Chapter 8: Economic Principles Choosing Input and Output Combinations

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Chapter 8 Economic Principles Choosing Input
and Output Combinations
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Chapter Objectives

• 1) To explain the use of substitution in
  economics and decision making
• 2.) To demonstrate how to compute a substitution
  ratio and a price ratio between two inputs
• 3.) To use the input substitution and price
  ratios to find the least-cost combination of two
  inputs
• 4.) To describe the characteristics of
  competitive, supplementary, and complementary
  enterprises
• 5.) To show the use of the output substitution
  and price ratios to find the profit maximizing
  combination of two enterprises.

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Introduction

• Substitution occurs daily in everyones life
• Ex when you buy Crest instead of a generic
  toothpaste
• Ex when you eat steak instead of hamburger
• Ex when you replace a human with a machine

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Introduction

• Substitution is not an all or nothing decision
• Usually relatively small changes in the mix
• Therefore, substitution is a type of marginal
  analysis that considers the changes in cost and
  or income

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Input Combinations

• Farm and ranch mangers must make decisions on how
  much to produce of a given product
• Most of these products require several inputs
• Therefore, the problem is determining how much of
  one input can be substituted for another at the
  least cost
• Ex forage and grain can be exchanged in a
  livestock feed ration

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Input Combinations

• The manager must select the least-cost
  combination of inputs to maximize profits from a
  given amount of output
• Good managers will be looking for different input
  combinations that will do the same job for less
  cost

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Input Substitution Ratio

• Lets look at an example where corn and barley
  are substitutes in a feed ration
• 1st Step determine whether it is physically
  possible to make a substitution, and if so at
  what rate
• Isoquant show a number of combinations of corn
  and barley that will produce the same quantity of
  output or weight gain in this example

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Input Substitution Ratio

• Substitution Ratio rate at which one input will
  substitute for another
• Substitution Ratio Amount of Input Replaced
• Amount of Input Added

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Input Substitution Ratio
CONSTANT RATE
A
4
B
Corn
5
Barley
Substitution Ratio 4 / 5 .8 Interpret 1 lb.
barley will only replace .8 lb. corn
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Input Substitution Ratio
DECREASING RATE
A
4
B
Corn
1
C
D
1
3
Barley
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Input Substitution Ratio

• Point A to B
• Substitution Ratio 4 / 1 4
• Interpret 1 lb. barley will replace 4 lb. Corn
• Point C to D
• Substitution Ratio 1 / 3 .33
• Interpret 1 lb. barley will only replace .33 lb.
  corn

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Input Substitution Ratio

• Many agricultural substitution problems have a
  decreasing substitution ratio
• As more of one input is substituted for another,
  it becomes increasingly difficult to make any
  further substitution and still maintain the same
  level of output
• More and more added input is needed to substitute
  for a unit of the input being replaced, causing
  the substitution ratio to decrease

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The Decision Rule

• Identifying the physical substitution that exists
  and calculating the substitution ratio are
  necessary steps, but they do not alone determine
  the least cost-combination.
• We need input prices!
• The ratio of the input prices can then be
  compared to the substitution ratio

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The Decision Rule

• Price Ratio ratio of the added input price
  divided by the replaced input price
• This is inverse to the substitution ratio
• Price ratio also called the Inverse Price Ratio
• Price Ratio Price of Input Added
• Price of Input Replaced

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The Decision Rule

• Substitution Ratio gt Price Ratio
• Lets look at an example and determine the
  least cost combination of input according to our
  Decision Rule

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Least Cost Feed Ration

• Feed Grain Hay Substitution Price
• Ration (lb.) (lb.) ratio ratio
• A 825 1350
• B 900 1130 2.93 1.47
• C 975 935 2.60 1.47
• D 1050 770 2.20 1.47
• E 1125 625 1.93 1.47
• F 1200 525 1.33 1.47
• G 1275 445 1.07 1.47

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The Decision Rule

• The substitution ratio will not change over time
  unless the underlying biological or physical
  relationships change
• The price ratio will change over time and a new
  solution will be found

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Enterprise Combinations

• A manager will also need to decide what
  combinations of enterprises will maximize profits
• A choice must be made from all enterprises
• Ex hogs, poultry, beef cattle, wheat, soybeans,
  vegetables, cotton

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Competitive Enterprises

• 1st Step to determine profit maximizing
  enterprise combinations, the physical
  relationship must be determined
• Given that there is limited land, capital, or
  other inputs, production from one enterprise can
  often be increased only by decreasing production
  in another enterprise
• Some of the limited input must be switched from
  one enterprise to another
• Trade-offs

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Competitive Enterprises

• Competitive Enterprises compete for the use of
  the same limited input at the same time.
• 2 Types of Competitive Enterprises
• Production Possibility Curve (PPC) all
  combinations of outputs that can be produced from
  the given input.
• Ex All combinations of corn and soybeans that
  can be produced from 100 acres of land

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Competitive Enterprises
12000
Corn
120
100 acres
40
120
40
4000
Barley
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Competitive Enterprises
12000
120
100 acres
80
Corn
240
40
4000
Soybeans
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Substitution Ratio

• Substitution Ratio Quantity of Output Lost
• Quantity of Output Gained
• For the 1st PPC
• 120 / 40 3
• Interpret 3 bushels of corn must be given
  up to gain 1 bushel of soybeans

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Substitution Ratio

• 2nd PPC
• 120 / 80 1.5 (near the top of the curve)
• Interpret 1.5 bushels of corn must be given up
  to gain 1 bushel of soybeans
• 240 / 40 6 (near the bottom of the curve)
• Interpret 6 bushels of corn must be given up to
  gain 1 bushel of soybeans
• These enterprises are still competitive, but
  have an increasing substitution ratio

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Price Ratio

• Price Ratio Price of Output Gained
• Price of Output Lost
• The decision rule is similar to earlier, but
  slightly different
• Substitution Ratio lt Price Ratio
• Notice the sign!!!
• Lets look at an example

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Profit Maximizing Enterprise Combination

• Combination Corn Wheat Subst. Price
• (bu.) (bu.) ratio ratio
• 1 0 6000
• 2 2000 5600 .20 .70
• 3 4000 5000 .30 .70
• 4 6000 4100 .45 .70
• 5 8000 3000 .55 .70
• 6 10000 1700 .65 .70
• 7 12000 0 .85 .70

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Supplementary Enterprises

• Competitive enterprise are the most common
• Supplementary Enterprises if the production from
  one enterprise can be increased without affecting
  the production level of the other
• Ex beef production from stocker steers run on
  winter wheat pasture can increase over a range
  without affecting the amount of wheat produced
• The PPC will show that this relationship exists
  to a point, and eventually becomes competitive

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Supplementary Enterprises

• A manager should continue to produce up to at
  least the point where the enterprises become
  competitive

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Supplementary Enterprises
Supplementary
Competitive
Wheat
Beef
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Complementary Enterprises

• Complementary Enterprises this relationship
  exists whenever the production function from one
  enterprise causes the production from the other
  to increase at the same time
• Ex leaving some land fallow may increase wheat
  production
• Enterprise that are complementary over some
  range, will then become competitive
• A manager would want to increase production at
  least to the point where it changes from
  complementary to competitive

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Complementary Enterprises
Competitive
Complementary
Wheat
Fallow
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Questions?