Abstract
The treatment of time is a question which cannot be avoided by economists despite some ingenious attempts to do just that. In the Arrow-Debreu world of general equilibrium there is no room for time. All deals are made at an instant and cover a complete set of contingent and futures markets. As time unfolds these predetermined deals are simply activated: no re-contracting is allowed. This treatment effectively eliminates time from the model and, in a sense, contributes to its theoretical elegance. Elegance was, however, not high in Chapter 1’s list of desirable properties of models. Time is important and an important modelling technique for dealing with it is the theory of differential equations.
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Further reading
Arrowsmith and Place (1982) is an excellent reference on ordinary differential equations which adopts a qualitative approach and contains several applications, some to economics. A more advanced text is Hirsch and Smale (1974).
Begg (1982) and Carter and Maddock (1984) discuss rational expectations models, complete with ‘jump variables’. George and Oxley (1985) discuss the notion of robustness and its relevance to rational expectations models.
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© 1988 Donald A.R. George
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George, D.A.R. (1988). Differential equations. In: Mathematical Modelling for Economists. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-19238-0_6
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DOI: https://doi.org/10.1007/978-1-349-19238-0_6
Publisher Name: Palgrave Macmillan, London
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