Fundamental Methods of Mathematical Economics, Volume 1984In this book, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. The book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets. |
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Page 116
... Cramer's Rule ( c ) F = 1 0 0 001 0 1 0 The method of matrix inversion just discussed enables us to derive a convenient , practical way of solving a linear - equation system , which is known as Cramer's rule . derivation of the rule nx ...
... Cramer's Rule ( c ) F = 1 0 0 001 0 1 0 The method of matrix inversion just discussed enables us to derive a convenient , practical way of solving a linear - equation system , which is known as Cramer's rule . derivation of the rule nx ...
Page 119
... Cramer's rule . The fact that d = O implies that | 4j | , for all j , must contain a whole column of zeros , and thus the solution will turn out to be x ; = | A ; \ 0 | A | = = 0 | A | ( j = = 1 , 2 , . . . , n ) Curiously enough , the ...
... Cramer's rule . The fact that d = O implies that | 4j | , for all j , must contain a whole column of zeros , and thus the solution will turn out to be x ; = | A ; \ 0 | A | = = 0 | A | ( j = = 1 , 2 , . . . , n ) Curiously enough , the ...
Page 120
... Cramer's rule ? Use Cramer's rule to solve the following systems of equations : ( a ) 2x1 - X2 = 2 3x2 + 2x3 = 16 5x1 ( b ) −x + y + z = a x - Y + z b = x + y - z = c 4 + 3x3 = 21 Show that Cramer's rule can be derived directly by the ...
... Cramer's rule ? Use Cramer's rule to solve the following systems of equations : ( a ) 2x1 - X2 = 2 3x2 + 2x3 = 16 5x1 ( b ) −x + y + z = a x - Y + z b = x + y - z = c 4 + 3x3 = 21 Show that Cramer's rule can be derived directly by the ...
Contents
The Nature of Mathematical Economics | 3 |
5 | 22 |
Three Equilibrium Analysis in Economics | 39 |
Copyright | |
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a₁ analysis apply axis b₁ b₂ chain rule choice variables coefficient column comparative statics comparative-static derivatives complementary function concave constant constraint convex set Cramer's rule curve d²z defined definite denoted determinant diagram difference equation difference quotient differential equation discussion domain dy/dx economic elements equilibrium Example exogenous variables exponential expression feasible region function f given graph identical implicit function implicit-function inequality input inverse inverse function isoquant Kuhn-Tucker lim q limit linear program marginal mathematical matrix maximization maximum minimum multiplier negative nonnegative objective function optimal solution parameters partial derivatives particular integral path payoff payoff matrix player polynomial positive problem quadratic quotient reader real numbers result rule satisfy scalar second derivative second-order condition slope solved specific substitution symbol theorem total derivative total differential vector write x₁ y₁ zero