21.2 The equilibrium and its graphical presentation

  21.2.1 The four-field-graphic

We now summarize all assumptions and close the model. The central equation is the equilibrium of the balance of payments.

F y,S,r = 0

This implicit function of three variables can be represented as an area in the ySr coordinate system. However, in the three-dimensional illustration a graphical analysis of the equilibrium, shocks and reactions is not possible. In particular, if the graphs of the IS-LM model are added for the illustration of policy measures, the many surfaces would obscure the essential points from any viewing direction. Therefore, we depict the equilibrium with three connected 2d graphs. In the figurative sense, we unfold the ySr-cube. We look at the yr-plane while keeping S constant, the yS-plane while keeping r constant and the rS-plane while keeping y constant. In each of the graphs, we show the relationship between the two variables, which results from F y,S,r = 0, if the third variable is kept constant at the value resulting from the other two graphs. For example, the rS-graph plots the implicitly defined curve F y0,S,r = 0 where y0 is the equilibrium resulting from the goods market.

If, for example, y changes in the yr-graph, this change is transferred to the yS-graph and the rS-graph, whereby a shift of the curve F y0,S,r = 0 occurs in the rS-graph, since the (locally fixed) value for y0 changes.

Each of the three graphs has a well-defined interpretation:

Using the IS-LM model, monetary or fiscal shocks and policy measures are illustrated and the transmission channels in the model can be traced.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de