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Reconciling IS-LM and endogenous money

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This post was sparked by conversations with people who have opposing views of how money creation works. Some people think that classical models such as IS-LM don't work with endogenous money theory, therefore the models need to be discarded: others think that there's nothing wrong with the model and the problem is endogenous money theory. Personally I think that simple models like IS-LM can be powerful tools to explain aspects of the working of a market economy, and it behooves us therefore to find ways of adapting them to work with an endogenous fiat money system. So this is my attempt to reconcile IS-LM with endogenous money. I don't claim that it is anything like the final word on the subject, so comments are welcome.  The IS-LM model looks like this: : where M is the quantity of money in circulation, L is the "liquidity preference" (the degree to which investors prefer to hold interest-bearing, less liquid assets rather than to zero-interest, highly liquid mon...