  There are many models of the Calvin cycle of photosynthesis in the
literature. When investigating the dynamics of these models one strategy is to
look at the simplest possible models in order to get the most detailed
insights. We investigate a minimal model of the Calvin cycle introduced by Hahn
while he was pursuing this strategy. In a variant of the model not including
photorespiration it is shown that there exists exactly one positive steady
state and that this steady state is unstable. For generic initial data either
all concentrations tend to infinity at lates times or all concentrations tend
to zero at late times. In a variant including photorespiration it is shown that
for suitable values of the parameters of the model there exist two positive
steady states, one stable and one unstable. For generic initial data either the
solution tends to the stable steady state at late times or all concentrations
tend to zero at late times. Thus we obtain rigorous proofs of mathematical
statements which together confirm the intuitive idea proposed by Hahn that
photorespiration can stabilize the operation of the Calvin cycle. In the case
that the concentrations tend to infinity we derive formulae for the leading
order asymptotics using the Poincar\'e compactification.
