  We present a number of examples and counterexamples to illustrate the results
on cost-efficiency in an incomplete market obtained in [BS24]. These examples
and counterexamples do not only illustrate the results obtained in [BS24], but
show the limitations of the results and the sharpness of the key assumptions.
In particular, we make use of a simple 3-state model in which we are able to
recover and illustrate all key results of the paper. This example also shows
how our characterization of perfectly cost-efficient claims allows to solve an
expected utility maximization problem in a simple incomplete market (trinomial
model) and recover results from [DS06, Chapter 3], there obtained using
duality.
