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 260
... condition constitutes the first - order condition for profit maximization . However , the fulfillment of the first - order condition may yield a minimum rather than a maximum ; thus we must check the second - order condition next . We ...
... condition constitutes the first - order condition for profit maximization . However , the fulfillment of the first - order condition may yield a minimum rather than a maximum ; thus we must check the second - order condition next . We ...
Page 331
... first - order condition dz O is satisfied at point A , the condition d2z < 0 at A for any values of dx and dy ( not both zero ) , is sufficient to establish the point as a peak and f ( x , y ) as a maximum value of the function z = f ...
... first - order condition dz O is satisfied at point A , the condition d2z < 0 at A for any values of dx and dy ( not both zero ) , is sufficient to establish the point as a peak and f ( x , y ) as a maximum value of the function z = f ...
Page 347
... first - order condition for extremum Let us explicitly consider a func- tion of three choice variables , z = f ( x1 , x2 , X3 ) with first partial derivatives f1 , f2 , and f3 and second partial derivatives fij ( = d2z / dx ; dx ...
... first - order condition for extremum Let us explicitly consider a func- tion of three choice variables , z = f ( x1 , x2 , X3 ) with first partial derivatives f1 , f2 , and f3 and second partial derivatives fij ( = d2z / dx ; dx ...
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a₁ analysis apply axis b₁ characteristic roots choice variables coefficient column comparative-static complementary function concave constant constraint convex set Cramer's rule curve d²z defined definite denoted determinant diagram difference equation differential equation discussion dual economic elements equilibrium Example EXERCISE exponential exponential function expression extremum feasible region first-order condition given graph identical indifference curves inequality input inverse isoquant Kuhn-Tucker limit linear program marginal mathematical matrix maximization maximum minimum multiplication negative nonlinear nonlinear programming nonnegative Note objective function optimal solution ordered pairs output parameters partial derivatives particular integral path payoff payoff matrix phase line player polynomial positive problem quadratic form quotient reader real numbers result rule satisfy scalar second derivative second-order condition slope Solve specific subset substitution symbol term theorem total differential vector write x₁ y₁ Y₁+1 zero