Before this moment I never really ventured deeply into the IS-LM model because it is a primitive simultaneous equations model based on identities. But then I realized that some macroeconomists, including of course Krugman, still think that this model is a good description of the economy at some level of simplification. So I decided that I would look into it.
What I discovered, exceeded my worst expectations. First of all, the model implies that real interest rates represented by variable r are not dependent on the rates of return on investment. This seems superficially correct if one looks only at the credit markets and forgets their interconnections with the ‘real’ sector. But if one does not forget that then it becomes clear that expected rates of return must be an important factor in the determination of real interest rates. When a bank decides whether to lend X dollars to project A or project B, the most important thing it must take into account is the expected profitability of the project. The demand for loans will also depend on that factor.
Now it is true that the interest rates at which banks will be prepared to provide loans will also depend on the interest rate they must pay to savers. But this dependence does not mean that the only way to counter money hoarding if hoarders want high interest rates is for someone to spend instead of them. If sufficiently ex ante productive projects are offered by entrepreneurs for financing banks can offer hoarders sufficient reward for giving their money to them. If no such projects can be offered it means that the relevant state of the economy with people hoarding money is a normal market situation that does not require any external meddling.
But this is not the worst thing about IS-LM. The worst thing about it is that what is attempted to be said with the mathematical metaphors contains a straightforward logical contradiction, unless savings are thought of as a mechanical response to income. The model starts from distinguishing income from planned expenditure. Income supposedly determines r and r supposedly determines the planned expenditure. All is well, until we come to the discussion of the market for loanable funds where it is casually said that if savings rise, the real interest rate will fall. This can be reconciled with a narrow interpretation of the model where savings behavior is a mechanic response to the changes in income but it is obviously not what the modern proponents of IS-LM like Krugman have in mind.
I am not making this obvious contradiction up. Krugman himself in a post on IS-LM for dummies explains that the model attempts to reconcile the two standard approaches to the determination of real interest rates – the standard loanable funds approach and the liquidity preference approach. He obviously means here not that people save mechanically but that they might start saving if their attitude to the future has changed.