Difference and differential equations: system of equations, solution and stability, application : business cycle, Solow growth model; Optimal control: Hamiltonian, Dorfman’s economic interpretation of maximum principle, open loop and closed loop solutions, phase diagrams and stability, endpoint problems, equality constrained problems, infinite horizon and transversality conditions, application : extraction of renewable and non-renewable resources, pollution control and political business cycle models; Dynamic programming: optimality principle, value function, Bellman equation, optimal strategies, finite and infinite time horizon, relationship between optimal control and dynamic programming, Hamilton-Jacobi-Bellman equation, application: the Ramsey-Cass-Koopmans growth model, overlapping generation model, debt dynamics; Calculus of Variation: brief introduction, Euler equation, relation between Calculus of Variation and Optimal Control, application: classical planning models.
