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1
Programing models 1

• Motivation
• Basic Elements
• A Simple Example
• General Assumptions
• Lagrangean Method of Solving LP-Problems
• Comparison with Behavioural Models

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Why Use LPs in Sectoral Analysis?

• Proven instrument individual farm planning and
  controlling.
• Long Tradition gt Experience, Trust
• Multiproduct interdependencies in agriculture
  are captured in the explicit
  representation of technologie (e.g.
  competition for scarce ressources...)
• Simple representation of policy instruments
  (e.g. quotas, premiums, set-aside...)
• Can be built upon technical Information

3
Basic Elements of LPs

• Objective funktion Economic objective which
• is to be optimized (Revenues, Costs...)
• Restrictions describe the possible application
  and
• combination of activities (e.g. Application of
  fix factors
• such as Area, Barns, Quotas Interproduct
  relationships such as Fodder use,
• crop rotation, etc.)
• Activities Production, sale,purchase,onfarm
  usage...
• Limitation fix factors, quotas, ..

4
Presentaion of LPs

• as a tableau with rows and columns (for
  example in EXCEL)
• in mathematic notation
• with sumation signs
• Vektors/Matrices

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Structure of an examplary farm LP
RHS constraints
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Example 1 mathematical presentation
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Example 1 Solution Space
X1
6
5
X2
6
4
8
Example 1 Objective function
X1
6
5
X2
6
4
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Example 1 Optimum
X1
6
5
X2
6
4
10
Solutions for different cs
X1
6
C1
5
X1
X2
6
4
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Deducting Supply and demand functions

• Parametrical price changes
• leaping reaction
• Supply function resembles a stairway

12
Basic Assumptions

• Objective function is linear for volume of
  activities
• Volume of activities can be fractioned
• Constraints are linear for volume of activities
• Adding up is fulfilled for rows
• proportionality in columns
• constant returns to scale
• and regarding a single activity, substitution
  elasticity of zero

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Lagrangean function (1)
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Lagrangean function (2) activities

• complementary slackness

• If the contribution of the objective value covers
  the
• opportunity costs of using fixed factors, then
  the activity
• can be introduced
• Should the objective value fall bellow, the
  volume of
• the activity must be zero (i.e. it will not be
  introduced)

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Lagrangeansatz (3) constraints

• complementary slackness

• If the constraint is binding, the dual value
  can be positive
• if the constraint is not binding, the dul
  value must be zero

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• Questions up to this point?

17
Comparison LP and Behavioural Model
Theoretic foundation
Profit maximization
Profit maximization
?
?
Technology
Explicit, linear
Implicit
Estimation
Estimation
Generation
Literatur
Solving behaviour
Leapin
Continual
Continual