  This paper presents a general framework for studying diverse beliefs in
dynamic economies. Within this general framework, the characterization of a
central-planner general equilbrium turns out to be very easy to derive, and
leads to a range of interesting applications. We show how for an economy with
log investors holding diverse beliefs, rational overconfidence is to be
expected; volume-of-trade effects are effectively modelled; the Keynesian
`beauty contest' can be modelled and analysed; and bubbles and crashes arise
naturally. We remark that models where agents receive private information can
formally be considered as models of diverse beliefs.
