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Farm Management. Chapter 8 Economic Principles  Choosing Input and Output Combinations. Chapter Outline. Input Combinations Enterprise Combinations. Input Combinations. Most products require two or more inputs, and the manager may choose the input combination or ratio to use.

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farm management

Farm Management

Chapter 8

Economic Principles 

Choosing Input and Output Combinations

chapter outline
Chapter Outline
  • Input Combinations
  • Enterprise Combinations
input combinations
Input Combinations

Most products require two or more

inputs, and the manager may choose

the input combination or ratio to use.

The economic question is whether

one input can be substituted for

another to reduce the cost.

types of input substitution
Types of Input Substitution
  • Constant rate (perfect substitution)
  • Decreasing rate
  • No substitution
choosing inputs
Choosing Inputs
  • We will address how to minimize cost for a given level of output.
    • We will do so by combining isocosts with isoquants
producing a given output at minimum cost

Q1is an isoquant

for output Q1.

Isocost curve C0 shows

all combinations of K and L

that can produce Q1at this

cost level.

K2

CO C1 C2 are

three

isocost lines

A

K1

Q1

K3

C0

C1

C2

L2

L1

L3

Producing a GivenOutput at Minimum Cost

Capital

per

year

Isocost C2 shows quantity

Q1 can be produced with

combination K2L2or K3L3.

However, both of these

are higher cost combinations

than K1L1.

Labor per year

input substitution when an input price change

If the price of labor

changes, the isocost curve

becomes steeper due to

the change in the slope -(w/L).

This yields a new combination

of K and L to produce Q1.

Combination B is used in place

of combination A.

The new combination represents

the higher cost of labor relative

to capital and therefore capital

is substituted for labor.

B

K2

A

K1

Q1

C2

C1

L2

L1

Input Substitution When an Input Price Change

Capital

per

year

Labor per year

cost in the long run
Cost in the Long Run
  • Isoquants and Isocosts and the Production Function
input substitution ratio
Input Substitution Ratio

Input substitution ratio =

amount of input replaced

amount of input added

a firm s expansion path

The expansion path illustrates

the least-cost combinations of

labor and capital that can be

used to produce each level of

output in the long-run.

$3000 Isocost Line

Expansion Path

$2000

Isocost Line

C

B

300 Unit Isoquant

A

200 Unit

Isoquant

A Firm’s Expansion Path

Capital

per

year

150

100

75

50

25

Labor per year

100

150

200

300

50

a firm s long run total cost curve

Expansion Path

F

E

D

A Firm’s Long-Run Total Cost Curve

Cost

per

Year

3000

2000

1000

Output, Units/yr

100

200

300

input price ratio
Input Price Ratio

Input price ratio =

price of input being added

price of input being replaced

decision rule
Decision Rule

input substitution ratio = input price ratio

If they cannot be exactly equal because

of the choices available in the table, get

as close as possible without letting

the price ratio exceed the substitution

ratio.

table 8 1 selecting a least cost feed ration
Table 8-1 Selecting a Least-Cost Feed Ration

grain at 4.4¢ and hay at 3.0¢

with different types of substitution
With Different Types of Substitution
  • With a constant rate of substitution, the least-cost combination will be all of one input and none of the other (unless the price ratio is exactly equal to the constant rate of substitution).
  • With a decreasing rate of substitution, the least-cost combination will usually include some of each input.
enterprise combinations
Enterprise Combinations

Another decision that must be made

is the combination of enterprises

to produce to maximize profits. If one

or more inputs is limited, there is an

upper limit on how much can be

produced.

enterprise relationships
Enterprise Relationships

The first step in determining the

profit-maximizing combination of

enterprises is to determine the

physical relationship among the

enterprises.

types of relationships
Types of Relationships
  • Competitive: output of one enterprise cannot be increased unless output of the other decreases
  • Supplementary: more output from one enterprise can be added without a change in the level of the other enterprise
  • Complementary: as output of one enterprise increases, output of the other increases also
product transformation curve

Each curve shows

combinations of output

with a given combination

of L,L & K.

O2

O1 illustrates a low level

of output. O2 illustrates

a higher level of output with

two times as much labor, land

and capital.

O1

Product Transformation Curve

Corn

Soybeans

production with two outputs economies of scope
Production with TwoOutputs--Economies of Scope
  • Observations
    • Product transformation curves are negatively sloped
    • Constant returns exist in this example
output substitution ratio
Output Substitution Ratio

Output Substitution Ratio =

quantity of output lost

quantity of output gained

output price ratio
Output Price Ratio

Output Price Ratio =

price of output gained

price of output lost

decision rule1
Decision Rule

output substitution ratio = output price ratio

If no available combination makes these

exactly equal, get as close as possible

without letting the price ratio drop below

the substitution ratio.

table 8 2 profit maximizing enterprise combination
Table 8-2Profit-Maximizing Enterprise Combination

corn at $2.80/bu, wheat at $4.00/bu

summary
Summary

This chapter emphasizes the use of

substitution principles to decide how

and what to produce. To decide

how to produce, the manager finds

the least-cost combination of inputs.

To decide what to produce, the manager

finds the profit-maximizing combination

of enterprises.