Many authors have described and modelled Keynesian effects in a Babysitting Cooperative (BSC), which has the underlying structure of a single good barter economy. We construct a simple model of the BSC economy to explore this issue, and find very surprising results. Outcomes depend on agents beliefs about the decision making process of others, as in the Keynesian beauty contest. For some structures of beliefs, money is neutral, while for others, money can have short and long run effects. The value of money can be high, low, or zero, depending purely upon expectational effects. Also, despite the fact that this is a single good economy, partial equilibrium supply and demand analysis do not work as expected. Some equilibria have excess supply, others have excess demand, and none have a match between supply and demand. Furthermore, flexible prices cannot fix this problem. An additional paradoxical property is that excessive trading can take place. Even though all trades are done with mutual consent, some of them decrease welfare, and banning certain types of trade can lead to Pareto improvements. Thus the superficially simple single good barter economy of BSC displays some subtle, complex and counter-intuitive properties.