Intertemporal choice concerns any decision process that involve future consequences.
From a technical point of view, the objective is to provide students with an advanced understanding of dynamic optimization with a focus on continuous time modeling and optimal control theory (Pontryagin maximum principle). The course emphasizes technical difficulties that researchers encounter frequently when they model real economic problems and proposes efficient solutions (free endpoint program, free ending time problem, transversally conditions, discontinuities, constraints on control and state variables, scratch value, endogenous date of regime change, etc.).
As part of the Macroeconomic specialization field, the course will emphasize the life cycle of consumption and savings as the canonical model of intertemporal choice and draw practical examples from this literature and its generalization to health, education and social security. The course will also deal with important problems in behavioral economics: memory, addiction and time consistency.
The notions and technics discussed in this course may also be useful for students from other fields than macroeconomics, especially, Financial economics, Economic theory, Public economics, Labor Economics
I. General introduction (1. Optimal control in economics and management. 2. Basic notions : A two period model of intertemporal Choice. 3. Mathematical prerequisites).
II. Optimal control (1. Basic problem: necessary and sufficient condition for optimality. 2. Free endpoint end free ending time problems, scratch values. 3. Constraints on the state and control variables. 4. Infinite horizon. 5. Multidimensional problem.
III. Various topics in life cycle theory (1. Consumption vs investment : a continuous time Fisherian separation theorem. 2. Education, 3. Health, 4. Uncertain lifetime. 5. Labor and Social security.).
III. Various topics in behavioral intertemporal choice (.1 A brief introduction to the axiomatic of intertemporal preferences, 2. Time consistency, 3. Memory and Addiction).).
– Caputo, M. (2005), Foundations of dynamic economic analysis: optimal control theory and applications, Cambridge University Press.
– Leonard, D. & Van Long, N. (1992), Optimal control theory and static optimization in economics, Cambridge: Cambridge University Press.