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Producer Decision Making. Two - Variable Inputs and Enterprise Selection. Chapter 5. Three Types of Relationships Producers Must Understand. 1 Factor - Product relationship deals with choosing the level of an input, in order to be efficient. .
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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.
A two - variable input production function can take on
the following form:
Y = f (X1, X2) where X1 and X2 can vary in
amounts
Two-Variable Input FunctionsA 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.
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 1and Water
fromWell 2
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.
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.
Example: Land and Fertilizer
As we decrease available land, we must use
increasingly more fertilizer to make up for the
lost land.
Is the rate at which resources substitute for
one another.
∆
∆
MRTS X1,X2 = X2 / X1
This ignores the sign
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.
Water
Fertilizer $ .50 lb
Water $ .10 Gallon
125
$ 10 spent on inputs
100
75
50
25
100 lbs. Cotton
5 10 15 20
Fertilizer
Water
Fertilizer $ .50 lb
125
Water $ .10 Gallon
$ 10 spent on inputs
100
75
50
.
25
100 lbs. Cotton
Fertilizer
5 10 15 20 25
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
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
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
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
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
Choosing the optimal combination of products to produce given fixed amounts of land, labor, capital and management.
Production Possibilities - The full range of products a farm can produce given the set of resources in the farm's control.
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.
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
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
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
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
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
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
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
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
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
