Dynamic Economics: Optimization by the Lagrange Method

By Gregory C. Chow | Go to book overview

List of Mathematical Statements
Bellman equation (2.11), 21 first-order conditions for dynamic optimization, 22
matrix Ricatti equation (2.27), 24
method of undetermined coefficients, 24
sufficient conditions for optimization, 27
necessary conditions of concave programming, 28
Lagrange theorem with inequality constraints, 29
sufficient conditions for concave programming, 29
quasi-concave programming, 29
solution (3.22)-(3.25) to multisector growth model, 36
equation (4.5) for price function of assets, 52
Kuhn-Tucker Theorem, 54
pricing function (4.19) of a one-period bond, 60
Lemma on existence and uniqueness of solution to a functional equation, 64
theorem on existence and uniqueness of competitive equilibrium in a cash- in-advance economy, 64
first-order conditions (4.45)-(4.47) for a multisector optimum growth model, 73
first-order conditions (4.52)-(4.54) for a multisector optimum growth model, 75
likelihood function (5.13) for simultaneous-equations, 87
generalized method of moments GMM estimator (5.31)-(5.32), 98
covariance matrix of GMM estimator (5.33), 98
chi-square test of restrictions on parameters estimated by GMM, 99
proposition on perfect equilibrium strategy for infinitely repeated games, 119
lemma on subgame perfect equilibrium strategy of a dynamic game with state variables, 120
necessary and sufficient conditions for an outcome path of the government's and the public's actions to be credible, 125
necessary and sufficient conditions for an outcome path of the government's and the public's actions to be credible in a dynamic game with state variables, 128
formulation of a principal-agent problem, 132
equilibrium of an economy with government taxation, 133
lemma on an optimum salary schedule

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