Lagos-Wright with a New Keynesian Flavor!
There is so much one can do with a simple 2 subperiod model. For a brief survey, take a look at this. More recently, however, I came across this yet another addition by Aruoba and Schorfheide in the latest issue of the American Economic Journal: Macroeconomics. The paper features a version of the Lagos-Wright (a 2 subperiod divisible goods divisible money search) model. The first subperiod is still the decentralized trade, but the second subperiod (centralized market) features a standard new Keynesian economy with rigid prices!