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Economics is a fascinating field of knowledge, essentially because it is capable of applying rigorous notions and tools from the exact sciences to the understanding of human behavior and of social relations, realities that clearly involve relevant traces of unpredictability. As a result, the economic science employs concepts that are unique to its own domain and that require a formal design that only mathematics can provide. These concepts include such powerful ideas as the ones of rationality or expectations. Traditional economic analysis makes use of a relatively simple benchmark model, according to which a representative agent resorts to all the available information in order to optimize her behavior. Typically, the agent maximizes expected consumption utility from the current period, t=0, to a pre-determined future date, subject to a resource constraint that can represent the way an individual household manages her budget or, alternatively, in a more broad view, the production possibilities frontier that the economy faces. The mentioned constraint takes the form of a differential equation or of a difference equation, depending on the notion of time that is more adequate to approach the problem under analysis.
