPP
(Inflection
Point)
X
$
TC = vx
Y
$
TVC
Minimum
AVC
V
Minimum
MC
(Inflection
Point)
v = price of x
X
X
Y
Figure 4.6 A Cost Function as an Inverse Production Function
18
o
MC = Supply
$
AVC
p3
p2
p1
y
Figure 4.7 Aggregate Supply When the Ratio MC/AC = 1/b
and b is less than 1
19
134
Corn Yield
136
Y
130
136
127
121
120
114
104
106
88 80
80
101
60
60
40
96
40
X1
20
X 2 20
0 0
Figure 5.1 Production Response Surface Based
on Data Contained in Table 5.1
105 115 125
96 100 1101 120
80
X2
134
129
134
70
129
60
125
50
120
40
30
115
20
110
10
0
105
0
10
20
30
40
50
60
70 X 80
Potash 1
Figure 5.2 Isoquants for the Production Surface in
Figure 5.1 Based on Data Contained in Table 5.1
20
x2
x2
x1
x2
x1
x
2
x1
y
0
x1
Figure 5.3 Illustration of Diminishing MRS x1x2
21
Figure 5.4 Isoquants and a Production Surface (Panel A)
Figure 5.4 Isoquants and a Production Surface (Panel B)
22
Figure 5.4 Isoquants and a Production Surface (Panel C)
Figure 5.4 Isoquants and a Production Surface (Panel D)
23
Figure 5.4 Isoquants and a Production Surface (Panel E)
Y
250
167
83
0
20
18
16
14
12
X2
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
X1
Figure 5.4 Isoquants and a Production Surface (Panel F)
24
X2
X1
Figure 5.5 Some Possible Production
Surfaces and Isoquant Map A .The Production Surface
5
X2
4
3
2
1
0
0
1
2
3
4
5
X1
Figure 5.5 Some Possible Production
Surfaces and Isoquant Map
B. The Isoquant Map
25
Y
10.00
6.67
3.33
0.00
10
10
8
8
6
6
4
X2 4
2
2
X1
0 0
Figure 5.5 Some Possible Production
Surfaces and Isoquant Map
C . The Production Surface
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
Figure 5.5 Some Possible Production
Surfaces and Isoquant Map
26
D . The Isoquants
Y
10.0
6.67
3.33
0.00
10
10
8
8
6
6
4
X2 4
X1
2
2
0 0
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
E. The Production Surface
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
F. The Isoquants
27
Y
10.00
6.83
3.67
0.50
10.0
10.0
8.1
8.1
6.2
6.2
4.3
4.3
X2
2.4
2.4
X1
0.5 0.5
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
K. The Production Surface
10.0
X2
8.1
6.2
4.3
2.4
0.5
0.5
2.4
4.3
6.2
8.1
10.0
X1
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
L. The Isoquants
28
Y
10.00
6.67
3.33
0.00
10
10
8
8
6 X1
6
4
X2 4
2
2
0 0
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
G. The Production Surface
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
H. The Isoquants
29
Y
0.181
0.040
-0.100
-0.241
10.0
10.0
8.1
8.1
6.2
6.2
X2
4.3
4.3
2.4
2.4
X1
0.5 0.5
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
I. The Production Surface
10.0
X2
8.1
6.2
4.3
2.4
0.5
0.5
2.4
4.3
6.2
8.1
10.0
X1
Figure 5.5 Some Possible Production Surfaces and Isoquant Maps
J. The Isoquants
30
3.0
x2
Ridge Line
for x 1
2.4
x2 *
1.8
Ridge Line
for x2
x 2**
1.2
x 2***
0.6
0.0
0.0
0.6
1.2
1.8
2.4
x1
3.0
y
y = f (x 1 | x 2 * )
y = f (x 1 | x 2** )
y = f (x 1 | x***
2 )
0.0
0.6
1.2
1.8
2.4
x1
3.0
Figure 5.6 Ridge Lines and a Family of Production Functions
For Input x1
31
Y
Maximum
50.00
33.33
16.67
0.00
10
10
8
8
6
6
X2
4
4
A. The Surface
X1
2
2
0
0
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
10
X2
8
6
Maximum
4
2
0
0
2
4
6
8
10
X1
B. The Contour Lines
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
32
Y
0.00
-16.67
-33.33
-50.00
10
10
Minimum
8
8
6
6
4
X2 4
2
2
C. The Surface
X1
0
0
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
10
X2
8
6
Minimum
4
2
0
0
2
4
6
8
10
X1
D. The Contour Lines
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
33
Y
25.00
8.33
Saddle
-8.33
-25.00
10
10
8
8
6
6
X2
4
4
2
2
E. The Surface
0
X1
0
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
10
X2
8
Saddle
6
4
2
0
0
2
4
6
8
10
X1
F. The Contour Lines
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
34
Y
25.00
8.33
Saddle
-8.33
-25.00
10
10
8
8
6
6
X2
4
4
G. The Surface
X1
2
2
0
0
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
10
X2
8
Saddle
6
4
2
0
H. The Contour Lines
0
2
4
6
8
10
X1
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
35
Y
220
47
Saddle
-127
-300
5
5
3
3
1
1
-1
I . The Surface
X2
-1
X1
-3
-3
-5
-5
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
5
X2
3
Saddle
1
-1
-3
-5
-5
J. The Contour Lines
36
-3
-1
1
3
5
X1
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
Y
200
Saddle
27
-147
-320
5
5
3
3
1
1
X2
-1
-1
K. The Surface
X1
-3
-3
-5
-5
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
5
X2
3
Saddle
1
-1
-3
-5
-5
I. The Contour Lines
-3
-1
1
3
5
X1
Figure 6.1 Alternative Surfaces and Contours Illustrating
Second Order Conditions
37
Global Maximum
Y
379
253
Local Max
Saddle
Saddle
Local Max
126
0
20
Local
Minimum Saddle
Saddle
16
Local Max
12
12
Surface
20
16
8
X2 8
4
X1
4
0 0
Figure 6.2 Critical Values for the Polynomial y = 40 x1 – 12 x12
+ 1.2 x13 –0.035x14+ 40 x2 – 12 x22 + 1.2 x23 –0.035x24
Contour Lines
Figure 6.2 Critical Values for the Polynomial y = 40 x1 – 12 x12
+ 1.2 x13 –0.035x14 + 40 x2 – 12 x22 + 1.2 x23 –0.035x24
38
3.0
o
X2 C /v2
2.4
Expansion
Path
1.8
v1
1.2
v2
0.6
0.0
o
C /v1
0.0
0.6
1.2
1.8
2.4
X1
3.0
Figure 7.1 Iso-outlay Lines and the Isoquant Map
Global Profit Maximum
(Pseudo Scale Lines Intersect)
Global Output Maximum
(Ridge Lines Intersect)
$
Constrained Output Maxima
(Bundle Allocated According to
Expansion Path Conditions)
Price of the Input
Bundle
Top Panel
The Input Bundle
X
VMP of
X
Figure 7.2 Global Output and Profit Maximization for the Bundle 39
Global Output Maximum
(Ridge Lines Intersect)
Y
Global Profit Maximum
(Pseudo Scale Lines Intersect)
250
Sample Isoquant
(Constrained Maximum
Below Global Output
or Profit Maximum)
167
83
0
20
18
16
14
12
10
8
Bottom Panel
6
4
X2
2
0
0
2
4
6
8
10
12
14
16
18
20
X1
Figure 7.2 Global Output and Profit Maximization for the Bundle
40
20
X2
18
16
14
Point on
Pseudo
Scale
Line
12
Point on
Ridge
Line
*
x2
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
X1
$
18
20
Output Maximum
for x1 Holding
x2 constant at x2*
Profit Maximum
for x Holding
1
x constant at x
*
2
2
py = f (x1 | x2* ) = TVP
MFC = v1
0
2
4
6
8
10
12
14
16
18
20
X1
VMP x 1 | x2*
Figure 7.3 Deriving a Point on a Pseudo Scale Line
41
20
X2
Global
Profit
Maximum
18
Global
Output
Maximum
16
14
12
Isocost
Lines
10
8
6
X
4
X
2
0
0
2
4
6
8
10
12
14
16
18
X1
Figure 7.4 The Complete Factor-Factor Model
42
20
Global Output Maximum
Y
Global Profit Maximum
250
167
Constrained
Output Maximum
83
0
20 18
16
14
12
10
8
X2
6
12
4
2
0 0
2
4
6
8
14
16
10
X1
Figure 7.5 Constrained and Global Profit and Output Maxima
along the Expansion Path
43
18 20
Revenue,
Profit
Global Revenue Maximization
$
250
Global Profit Maximization
Ridge Line 2
Ridge Line 1
Pseudo Scale Line 2
153
Pseudo Scale Line 1
57
0
0
-40
20 18
16 14
12
10
8
6
X2
4
2
0 0
Total Revenue Surface
2
4
6
8
10
12
X1
Profit Surface
Figure 8.1 TVP- and Profit-Maximizing Surfaces
44
18 20
14 16
20
X2
18
Global Output Max
16
14
Global Profit Max
12
10
8
6
4
2
0
0
2
4
6
8
10
X1
Isorevenue Lines
12
14
16
18
Isoprofit Lines
Figure 8.2 Isorevenue and Isoproduct Contours
45
20
x2
Solution
Isoquant
y'
Budget
Constraint
x1
Figure 8.3 A Corner Solution
46
Y
250
167
83
0
A
20
18
16
14
12
10
C
B
8
6
X2
4
2
2
0
0
8
6
4
10
12
14
16
18
20
X1
Figure 8.4 A. Point B Less than A and C
Y
250
167
83
B
A
0
20
18
16
14
12
10
X2
8
6
4
2
0
C
0
2
Figure 8.4 B. Point B Equal to A and C
4
6
8
10
12
14
16
X1
47
18
20
Y
250
167
B
83
A
0
20
18
16
C
14
12
10
X2
8
6
4
2
2
0
0
8
6
4
12
10
14
16
18
X1
Figure 8.4 C . Point B Greater than A and C
Y
250
B
167
83
A
0
20
18
C
16
14
12
10
X2
48
8
6
4
2
0
0
2
4
6
8
10
Figure 8.4 D. Point B Greater than A and C
12
X1
14
16
18
20
20
Y
Y
250
250
167
167
83
83
B
A
0 20
18 16
14
A
12 10
X2
C
B
8 6
4 2
10
6 8
2 4
0 0
16
12 14
0
18 20
20 18
16 14
12
10 8
X2
X1
6
4
2
C
0 0
2
4
6
8
10 12
14 16
18 20
X1
Y
Y
250
250
B
167
167
B
83
83
A
A
C
0
0
20 18
16 14
12 10
X2
8
6
4 2
0
0 2
4
6
8
10
16 18
12 14
X1
20
20 18
C
16
14
12
10
X2
8
6
4
2
0
0 2
4
6
8
10
12
X1
Figure 8.4 Constrained Maximization under Alternative
Isoquant Convexity or Concavity Conditions
49
14
16
18 20
20
Global
Profit
Maximum
=1
Land
18
Global
Output
Maximum
=0
16
14
12
10
A
B
8
L*
C
L*
R
6
X
4
X
2
0
0
2
4
6
8
10
12
14
16
18
X (a bundle of all inputs but land)
Figure 8.5 The Acreage Allotment Problem
50
20
x2
x2
D
D
C
B
C
40
30
20
10
A
0
30
B
20
10
A
x1
0A > AB > BC > CD
0
40
x1
0A < AB < BC < CD
x2
D
C
B
A
40
30
20
10
0
0A = AB = BC = CD
x1
Figure 9.1 Economies, Diseconomies and Constant Returns to Scale
For a Production Function with Two Inputs
51
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
Figure 10.1 Isoquants for the Cobb-Douglas Production Function
52
A . Surface y = x10.4x20.6
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
B. Isoquants y =
x10.4x20.6
Figure 10.2 Surfaces and Isoquants for the Cobb-Douglas
Type Production Function
53
C. Surface y = x10.1x20.2
10
X2
8
6
4
2
0
0
2
D. Isoquants y = x10.1x20.2
54
4
6
8
10
X1
Figure 10.2 Surfaces and Isoquants for the Cobb-Douglas
Type Production Function
E. Surface y = x10.6x20.8
10
X2
8
6
4
2
0
0
2
F. Isoquants y = x10.6x20.8
4
6
8
10
X1
Figure 10.2 Surfaces and Isoquants for the Cobb-Douglas
Type Production Function
55
G . Surface y = x10.4x21.5
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
H. Isoquants y = x10.4x21.5
Figure 10.2 Surfaces and Isoquants for the Cobb-Douglas
Type Production Function
56
I. Surface y = x11.3x21.5
10
X2
8
6
4
2
00
2
4
6
8
10
X1
J. Isoquants y = x11.3x21.5
Figure 10.2 Surfaces and Isoquants for a Cobb-Douglas
Type Production Function
57
A. Surface
10
X2
8
6
4
2
0
0
B. Isoquants
58
2
4
6
8
10
X1
Figure 11.1 The Spillman Production Function
3
X2
-
Ridge Line 2
2
2
Maximum
Output
2
1
0
0
1
2
X1
-
1
3
1
Figure 11.2 Isoquants and Ridge Lines for the Transcendental,
g1 = g2 -2; a1 = a2 = 4; g3 = 0
59
A. Surface g1 = g2 = -2; a1 = a2 = 4; g3= 0
4
X2
3
2
1
0
0
1
2
3
4
X1
B. Isoquants g1 = g2 = -2; a1 = a2 = 4; g3= 0
Figure 11.3 The Transcendental Production Function
Under Varying Parameter Assumptions
60
C. Surface g1 = g2 = -2; a1 = a2 = 4; g3= 0.2
3.90
X2
2.92
1.95
0.97
0.00
0.00
0.97
1.95
2.92
3.90
X1
D. Isoquants g1 = g2 = -2; a1 = a2 = 4; g3= 0.2
Figure 11.3 The Transcendental Production Function
Under Varying Parameter Assumptions
61
E . Surface g1 = g2 = -2; a1 = a2 = 4; g3= 0.3
4
X2
3
2
1
0 0
1
2
3
4
X1
F. Isoquants g1 = g2 = -2; a1 = a2 = 4; g3= 0.3
Figure 11.3 The Transcendental Production Function
Under Varying Parameter Assumptions
62
G. Surface g1 = g2 = -2; a1 = a2 = 0.5; g3= 0
0.5
X2
0.4
0.3
0.2
0.1
0.0 0.0
0.1
0.2
0.3
0.4
0.5
X1
H. Isoquants g1 = g2 = -2; a1 = a2 = 0.5; g3= 0
Figure 11.3 The Transcendental Production Function
Under Varying Parameter Assumptions
63
I. Surface g1 = g2 = 1; a1 = a2 = 0.5; g3= 0
1.00
X2
0.75
0.50
0.25
0.00
0.00
0.25
0.50
X1
0.75
1.00
J. Isoquants g1 = g2 = 1; a1 = a2 = 0.5; g3= 0
Figure 11.3 The Transcendental Production Function
Under Varying Parameter Assumptions
64
A. Surface
20
X2
16
12
8
4
0
0
4
8
12
16
20
X1
B. Isoquants
Figure 11.4 The Polynomial
y = x1 + x12 – 0.05 x13 + x2 + x22 – 0.05 x23 + 0.4 x1 x2
65
F
x2
M
H
D
P2
Midpoint
K
P1
B
y*
0
C
J
A
E
L
G
Figure 12.1 The Arc Elasticity of Substitution
66
X1
A. Case 1 Surface r =100
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
B. Case 1 Isoquants r = 100
Figure 12.2 Production Surfaces and Isoquants for the CES Production
Function under Varying Assumptions about r
67
C. Case 2 Surface r = 0.5
10
X2
8
6
4
x2 = (k/l)-1/r 2
0 0
2
4
6
8
10
X1
x1 = (k/l)-1/r
D. Case 2 Isoquants r = 0.5
Figure 12.2 Production Surfaces and Isoquants for the CES
Production Function under Varying Assumptions about r
68
E. Case 3 Surface r = 0
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
F. Case 3 Isoquants r = 0
Figure 12.2 Production Surfaces and Isoquants for the CES Production
Function under Varying Assumptions about r
69
G. Case 4 Surface r = -0.5
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
J Case 4 Isoquants r = -0.5
Figure 12.2 Production Surfaces and Isoquants for the CES Production
Function under Varying Assumptions about r
70
I . Case 5 Surface r approaches -1
10
X2
8
6
4
2
0
0
2
4
6
8
10
X1
J. Case 5 Isoquants r approaches -1
Figure 12.2 Production Surfaces and Isoquants for the CES Production
Function under Varying Assumptions about r
71
$
MFC1
MFC2
AVP
MFC3
Input (x)
Demand
MFC4
x
VMP
Figure 13.1 The Demand Function for Input x (No Other Inputs)
72
x2
x2
x2
y"
y"
y'
y"
y'
x1
x1
A
y'
B
x1
C
Figure 13.2 Possible Impacts of an Increase in the Price of x1
on the use of x2
73
$
MFC1
AVP3
AVP2
MFC2
AVP1
Input (x)
Demand
MFC3
x1
VMP3
VMP2
VMP1
Figure 13.3 Demand for Input x1 when a Decrease in the Price
of x1 Increases the Use of x2
74
Maximum TR
p
Total
Revenue
2
TR = ay – by
|Ep| > 1
|Ep| = 1
Demand
p = a - by
|Ep| < 1
0
T
M
y
|Ep| = - Ep
Marginal Revenue
MR = a - 2by
Figure 14.1 Total Revenue, Marginal Revenue,
and the Elasticity of Demand
75
$
$
p o TPP
p o TPP
n
TVP
p TPP
n
TVP
o
p TPP
o
n
x
x
n
x
x
A
x
x
B
$
o
p TPP
o
o
n
n
o
o
p = p (y )
n
p = p (y )
y
n
p TPP
TVP
= y (x )
n
y = y (x )
o
C
x
n
x
x
Figure 14.2 Possible TVP Functions Under Variable Product Prices
76
Guns
Production
Possibilities Curve
for a Resource
Bundle X o
Butter
Figure 15.1 A Classic Production Possibilities Curve
77
Corn
(bu. per
acre)
136
TPP
111
x (other inputs)
Panel A
Figure 15.2 Deriving a Product Transformation
Function from Two Production Functions
78
Soybeans
(bu. per
acre)
55
TPP
x (other inputs)
Panel B
Figure 15.2 Deriving a Product Transformation Function
from Two Production Functions
79
Soybeans (bu. per acre)
55
50
45
x = 10
40
35
30
25
20
15
10
5
0
0
10
20
30
40
50
60 70 80 90 100 110 120 130 140
136
111
Corn (bu. per acre)
Panel C
Figure 15.2 Deriving a Product Transformation Function
from Two Production Functions
80
y2 Supplementary
y2
Range
Competitive
y2
y1
y1
Supplementary
y2
Complementary
Range
y1
y1
Complementary
Joint
Figure 15.3 Competitive, Supplementary,
Complementary and Joint Products
81
X
Y1
Y2
A. Surface ν approaches -1
10
Y2
8
6
4
2
0
0
2
4
6
8
10
Y1
B. Isoproduct Contours ν approaches -1
Figure 15.4 Isoproduct Surfaces and Isoproduct Contours for a
CES Type of Function, ν <-1
82
X
10.00
6.67
3.34
0.01
10
10
8
8
6
Y2
4
4
Y1
6
2
2
C. Surface ν = -2
0
0
10
Y2
8
6
4
2
0
0
2
4
6
8
10
Y1
D. Isoproduct Contours ν = -2
Figure 15.4 Isoproduct Surfaces and Isoproduct Contours
for a CES Type of Function, ν <-1
83
X
10.00
6.67
3.33
0.00
10
10
8
8
6
4
Y2 4
Y1
6
2
2
0
E. Surface ν = -5
0
10
Y2
8
6
4
2
0
0
2
4
6
8
10
Y1
F. Isoproduct Contours ν = -5
Figure 15.4 Isoproduct Surfaces and Isoproduct Contours
for a CES Type of Function, ν <-1
84
X
10.00
6.67
3.33
0.00
10
10
8
8
6
4
4
Y2
Y1
6
2
2
0
0
G. Surface ν = -200
10
Y2
8
6
4
2
0
0
2
4
6
8
10
Y1
H. Isoproduct Contours ν = -200
Figure 15.4 Isoproduct Surfaces and Isoproduct Contours
for a CES Type of Function, ν <-1
85
Figure 16.1 A Family of Product Transformation Functions
86
10
Y2
Product
Transformation
Functions
Output
Expansion
Path
8
Ro
p2
6
Isorevenue
Lines
4
2
p
1
0
0
2
4
Y1
6
p
2
Ro
8
p
10
1
Figure 16.2 Product Transformation Functions, Isorevenue
Lines and the Output Expansion Path
87
Tobacco
Global
Profit
Maximum
Output Pseudo
Scale Line for
Tobacco
10
Output Pseudo
Scale Line
For Other Crops
(Y)
Output
Expansion
Path
A
8
6
B
T*
C
4
2
0
0
2
4
6
8
Figure 16.3 An Output Quota
88
10
12
Y
Forage
(z2 )
Isoquants for
Beef Production
MRSx x
= RPTz z
1 2
1 2
Product
Transformation
Function for
Grain and
Forage
Grain (z1 )
Forage
(z2 )
Sell
Isocost or
Isorevenue
Produce
pz
Line
1
p z2
Produce
Purchase
Figure 17.1 An Intermediate Product Model
Grain (z1 )
89
$ per bu.
MC
MR =
Price of
Corn
C
B
AC
AVC
A
Output
of Corn
Figure 19.1 Output of Corn and Per Bushel Cost of Production
90
Probabilities
and Outcomes
are Known
Risky Events
Probabilities
And Outcomes
Are not known
Uncertain Events
Figure 20.1 A Risk and Uncertainty Continuum
91
Utility
Utility
Risk-Averse
Income
Risk-Neutral
Income
Utility
Risk-Preferrer
Income
Figure 20.2 Three Possible Functions Linking Utility to Income
92
Expected
Income
Expected
Income
Income Variance
Risk-Averse
Income Variance
Risk-Neutral
Expected
Income
Risk Preferrer
Income Variance
Figure 20.3 Indifference Curves Linking the Variance of
Expected Income with Expected Income
y2
Curve B
Curve A
Curve C
y1
Figure 20.4 Long Run Planning: Specialized and Non-Specialized
Facilities
93
y212
Constraint 1 (Amount of x1 Available)
10
8
6 2/3
6
Feasible
Region
4
Constraint 2 (Amount of x2 Available)
5
y2 4
Product
Transformation
Objective Function
Function
2
Feasible
Region
4
0
2 2/3
0
2
4
6
8
10
12
14
y1
Figure 22.1 Linear Programming Solution in Product Space
94
16
4
x2
3
Feasible
Feasible
Region
Isoquant
Isoquant
2
Constraint 2
12
16
1
Constraint 1
Objective Function
x1
0
0
1
2
3
4
5
Figure 24.2 Linear Programming Solution in Factor Space
95
x2
x2
x1
Diagram A
x1
Diagram B
x2
Diagram C
x1
Figure 23.1 Some Possible Impacts of Technological Change
96
X2
X2
Assumption 1 Holds
X2
X1
Assumption 1 Fails
X1
X2
Assumption 2 Fails
X1
Assumption 2 Holds
X1
Figure 24.1 Assumptions (1) and (2) and the Isoquant Map
97
X2
P1
X’2
P2
X”2
X’1
X”1
X1
Figure 24.2 A Graphical Representation of the Elasticity of Substitution
98