Producer Decision Making

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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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Presentation Transcript
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.

2 Factor - Factor relationship deals with choosing between competing factors.

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

Choosing the optimal proportion of the

inputs in order to efficiently produce

output.

Factor - Factor
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

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.

.

.

.

.

.

A

B

C

D

E

X1

X2

Y

Isoproduct Contours

(Isoquants)

Isoproduct Contours

X2

Perfect Substitutes

Y

X1

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 1and Water

fromWell 2

Isoproduct Contours

X2

Perfect Complements

Y

X1

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.

Isoproduct Contours

X2

Imperfect Substitutes

Y

X1

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.

Imperfect Substitutes

Example: Land and Fertilizer

As we decrease available land, we must use

increasingly more fertilizer to make up for the

lost land.

Marginal Rate of Substitution

Is the rate at which resources substitute for

one another.

MRTS X1,X2 = X2 / X1

This ignores the sign

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.

What is the Optimum or Least Cost Combination

of inputs to use?

Water

100 lbs. Cotton

Fertilizer

Least Cost Combination

Water

Fertilizer \$ .50 lb

Water \$ .10 Gallon

125

\$ 10 spent on inputs

100

75

50

25

100 lbs. Cotton

5 10 15 20

Fertilizer

Least Cost Combination

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

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

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

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

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

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

Product - Product

Choosing the optimal combination of products to produce given fixed amounts of land, labor, capital and management.

Product - Product

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

7

6

5

4

3

2

1

Grain Sorghum 1000 bushels

2 4 6 8 10 12

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.

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

Product - Product

Y2

Y2

7

Y1

6

5

4

3

2

1

Y1

2 4 6 8 10 12

Product - Product

Soybeans 1000 Bushels

7

.

6

A

5

4

3

2

1

Grain Sorghum 1000 bushels

2 4 6 8 10 12

Product - Product

Soybeans 1000 Bushels

7

6

5

4

.

3

B

2

1

Grain Sorghum 1000 bushels

2 4 6 8 10 12

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

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

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

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

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

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

Point of Revenue Maximization

Y2 / Y1 = PY1 / PY2

Y2

Y2

Y1

PY1 / PY2

Y1

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

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