Supermodular Correspondences

Apr 2016 | 795

Authors: John Quah


Supermodular functions are widely used in economics to model complementarity. For example, a firm's production function is supermodular if the marginal productivity of each factor increases with the usage of other factors. This in turn guarantees that when the price of a factor falls, the firm's demand for all factors increase. We generalise the notion of supermodular functions so the concept is also applicable to correspondences.  Supermodular correspondences arise naturally in a variety of settings. To illustrate the use of the concept and our results, we apply them to study, amongst other things, the optimising behaviour of firms producing multiple output goods and of agents with ambiguity aversion.

JEL Codes: C61, D21, D24

Keywords: supermodular correspondence, monotone comparative statics, multi- output production, ambiguity aversion

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