Ch' 5b Linear Models

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Ch. 5b Linear Models Matrix Algebra

• 5.5 Cramer's Rule
• 5.6 Application to Market and National-Income
  Models
• 5.7 Leontief Input-Output Models
• 5.8 Limitations of Static Analysis

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5.2 Evaluating a third-order determinantEvaluati
ng a 3rd order determinant by Laplace expansion
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5.5 Deriving Cramers Rule (nxn)
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5.5 Deriving Cramers Rule (3x3)
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5.5 Deriving Cramers Rule (3x3)
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5.5 Deriving Cramers Rule (3x3)
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5.5 Deriving Cramers Rule (3x3)
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5.5 Deriving Cramers Rule (nxn)
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5.5 Deriving Cramers Rule (nxn)
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5.5 Deriving Cramers Rule (nxn)
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5.6 Applications to Market and National-income
Models Matrix Inversions
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5.6 Macro model

• Section 3.5, Exercise 3.5-2 (a-d), p. 47 and
• Section 5.6, Exercise 5.6-2 (a-b), p. 111
• Given the following model
• (a) Identify the endogenous variables
• (b) Give the economic meaning of the parameter g
• (c) Find the equilibrium national income
  (substitution)
• (d) What restriction on the parameters is needed
  for a solution to exist?
• Find Y, C, G by (a) matrix inversion (b) Cramers
  rule

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5.6 The macro model (3.5-2, p. 47)

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5.6 The macro model (3.5-2, p. 47)
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5.6 Application to Market National Income
Models Cramers rule (3.5-2, p. 47)
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5.6 Application to Market National Income
Models Matrix Inversion (3.5-2, p. 47)


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5.6 Application to Market National Income
Models Matrix Inversion (3.5-2, p. 47)


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5.7 Leontief Input-Output Models Miller and Blair
2-3, Table 2-3, p 15 Economic Flows ( millions)
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5.7 Leontief Input-Output Models Miller and Blair
2-3, Table 2-3, p 15 Inter-industry flows as
factor shares
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model Miller Blair, p. 102
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.7 Leontief Input-Output Models Structure of an
input-output model
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5.8 Limitations of Static Analysis

• Static analysis solves for the endogenous
  variables for one equilibrium
• Comparative statics show the shifts between
  equilibriums
• Dynamics analysis looks at the attainability and
  stability of the equilibrium

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5.6 Application to Market and National-Income
Models Market model National-income
model Matrix algebra vs. elimination of
variables

• Why use matrix method at all?
• Compact notation
• Test existence of a unique solution
• Handy solution expressions subject to manipulation