Elements of Dynamic OptimizationDesigned to be used with Chiang's "Fundamental Methods of Mathematical Economics", or independently at advanced undergraduate or graduate level, this text presents an in-depth exploration of dynamic optimization in economics. |
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A₁ apply arbitrary constants assumed boundary conditions c₁ c₂ calculus of variations capital concave conditions y(0 control path control variable convergence costate variable definite denote derivative differential equation dt subject dynamic optimization equation of motion Euler equation Euler-Lagrange equation example EXERCISE expression F function F₁ firm first-order fixed terminal given Hamiltonian horizontal terminal line improper integral inequality infinite-horizon initial point integrand function investment Lagrange multiplier Lagrangian linear marginal Maximize maximum principle minimize necessary condition negative nonnegative objective functional optimal control problem optimal control theory optimal path phase diagram positive principal minors production function r₁ r₂ result satisfied second-order shadow price solution solve specific substitution sufficient condition term terminal condition terminal point terminal value theorem tion transversality condition truncated vertical terminal u₁ utility vertical terminal line y₁ ymin zero ән ди ду