  This is a supplement to the paper "Liquidity based modeling of asset price
bubbles via random matching". The supplement is organized as follows. First, we
prove Theorem 3.13 in [1] which provides the existence of the dynamical system
D introduced in Definition 3.6 in [1]. Second, we show some properties of D
which are summarized in Theorem 3.14 in [1]. In the following, we only state
the basic setting and refer to [1] for definitions.
