Agricultural Economics

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AgEc 301 Agricultural Economics I
Slide Set 6 Chapter 8
Production Analysis
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The Production Process

• At the heart of every creative endeavor is the
  production process.
• Great innovations coupled with inefficient
  production make for bankrupt companies.

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Productive Efficiency

• Its not about what or how to produce, its about
  both.

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The Production Function

• The production function specifies the maximum
  output that can be produced for a given amount of
  input.
• Or
• The production function shows the minimum
  quantity of input necessary to produce a given
  level of output.

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The Production Function

• We will begin by examining a simple two-input,
  one-output system. Consider inputs X and Y and
  output Q. The production relationship could be
  expressed as
• Q f(X,Y)

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Discrete vs. Continuous

• A discrete production function involves distinct,
  or lumpy patterns of input combinations (e.g.
  table 8.1 in your text).
• A continuous function is one in which inputs can
  be varied in an unbroken fashion.

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An example of a discrete function
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Production Functions

• Note that very few production relationships exist
  where output continues to increase as more inputs
  are added. This is due primarily to the
  existence of one or more inputs which are fixed.

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Optimizing Production

• As we have discussed previously, the optimization
  process involves analyzing the relation between
  the total and marginal values of the function.
• Total product
• Average product
• Marginal product

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Total Product

• Total product is simply the output form a
  production system. In the function
• Q f(X,Y)
• Q represents Total Product.

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Holding Y Constant
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TP, MP, AP

• TP f(X,Y)
• MPX
• APX TP/X Q/X

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Stage I
Stage III
Stage II
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Stage II

• You do not want to produce at a level of input
  lower than where AP is maximized.
• Why?

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Stage II

• You never want to produce at a level of input
  greater than the point where MP 0.
• Why?

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The Law of Diminishing Returns

• The law of diminishing returns states that as the
  quantity of a variable input increases, with the
  quantities of all other factors held constant,
  the resulting change in output eventually
  diminishes.

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The Law of Diminishing Returns

• The marginal product (first derivative of the
  total product) must eventually decline as more of
  the variable factor is combined with other fixed
  resources.

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The Function Coefficient

• The function coefficient is the output elasticity
  of X. It can be defined mathematically as
• This will be greater than, equal to or less than
  1, depending on the relationship of MPX and APX

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Input Combination Choice

• It is often useful to examine the productivity of
  factors of production using isoquant analysis.
• Isoquant analysis explicitly recognizes
  interactions between two inputs in the production
  of one output.

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Some Definitions

• Isoquant equal quantity, denotes a curve that
  represents the different combinations of inputs
  that can be used to produce a given level of
  output. All points on the curve result in the
  same (equal) level of output.

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Some Definitions

• In the definition of isoquant, the term
  efficiency refers to what economists call
  technical efficiency.
• Technical efficiency implies the least cost
  production of the target level of output.

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Input Factor Substitution

• The shape of the isoquant reveals a lot about the
  substitutability of input factors.
• In some production systems input substitution is
  easily accomplished. The flatter the isoquant,
  the easier the substitution.

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Input Factor Substitution

• Most multiple input production systems will
  display some sort of factor substitutability.
• The nature of that substitutability may change
  over the length of the isoquant.

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Isoquant Shape
No substitution (perfect compliments
Perfect substitutes
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Imperfect substitutes
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Marginal Rate of Technical Substitution

• The marginal rate of technical substitution
  (MRTS) is the amount of one input factor that
  must be substituted for one unit of another input
  factor to maintain a constant level of output.

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MRTS

• Algebraically, MRTS is
• MRTS MPX1/MPX2
• Which is the slope of the isoquant.

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Rational Limits of Input Substitution

• It is irrational for a firm to combine resources
  in such a way that the marginal product of any
  input is negative.
• On an isoquant, this would occur where the slope
  is positive.

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Rational Limits

• The rational limits are where the isoquants
  become positively sloped. These limits are
  indicated by points of tangency with lines drawn
  perpendicular to the X and Y axis.

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Ridge Lines

• If these points of tangency are connected on the
  isoquant map, the resulting lines are called
  ridge lines.
• The rational input combinations lie between these
  ridge lines.

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