Chapter 7 Economic Principles Choosing Production Levels

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Chapter 7Economic Principles Choosing
Production Levels
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Introduction

• Economic principles consist of a set of rules,
  which together ensure that the choice or decision
  made will result in maximum profit
• Steps
• Acquire physical and biological data
• Acquire price data
• Apply economic decision making rule to maximize
  profit

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Marginalism

• Marginal incremental changes, increases or
  decreases, that occur at the edge or the margin
• May be useful to substitute the word additional
  or extra whenever the word marginal is used
• Ex You may be interested in how cotton yield
  changes from using an additional 50 of fertilizer

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Marginalism

• To calculate, it is necessary to find the
  difference between an original value and the new
  value that resulted from the change in the
  controlling factor
• We will use a small triangle for shorthand
  meaning the change in
• Ex corn yield would be read as the change
  in corn yield and would be the difference in corn
  yield before and after some change in an input
  affecting yield

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Production Function

• Relationship between inputs and outputs
• Can be presented in the form of a table, graph,
  or mathematical equation

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Production Function

• Input Output (TPP)0 0
• 1 12
• 2 30
• 3 44
• 4 54
• 5 62
• 6 68
• 7 72
• 8 74
• 9 72
• 10 68

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Average Physical Product

• Average Physical Product (APP) is the average
  amount of output produced per unit of input at
  each input level
• Measures productivity
• Ex APP 5 means that 5 units of output were
  produced on average per unit of input
• Ex APP 3 means that 3 units of output were
  produced on average per unit of input
• APP TPP / Input

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Production Function APP
Input Output (TPP) APP0 0 0 1 12
12 2 30 15 3 44 14.7 4 54 13.5 5 62 1
2.4 6 68 11.3 7 72 10.3 8 74
9.3 9 72 8 10 68 6.8
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Marginal Physical Product

• Marginal Physical Product (MPP) is the
  additional or extra TPP produced by using an
  additional unit of input
• Ex MPP 5 means that 5 additional units of TPP
  are produced from an additional unit of input
• MPP TPP / Input

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Production Function (APP MPP)
Input Output (TPP) APP
MPP0 0 0 1 12 12 12 2 30 15 18 3 44
14.7 14 4 54 13.5 10 5 62 12.4
8 6 68 11.3 6 7 72 10.3 4 8 74
9.3 2 9 72 8 -2 10 68 6.8 -4
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Graphical Analysis

• TPP increases at an increasing rate at the
  beginning of the production process
• Then TPP while still increasing, does so at a
  decreasing rate
• Finally, as more input is used, output actually
  declines
• MPP measures this relationship

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Graphical Analysis

• Whenever, MPP gt APP, APP is increasing
• WHY???
• Whenever, MPP lt APP, APP is decreasing
• WHY???
• The Production Function can be divided into 3
  stages

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Law of Diminishing Marginal Returns

• Law of Diminishing Marginal Returns as
  additional units of input are used in combination
  with one or more fixed inputs, marginal
  productivity will eventually begin to decline
• Often the case in agriculture
• Law is based on biological processes, resulting
  from the inability of plants and animals to
  provide the same response indefinitely to
  successive increases in input

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How much input to use?

• NOT Stage 3
• For an input level in Stage 3, the same output
  could be obtained with less input from one of the
  other stages
• NOT Stage 1
• APP is still increasing, incentive to produce
  more
• Soon we will show that profit can be increased
  even if productivity is decreasing
• STAGE 2 Optimal!
• We now have a range of inputs and output narrowed
  down
• We must have price information to determine where
  in Stage 2 maximizes profit

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Marginal Value Product

• Marginal Value Product (MVP) additional or
  marginal income received from using an additional
  unit of input
• MVP TVP / Input
• TVP TPP Output price

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Production Function
Input TPP APP MPP TVP MVP0 0
0 0 1 12 12 12 24 24 2 30 15 18 60
36 3 44 14.7 14 88 28 4 54 13.5 10 108 20 5 6
2 12.4 8 124 16 6 68 11.3 6 136 12 7 72 10.3
4 144 4 8 74 9.3 2 148 4 9 72 8
-2 144 -4 10 68 6.8 -4 136 -8
Input Price 12 Output Price 2
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Marginal Input Cost

• Marginal Input Cost change in total input cost,
  or the additional total input cost caused by an
  additional unit of input
• MIC TIC / Input
• TIC Input level Input price
• If the input price does not change as more input
  is purchased, then MIC input price

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Production Function
Input Price 12 Output Price 2
Input TPP APP MPP TVP MVP TIC
MIC0 0 0 0
0 1 12 12 12 24 24 12 12 2 30 15 18 60 36
24 12 3 44 14.7 14 88 28 36 12 4 54 13.5 10 108
20 48 12 5 62 12.4 8 124 16
60 12 6 68 11.3 6 136 12 72 12 7 72 10.3
4 144 4 84 12 8 74 9.3 2 148 4
96 12 9 72 8 -2 144 -4 108 12 10 68 6.8
-4 136 -8 120 12
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The Input Decision Rule

• MVP MIC
• If they are not equal MVP gt MIC
• When MVP gt MIC additional income received from
  using one more unit of input exceeds the
  additional cost of that input
• Therefore, additional profit is made with each
  additional unit of input
• If MVP lt MIC, more profit can be made with less
  input
• Can also use the rule MPP Price Input / Price
  Output

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How much Output to Produce?

• We just looked at how much input to use to
  maximize profit.
• There is a related question.
• How much output to produce?

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Marginal Revenue

• Marginal Revenue (MR) change in income or
  additional income received from selling one more
  unit of output
• MR TR / TPP
• TR TVP TPP output price
• MR will uaually equal the price of the output.
• The additional income received from selling one
  more unit of output will equal the price received
  for that output.
• The formula should be used if the output price
  changes with the quantity sold

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Production Function
Input Price 12 Output Price 2
Input TPP APP MPP TVP TR MR
0 0 0 0 0
1 12 12 12 24 24 2 2 30 15 18 60
60 2 3 44 14.7 14 88 88 2 4 54 13.5 10 108 1
08 2 5 62 12.4 8 124 124 2 6 68 11.3
6 136 136 2 7 72 10.3 4 144 144 2 8 74
9.3 2 148 148 2 9 72 8 -2 144 144 10 68
6.8 -4 136 136
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Marginal Cost

• Marginal Cost (MC) change in cost, or the
  additional cost incurred from producing one more
  additional unit of output
• MC TIC / TPP

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Production Function
Input Price 12 Output Price 2
Input TPP APP MPP TVP TR MR
MC 0 0 0 0 0
1 12 12 12 24 24 2 1.00 2 30 15 18 60
60 2 .67 3 44 14.7 14 88 88 2
.86 4 54 13.5 10 108 108 2
1.20 5 62 12.4 8 124 124 2 1.50 6 68 11.3
6 136 136 2 2.00 7 72 10.3 4 144 144 2 3.00 8
74 9.3 2 148 148 2 6.00 9 72 8
-2 144 144 10 68 6.8 -4 136 136
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The Output Decision Rule

• MR MC
• MR gt MC the additional unit of output increases
  profit because the additional income exceeds the
  additional cost
• MR lt MC producing the additional unit of output
  will decrease profit
• NOTICE!!!The optimal level of output corresponds
  with the optimal level of input on the production
  function

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Applying the Marginal Principles

• Common management decision is how much fertilizer
  to apply per acre for a certain crop
• Using the production function data, which can be
  obtained from experimental data, we can generate
  MVPs for each crop at various input levels

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Equal Marginal Principle

• Manager must decide or allocate the input among
  several alternatives.
• The equal marginal principle states that a
  limited input should be allocated among
  alternative uses in such a way that the MVP of
  the last unit used on each alternative are equal.

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Example

• Assume you can apply water in increments of 4
  acre-inches per 100 acres (or 400 acre-inches at
  a time)
• You have 3 crops on 100 acres of land each
  (wheat, grain sorghum, and cotton)
• How should you allocate the water to make the
  most money?
• FIRST obtain the MVPs for each crop

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• MVPs ()
• Water Wheat Grain Sorghum Cotton
• (acre-inch) (100 ac.) (100 ac.)
  (100 ac.)
• 0
• 4 1200 1600 1800
• 8 800 1200 1500
• 12 600 800 1200
• 16 300 500 800
• 20 50 200 400

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Example

• Assume you have 2400 acre-inches of water
  available to you.
• To determine where to apply the water, refer to
  the MVPs
• The first 400 acre-inches should go to cotton
  because it has the highest MVP