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 control path control variable convergence costate variable denote derivative differential equation discount factor dt subject dynamic optimization equation of motion Euler equation Euler-Lagrange equation example EXERCISE expression F function firm first-order fixed terminal given Hamiltonian horizontal terminal line improper integral inequality infinite-horizon initial point integrand function investment Lagrange multiplier Lagrangian linear Maximize maximum principle minimize necessary condition negative nonnegative objective functional optimal control problem optimal control theory optimal path positive principal minors production function profit r₁ r₂ restriction result satisfied second-order shadow price solve specific substitution sufficient condition term terminal condition terminal point terminal value theorem tion transversality condition truncated vertical terminal u₁ vertical terminal line y₁ ymin zero ән ди ду