  We prove that the "Immediate Exchange Model" of econophysics has a discrete
dual, where the duality functions are those connecting the Brownian Energy
Process and the Symmetric Inclusion Process. As a consequence, we recover
invariance of products of Gamma distributions with shape parameter 2, and
obtain ergodicity results. Next we show similar properties of a generalized
model, where the exchange fraction is $Beta(s,t)$ distributed (instead of
uniform), and product measures with $\mbox{Gamma}(s+t)$ marginals are
invariant. We prove that the discrete dual has the self-duality property, and
prove full SU(1,1) for both the continuous and discrete model.
