Catastrophe theory and economic modelling at the back of an envelope

Abstract

Catastrophe theory (CT) emerged out of problems in pure mathematics. The insights and language of differential topology, from which CT sprang, are foreign to most economists. The purpose of this paper is to explain how to use Abstract CT in economic modelling. To this end, we spell out a step-by-step procedure that can be understood without a knowledge of differential topology. The corollary advantage of our systematic procedure is that it brings into sharp focus the limited relevance of CT for economic modelling. The paper is developed in four stages. The first stage provides a gentle introduction to the key mathematical concepts for readers new to CT. The second stage consists of a brief description of the structure of economic modelling. In the third stage, a procedure about how to use CT in economic modelling is spelled out. The last stage summarises the main ideas of CT and points out the snags that a modeller will inevitably encounter when applying CT to economics.