## Fundamental Methods of Mathematical EconomicsStatic (or equilibrium) analysis; Comparative-static analysis; Optimization problems; Dynamic analysis; Mathematical programming and game theory. |

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Page 324

Even though f, and f, have been separately defined, they will—according to a

proposition known as Young's theorem—be

the two cross partial derivatives are both continuous. In that case, the sequential

...

Even though f, and f, have been separately defined, they will—according to a

proposition known as Young's theorem—be

**identical**with each other as long asthe two cross partial derivatives are both continuous. In that case, the sequential

...

Page 420

2 = lim - x-co 1 Again, this answer is

method in Example 3 of Sec. 6.4. It may turn out that the right-side expression in (

12.55) again falls into the 0|0 or the ooloo format, same as the left-side

expression.

2 = lim - x-co 1 Again, this answer is

**identical**with that obtained by anothermethod in Example 3 of Sec. 6.4. It may turn out that the right-side expression in (

12.55) again falls into the 0|0 or the ooloo format, same as the left-side

expression.

Page 500

capital-labor ratio is (by definition) unvarying over time—capital must thereafter

grow apace with labor, at the

investment must grow at the rate A (see Exercise 14.7-2). Note, however, that “

must” is ...

capital-labor ratio is (by definition) unvarying over time—capital must thereafter

grow apace with labor, at the

**identical**rate A. This will imply, in turn, that netinvestment must grow at the rate A (see Exercise 14.7-2). Note, however, that “

must” is ...

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### Contents

Two Economic Models | 8 |

Three Equilibrium Analysis in Economics | 39 |

Four Linear Models and Matrix Algebra | 59 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

analysis apply axis characteristic roots choice variables coefficient column comparative-static complementary function concave constant constraint convergence convex set Cramer's rule curve defined definite demand denoted determinant diagram difference equation difference quotient differential equation discussion dēz dual economic elements equal equilibrium Example EXERCISE exponential function expression extreme point extremum feasible region first-order condition given graph homogeneous identical illustrated indifference curves inequality input inverse isoquant Kuhn–Tucker limit linear program linearly independent logarithms marginal mathematical maximization maximum minimum multiplication negative nonlinear nonnegative notation Note objective function obtain optimal solution parameters partial derivatives particular integral path payoff matrix phase line player polynomial positive problem quadratic form quotient reader real numbers result rule satisfy scalar second derivative second-order condition slope ſē Solve specific substitution symbol theorem total differential vector write zero