Chapter 37: The Phase Diagram Technique for Analyzing the Stability of Multiple-market Equilibrium
37. The phase diagram technique for analyzing the stability of multiplemarket equilibrium D. Wade Hands The phase diagram technique is a tool for analyzing the stability of equilibrium (or equilibria) in a two-variable economic model. The technique starts from a standard two-variable diagram, but adds arrows to indicate the direction of movement away from any non-equilibrium position. As a tool of mathematical analysis, the phase diagram is a rather blunt instrument; it is limited to two-dimensional models (or those that can be reduced to two dimensions) and only captures the rough qualitative properties of the underlying dynamic model. If the dynamics are given explicitly by a system of differential (or difference) equations, more detailed information can be obtained by solving or integrating the dynamic system and directly analyzing the timepath of the variables. Nonetheless, the phase diagram technique provides a very convenient and intuitive way of deriving a wealth of information about the dynamics of a wide range of multiple-market economic models. The phase diagram has been used in the analysis of multi-market stability since Alfred Marshall introduced it into economics in his Pure Theory of Foreign Trade during the 1870s, and it played an important role in the literature on the stability of Walrasian general equilibrium during the late 1950s and 1960s. Over the years, the phase diagram technique has also been employed in many other areas of economic theory, including macroeconomics, growth theory, development economics and a number of areas within applied microeconomics. The technique has also been...
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