Singularity Theory in Comparative Statics and Comparative Dynamics

Singularity Theory (ST), Comparative Statics (CS) and Comparative Dynamics (CD) all deal with the displacement of equilibrium of trajectory caused by a slight change of some parameter, with CS focusing particularly on comparing static equilibria, CD on comparing dynamic paths and ST on degenerate critical points where the tool of both CS and CD become inadequate. This paper purports to bring the three together, since they deal with essentially the same problems, with an emphasis on ST and its place in Economics.