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Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
- A wide variety of economic problems lead to differential, difference, and integral equations. Ordinary differential equations appear in models of economic dynamics. Integral equations appear in dynamic programming problems and asset pricing models. Discrete-time dynamic problems lead to difference equations.
- Mathematical modeling is a mixed blessing for economics. Mathematical modeling provides real advantages in terms of precision of thought, in seeing how assumptions are linked to conclusions, in generating and communicating insights, in generalizing propositions, and in exporting knowledge from one context to another. In my opinion, these advantages are monumental, far outweighing the costs. But the costs are not zero. Mathematical modeling limits what can be tackled and what is considered legitimate inquiry. You may decide, with experience, that the sorts of models in this book do not help you understand the economic phenomena that you want to understand.
- David M. Kreps, Microeconomic Foundations I: Choice and Competitive Markets (2013), Preface