Producer Decision Making Two - Variable Inputs and Enterprise Selection Chapter 5.

Producer Decision Making

Two - Variable Inputs and Enterprise Selection

Chapter 5

Three Types of Relationships Producers

Must Understand

3 Product - Product relationship deals with choosing between competing products.

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.

Factor - Factor

Choosing the optimal proportion of the

inputs in order to efficiently produceoutput.

Two-Variable Input Functions

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 Functions

A two - variable input production function can alsotake on another form:

Y = f (X1, X2 X3, X4) where X1 and X2 can vary

in amounts and X3, X4 are fixed.

..

..

.

A

B

C

DE

X1

X2

Y

(Isoquants)

Isoproduct Contours

X1

X2

Perfect Substitutes

Y

Isoproduct Contours

Perfect SubstitutesPerfect substitutes are able to replace one anotherwithout affecting output.For every unit decrease in one input a constant unitincrease in the other input will hold output at thesame level.Example : Water From Well 1 and Water from Well 2

Isoproduct Contours

Isoproduct Contours

X1

X2

Y

Perfect Complements

Perfect Complements

Perfect Complements must be used in a constantproportion to be

efficient.Therefore, an additional amount of one resource will donothing for output. There is no decision for thedetermining the ratio of use.Example: Tractor and Plow.

Isoproduct Contours

X1

X2

Y

Imperfect Substitutes

Isoproduct Contours


The most common problem faced by producers. Factorswill substitute for one another, but not at aconstant rate.Successive equal incremental reductions in oneinput, must be matched by increasingly largerincreases in the other input in order to hold outputconstant.This is what gives the curved shape to the isoquant.

Imperfect SubstitutesExample: Land and FertilizerAs we decrease available land, we must useincreasingly more fertilizer to make up for thelost land.


Land Fertilizer

10 100

9 220

8 360

7 520

6 700

Marginal Rate of Substitution

Is the rate at which resources substitute for

one another.


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.


X1

X2

Y

X2

X1

Diminishing Marginal Rate of Substitution

∆

∆

X1

X2

Y

X2

X1


∆

∆

X1

X2

YX2

X1


∆

∆

X1

X2

Y=50

X2

Y=25


∆

Fertilizer

Water

100 lbs. Cotton

What is the Optimum or Least Cost Combination of inputs to use?

Fertilizer

Water

100 lbs. Cotton

Water $ .10 Gallon

Fertilizer $ .50 lb

$ 10 spent on inputs

5 10 15 20

100

75

50

25

125

Least Cost Combination

Fertilizer

Water

100 lbs. Cotton

Water $ .10 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.


Fertilizer

Water

100 lbs. Cotton

Water $ .10 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.

.


Fertilizer

Water

100 lbs. Cotton

Water $ .10 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.

.


Fertilizer

Water

100 lbs. Cotton

Water $ .10 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.

.

.Optimal input level 12 lbs. Fertilizer

40 Gal. Water


Fertilizer

Water

100 lbs. Cotton

Water $ .20 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.

.

.

Optimal input level 16 lbs. Fertilizer 10 Gal. Water

Change in Price of input

Fertilizer

Water

100 lbs. Cotton

Water $ .20 Gallon

Fertilizer $ .50 lb


5 10 15 20 25

125

100

75

50

25

.

..

Optimal input level 16 lbs. Fertilizer 10 Gal. Water

Change in Price of input

80 lbs. Cotton

Product - Product

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.

Product - Product

Soybeans 1000 Bushels

Grain Sorghum 1000 bushels

7

6

5

4

3

2

1

2 4 6 8 10 12

Product - Product

Marginal Rate of Product Substitution

Measures the differing rates at which either ofthe products will replace (substitute for) theother along the production possibilities curve.

Product - Product

Marginal Rate of Product Substitution

Measures the differing rates at which either ofthe products will replace (substitute for) theother along the production possibilities curve.

MRPS Y1 Y2 = Y2 / Y1

Product - Product

Y2

Y1

7

6

5

4

3

2

1

2 4 6 8 10 12

Y2

Y1

Product - Product

A.



7

6

5

4

3

2

1

2 4 6 8 10 12

Product - Product



7

6

5

4

3

2

1

2 4 6 8 10 12

B.

Product - Product

Isorevenue Line— Finding the optimum combination

Price Grain Sorghum $2.50

Price Soybeans $3.75



7

6

5

4

3

2

1

2 4 6 8 10 12

Product - Product

Isorevenue Line



Isorevenue Line $22,500

$22,500 $3.75

= 6,000 SB



7

6

5

4

3

2

1

2 4 6 8 10 12

.

Isorevenue Line




$22,500 $2.50 = 9,000 GS



7

6

5

4

3

2

1

2 4 6 8 10 12.

.

Isorevenue Line




Slope = PY1

PY2



7

6

5

4

3

2

1

2 4 6 8 10 12

.

.

Isorevenue Line





7

6

5

4

3

2

1

2 4 6 8 10 12

Isorevenue Line





7

6

5

4

3

2

1

2 4 6 8 10 12

Point of Revenue Maximization

Y2 / Y1 = PY1 / PY2

Y2

Y1

PY1 / PY2

Y2

Y1

Isorevenue Line - Optimum



Farmer would produce9,000 bushels GS4,000 bushels SB

Revenue = ?



7

6

5

4

3

2

1

2 4 6 8 10 12

.



Farmer would produce9,000 bushels GS4,000 bushels SB

Revenue = $37,500



7

6

5

4

3

2

1

2 4 6 8 10 12

.

Isorevenue Line - Optimum

Producer Decision Making Two - Variable Inputs and Enterprise Selection Chapter 5.

Documents

x1 x2 y x1

sign slide

x1 x2 y perfect complements

mrts x1

cost combination slide

constant rate

variable input functions

variable inputs