Producer Decision Making

1
Producer Decision Making
Two - Variable Inputs and Enterprise Selection
Chapter 5
2
Three Types of Relationships Producers Must
Understand
1 Factor - Product relationship deals with
choosing the level of an input, in order to be
efficient.
2 Factor - Factor relationship deals with
choosing between competing factors.
3 Product - Product relationship deals with
choosing between competing products.
3
Factor - Factor

• Choosing the optimal proportion of the

• inputs in order to efficiently produce

• output.

4
Two-Variable Input Functions

• A two - variable input production function can
  take on

• the following form

• amounts

• Y f (X1, X2) where X1 and X2 can vary in

5
Two-Variable Input Functions
A two - variable input production function can
also
take on another form
Y f (X1, X2 X3, X4) where X1 and X2 can vary

in amounts and X3, X4 are
fixed.
6
Isoproduct Contours

• X2

• .

• A

• .

• B

• .

• C

(Isoquants)

• .

• D

• .

• E

• Y

• X1

7
Isoproduct Contours
X2
Perfect Substitutes
Y
X1
8
Isoproduct Contours
Perfect Substitutes
Perfect substitutes are able to replace one
another
without affecting output.
For every unit decrease in one input a constant
unit
increase in the other input will hold output at
the
same level.
Example Water From Well 1 and Water
from Well 2
9
Isoproduct Contours
X2
Perfect Complements
Y
X1
10
Isoproduct Contours
Perfect Complements
Perfect Complements must be used in a constant
proportion to be efficient.
Therefore, an additional amount of one resource
will do
nothing for output. There is no decision for the
determining the ratio of use.
Example Tractor and Plow.
11
Isoproduct Contours
X2
Imperfect Substitutes
Y
X1
12
Imperfect Substitutes
The most common problem faced by producers.
Factors
will substitute for one another, but not at a
constant rate.
Successive equal incremental reductions in one
input, must be matched by increasingly larger
increases in the other input in order to hold
output
constant.
This is what gives the curved shape to the
isoquant.
13
Imperfect Substitutes
Example Land and Fertilizer
As we decrease available land, we must use
increasingly more fertilizer to make up for the
lost land.
14
Imperfect Substitutes
Land Fertilizer
10 100
9 220
8 360
7 520
6 700
15
Marginal Rate of Substitution

• Is the rate at which resources substitute for

• one another.

16
Marginal Rate of Substitution
Is the rate at which resources substitute for
one another.
?
?
MRTS X1,X2 X2 / X1
This ignores the sign
17
Marginal Rate of Substitution
Diminishing Marginal Rate of Substitution - as
one input is increased one unit at a time, the
units of the other inputs needed to produce the
same level of output become fewer.

18
Diminishing Marginal Rate of Substitution
X2
?
X2
Y
X1
?
X1
19
Diminishing Marginal Rate of Substitution
X2
?
X2
Y
X1
?
X1
20
Diminishing Marginal Rate of Substitution
X2
Y
?
X2
X1
?
X1
21
Diminishing Marginal Rate of Substitution
X2
?
X2
Y50
Y25
X1
22
What is the Optimum or Least Cost Combination of
inputs to use?
Water
100 lbs. Cotton
Fertilizer
23
Least Cost Combination
Water
Fertilizer .50 lb
Water .10 Gallon
125
10 spent on inputs
100
75
50
25
100 lbs. Cotton
Fertilizer
5 10 15 20
24
Least Cost Combination
Water
Fertilizer .50 lb
Water .10 Gallon
125
10 spent on inputs
100
75
50
.
25
100 lbs. Cotton
Fertilizer
5 10 15 20 25
25
Least Cost Combination
Water
Fertilizer .50 lb
.
Water .10 Gallon
125
10 spent on inputs
100
75
50
25
.
100 lbs. Cotton
Fertilizer
5 10 15 20 25
26
Least Cost Combination
Water
Fertilizer .50 lb
.
Water .10 Gallon
125
10 spent on inputs
100
75
50
25
.
100 lbs. Cotton
Fertilizer
5 10 15 20 25
27
Least Cost Combination
Water
Fertilizer .50 lb
.
125
Water .10 Gallon
100
10 spent on inputs
75
Optimal input level
.
12 lbs. Fertilizer
50
40 Gal. Water
.
25
100 lbs. Cotton
5 10 15 20 25
Fertilizer
28
Change in Price of input
Water
Fertilizer .50 lb
125
Water .20 Gallon
100
10 spent on inputs
75
.
Optimal input level
16 lbs. Fertilizer
50
10 Gal. Water
.
25
.
100 lbs. Cotton
Fertilizer
5 10 15 20 25
29
Change in Price of input
Water
Fertilizer .50 lb
125
80 lbs. Cotton
Water .20 Gallon
100
10 spent on inputs
75
.
Optimal input level
16 lbs. Fertilizer
50
10 Gal. Water
.
25
.
100 lbs. Cotton
Fertilizer
5 10 15 20 25
30
Product - Product
Choosing the optimal combination of products to
produce given fixed amounts of land, labor,
capital and management.
31
Product - Product
Production Possibilities - The full range of
products a farm can produce given the set of
resources in the farm's control.
32
Product - Product
Soybeans 1000 Bushels
7
6
5
4
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10
12
33
Product - Product
Marginal Rate of Product Substitution
Measures the differing rates at which either of
the products will replace (substitute for) the
other along the production possibilities curve.
34
Product - Product
Marginal Rate of Product Substitution
Measures the differing rates at which either of
the products will replace (substitute for) the
other along the production possibilities curve.
MRPS Y1 Y2 Y2 / Y1
35
Product - Product
Y2
Y2
7
Y1
6
5
4
3
2
1
Y1
2 4 6 8 10
12
36
Product - Product
Soybeans 1000 Bushels
7
.
6
A
5
4
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
37
Product - Product
Soybeans 1000 Bushels
7
6
5
4
.
3
B
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
38
Product - Product
Soybeans 1000 Bushels
Isorevenue Line Finding the optimum combination
7
6
5
Price Grain Sorghum 2.50
4
Price Soybeans 3.75
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
39
Isorevenue Line
Soybeans 1000 Bushels
.
7
Price Grain Sorghum 2.50
6
Price Soybeans 3.75
5
Isorevenue Line 22,500
4
22,500
6,000 SB
3
3.75
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
40
Isorevenue Line
Soybeans 1000 Bushels
.
Price Grain Sorghum 2.50
7
Price Soybeans 3.75
6
Isorevenue Line 22,500
5
22,500
9,000 GS
2.50
4
3
2
.
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
41
Isorevenue Line
Soybeans 1000 Bushels
.
7
Price Grain Sorghum 2.50
6
Price Soybeans 3.75
5
Isorevenue Line 22,500
4
Slope PY1
3
PY2
2
.
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
42
Isorevenue Line
Soybeans 1000 Bushels
7
Price Grain Sorghum 2.50
6
Price Soybeans 3.75
5
4
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
43
Isorevenue Line
Soybeans 1000 Bushels
Price Grain Sorghum 2.50
7
Price Soybeans 3.75
6
5
4
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
44
Point of Revenue Maximization
Y2 / Y1 PY1 / PY2
Y2
Y2
Y1
PY1 / PY2
Y1
45
Isorevenue Line - Optimum
Soybeans 1000 Bushels
Price Grain Sorghum 2.50
7
Price Soybeans 3.75
6
Farmer would produce
5
9,000 bushels GS
.
4,000 bushels SB
4
Revenue ?
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12
46
Isorevenue Line - Optimum
Soybeans 1000 Bushels
Price Grain Sorghum 2.50
7
Price Soybeans 3.75
6
Farmer would produce
5
9,000 bushels GS
.
4,000 bushels SB
4
Revenue 37,500
3
2
1
Grain Sorghum 1000 bushels
2 4 6 8 10 12