How Much Fertilizer Should I Put On

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How Much Fertilizer Should I Put On?

• Producer Decision Making

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What Is N, P, and K?

• N Nitrogen
• P Phosphorus
• K Potassium

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• http//www.tfi.org/media/nutrientsInTheSoil.mpg
• http//www.tfi.org/media/betterBread.mpg

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What does fertilizer do to a plant?How much
should be applied?
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Purpose

• Producers Face a three-fold decision problem
• What to produce?
• How much to produce?
• How to produce?

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Definitions

• Resource (an input)
• A factor that can be used to produce a product
  that can satisfy a human want or desire
• Land, labor, management, capital

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Definitions

• Landnot just the soil but all the natural
  environment
• Payment to land is rent
• Laborthe physical act of performing a task
• Earnings to labor is its wage
• Managementthe responsibility of decision making
• Rewards to management is profit
• Capitalevery manufactured thing that can be used
  to aid or enhance production
• Earnings of capital is its interest

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Production Function

• Different quantities and combinations of land,
  labor, capital and management will produce
  different amounts of a product.
• Y f(X1, X2, X3, , Xn)
• Relationship between the resource and its product
• Y Total Physical Product TPP

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Physical Relationships

• Y f(X1 X2, X3, , Xn)
• Y f(X1)
• Variable Inputs
• Fixed Inputs

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Law of Diminishing Returns

• As successive amounts of a variable input are
  combined with a fixed input in a production
  process, the TPP will increase, reach a maximum,
  and eventually decrease.
• Examples?

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Law of Diminishing Returns

• Marginal Physical Product (MPP)
• The amount added to total product when another
  unit of the variable input is used.
• A measure of the slope of the TPP curve
• (Change in Output) (Change in Input)
• ?TPP/?X ?Y/?X

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Average Physical Product (APP)

• How productive the variable is on the average or
  per unit of X.
• APP Output Input
• Y/X

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Stages of Production

• Stage l
• TPP increased throughout Stage l, first at an
  increasing rate, then at a decreasing rate
• MPP increasing then decreasing
• At the end of Stage l, APP is max and MPPAPP

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Stages of Production

• Stage II
• TPP increases at a decreasing rate
• APP decreasing
• MPP decreases and the reaches 0
• MPP0 when TPP is at a maximum

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Stages of Production

• Stage III
• TPP is decreasing
• APP is decreasing
• MPP is decreasing

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Economic Feasibility

• What does it cost?
• Is it worth it?
• Is there a more profitable way of doing this?

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Value Relationships

• Assumptions
• There are so many firms producing this product
  that the actions of any one firm will have no
  influence whatsoever on either input or product
  prices.
• The market does not differentiate one firms
  product from that of anotherproduce a
  homogeneous product.

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Lets Include Costs and Prices

• Market price of resource X1 is 5.00 per unit
• Market price of output Y is 1.00 per unit
• Question
• What is the proper amount of X1 to use so as to
  maximize profits?

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Definitions

• Total Value Product (TVP) TPP Py
• Dollars worth of output produced by the different
  amounts of the input X1 used.
• Average Value Product (AVP) TVP/X1
• Marginal Value Product (MVP) ?TVP/?X1
• How much additional value of output is produced
  by each additional amount of the variable input
  used.

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Definitions

• Marginal Factor Cost (MFC) Px1
• The amount that is added to total cost when one
  more unit of the variable input X1 is used.
• Because the market price of X1 is 5.00 per unit,
  using another unit of that resource will add
  5.00 to total costs.

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Definitions

• Total Revenue (TR) Y produced Py
• Total Cost x1 (TCx1) Px1 X1 used
• (Total Variable Cost (TVC))
• Net Revenue (NR) TR TCx1
• Not equal to profit because we have not
  identified all fixed costs.

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Optimum (most profitable)

• Where one more unit of the variable input adds to
  revenue just what it adds to costs
• Where MVP MFC

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Optimum (most profitable)

• Where MVP MFC is the same point where Net
  Revenue is maximum
• Profit will also be max here because fixed costs
  will not affect optimal output and rate of
  resource use.

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Optimum (most profitable)

• The MFC curve crosses the MVP curve twice.
  Therefore, we need the additional condition that
  MVP must be declining and less than AVP, which
  forces us into Stage II.

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Adjusting to Price Changes

• What happens when the Py increases? decreases?
• What happens when the price of the resource (Px1)
  changes?

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Price of output increases from 1/unit to 2/unit.
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Price of input increases from 5/unit to 10/unit.
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Price of output increases from 1/unit to 2/unit.
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Price of input increases from 5/unit to 10/unit.