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# Chiang_Ch4 - Chiang Wainwr ight M at hemat ical Economics...

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Chiang & Wainwright Chiang & Wainwright Mathematical Mathematical Economics Economics Chapter 4 Linear Models and Matrix Algebra 1 Chiang_Ch4.ppt Stephen Cooke U. Idaho

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Ch 4 Linear Models and Matrix Ch 4 Linear Models and Matrix Algebra Algebra 4.1 Matrices and Vectors 4.2 Matrix Operations 4.3 Notes on Vector Operations 4.4 Commutative, Associative, and Distributive Laws 4.5 Identity Matrices and Null Matrices 4.6 Transposes and Inverses 4.7 Finite Markov Chains 2 Chiang_Ch4.ppt Stephen Cooke U. Idaho
Objectives of math for economists  Objectives of math for economists  To understand mathematical economics problems by stating the unknown, the data and the conditions To plan solutions to these problems by finding a connection between the data and the unknown To carry out your plans for solving mathematical economics problems To examine the solutions to mathematical economics problems for general insights into current and future problems (Polya, G. How to Solve It, 2 nd ed, 1975) 3 Chiang_Ch4.ppt Stephen Cooke U. Idaho

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One Commodity Market Model One Commodity Market Model (2x2 matrix) (2x2 matrix) Economic Model (p. 32) 1) Q d =Q s 2) Q d = a – bP (a,b >0) 3) Q s = -c + dP (c,d >0) Find P* and Q* Scalar Algebra Endog. :: Constants 4) 1Q + bP = a 5) 1Q – dP = -c 4 d A x d Ax c a P Q d b 1 * 1 1 - = = - = - d b bc ad Q d b c a P + - = + + = * * Matrix Algebra Chiang_Ch4.ppt Stephen Cooke U. Idaho
One Commodity Market Model One Commodity Market Model (2x2 matrix) (2x2 matrix) 5 d A x c a d b P Q d Ax c a P Q d b 1 * 1 * * 1 1 1 1 - - = - - = = - = - Matrix algebra Chiang_Ch4.ppt Stephen Cooke U. Idaho

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General form of 3x3 linear General form of 3x3 linear matrix matrix parameters endog. vars exog. vars. & constants Scalar algebra form  parameters & endogenous variables  exog. vars & const. a 11 x + a 12 y + a 13 z = d 1 a 21 x + a 22 y + a 23 z = d 2 a 31 x + a 32 y + a 33 z = d 3 6 = 3 2 1 33 32 31 23 22 21 13 12 11 d d d z y x a a a a a a a a a Matrix algebra form Chiang_Ch4.ppt Stephen Cooke U. Idaho
1. Three Equation National Income 1. Three Equation National Income Model Model (3x3 matrix) (3x3 matrix) Let ( Exercise 3.5-1, p. 47 ) Y = C + I + G 0 C = a + b(Y-T)  (a > 0, 0<b<1) T = d + tY (d > 0, 0<t<1) Endogenous variables? Exogenous variables? Constants? Parameters? Why restrictions on the parameters? 7 Chiang_Ch4.ppt Stephen Cooke U. Idaho

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2. Three Equation National Income 2. Three Equation National Income Model Model Exercise 3.5-2, p.47 Exercise 3.5-2, p.47 Endogenous: Y, C, T: Income (GNP), Consumption, and Taxes Exogenous: I 0 and G 0 : autonomous Investment & Government spending Constants a & d: autonomous consumption and taxes Parameter t is the marginal propensity to tax gross income 0 < t < 1
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Chiang_Ch4 - Chiang Wainwr ight M at hemat ical Economics...

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