### 21.2 The equilibrium and its graphical presentation

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

$$F\left(y,S,r\right)=0$$ |

This implicit function of three variables can be represented as an area in the
$\mathit{ySr}$
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
$\mathit{ySr}$-cube. We look at
the $\mathit{yr}$-plane while
keeping $S$ constant,
the $\mathit{yS}$-plane while
keeping $r$ constant
and the $\mathit{rS}$-plane
while keeping $y$
constant. In each of the graphs, we show the relationship between the two variables, which results
from $F\left(y,S,r\right)=0$, if the third
variable is kept constant at the value resulting from the other two graphs. For example, the
$\mathit{rS}$-graph plots the
implicitly defined curve $F\left({y}_{0},S,r\right)=0$
where ${y}_{0}$ is
the equilibrium resulting from the goods market.

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

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

- The $\mathit{yr}$-plane
represents the domestic goods market. In this market, the IS-LM curves
are also plotted, which can be used to illustrate shocks and policy
measures.
- The $\mathit{yS}$-plane
represents the international goods market.
- Die $\mathit{rS}$-plane
represents the international capital market.

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