Presentation is loading. Please wait.

Presentation is loading. Please wait.

Ch. 5b Linear Models & Matrix Algebra 5.5Cramer's Rule 5.6Application to Market and National-Income Models 5.7Leontief Input-Output Models 5.8Limitations.

Similar presentations


Presentation on theme: "Ch. 5b Linear Models & Matrix Algebra 5.5Cramer's Rule 5.6Application to Market and National-Income Models 5.7Leontief Input-Output Models 5.8Limitations."— Presentation transcript:

1 Ch. 5b Linear Models & Matrix Algebra 5.5Cramer's Rule 5.6Application to Market and National-Income Models 5.7Leontief Input-Output Models 5.8Limitations of Static Analysis 1

2 5.2 Evaluating a third-order determinant Evaluating a 3rd order determinant by Laplace expansion 2 Ch. 5a Linear Models and Matrix Algebra

3 5.5 Deriving Cramers Rule (nxn) Ch. 5b Linear Models and Matrix Algebra

4 5.5 Deriving Cramers Rule (3x3) Ch. 5b Linear Models and Matrix Algebra

5 5.5 Deriving Cramers Rule (3x3) Ch. 5b Linear Models and Matrix Algebra

6 5.5 Deriving Cramers Rule (3x3) Ch. 5b Linear Models and Matrix Algebra

7 5.5 Deriving Cramers Rule (3x3) Ch. 5b Linear Models and Matrix Algebra

8 5.5 Deriving Cramers Rule (nxn) Ch. 5b Linear Models and Matrix Algebra

9 5.5 Deriving Cramers Rule (nxn) Ch. 5b Linear Models and Matrix Algebra

10 5.5 Deriving Cramers Rule (nxn) Ch. 5b Linear Models and Matrix Algebra

11 5.6Applications to Market and National-income Models: Matrix Inversions Ch. 5b Linear Models and Matrix Algebra

12 5.6 Macro model Section 3.5, Exercise (a-d), p. 47 and Section 5.6, Exercise (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 Ch. 5b Linear Models and Matrix Algebra

13 5.6 The macro model (3.5-2, p. 47) Ch. 5b Linear Models and Matrix Algebra

14 5.6 The macro model (3.5-2, p. 47) Ch. 5b Linear Models and Matrix Algebra

15 5.6 Application to Market & National Income Models: Cramers rule (3.5-2, p. 47) Ch. 5b Linear Models and Matrix Algebra

16 5.6 Application to Market & National Income Models: Matrix Inversion (3.5-2, p. 47) Ch. 5b Linear Models and Matrix Algebra

17 5.6 Application to Market & National Income Models: Matrix Inversion (3.5-2, p. 47) Ch. 5b Linear Models and Matrix Algebra

18 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Miller and Blair 2-3, Table 2-3, p 15 Economic Flows ($ millions) Inputs (cols) Outputs (rows) Sector 1 (z i1 ) Sector 2 (z i2 ) Final demand (d i ) Total gross output (x i ) Intermediate inputs: Sector Intermediate inputs: Sector Primary inputs (w i ) Total outlays (x i )

19 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Miller and Blair 2-3, Table 2-3, p 15 Inter-industry flows as factor shares Inputs (cols) Outputs (rows) Sector 1 (z i1 /x 1 =a i1 ) Sector 2 (z i2 /x 2 =a i2 ) Final demand (d i ) Total output (x i ) Intermediate inputs: Sector Intermediate inputs: Sector Primary inputs (w i /x i ) Total outlays (x i /x i )

20 5.7 Leontief Input-Output Models Structure of an input-output model Ch. 5b Linear Models and Matrix Algebra

21 5.7 Leontief Input-Output Models Structure of an input-output model Ch. 5b Linear Models and Matrix Algebra

22 5.7 Leontief Input-Output Models Structure of an input-output model Ch. 5b Linear Models and Matrix Algebra

23 5.7 Leontief Input-Output Models Structure of an input-output model Ch. 5b Linear Models and Matrix Algebra

24 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model Miller & Blair, p. 102

25 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

26 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

27 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

28 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

29 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

30 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

31 Ch. 5b Linear Models and Matrix Algebra Leontief Input-Output Models Structure of an input-output model

32 5.8Limitations 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 Ch. 5b Linear Models and Matrix Algebra

33 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 Ch. 5b Linear Models and Matrix Algebra


Download ppt "Ch. 5b Linear Models & Matrix Algebra 5.5Cramer's Rule 5.6Application to Market and National-Income Models 5.7Leontief Input-Output Models 5.8Limitations."

Similar presentations


Ads by Google