The IS/LM model (Investment—Saving/Liquidity preference—Money supply) is a macroeconomic tool that demonstrates the relationship between interest rates and real output in the goods and services market and the money market. The intersection of the IS and LM curves is the "general equilibrium" where there is simultaneous equilibrium in both markets.
Click link for interactive model.
I like the IS-LM model because it keeps the student focused on the important connections between the money supply, interest rates, and economic activity, whereas the IS-MP model leaves some of that in the background. The IS-MP model also has some quirky features: In this model, for instance, an increase in government purchases causes a permanent increase in the inflation rate. No one really believes that result as an empirical prediction, for the simple reason that the monetary policy reaction function would change if the natural interest rate (that is, the real interest rate consistent with full employment) changed. This observation highlights that neither model's exogeneity assumption should be taken too seriously. In the end, I remain open-minded, but at this point I prefer the IS-LM model when teaching (at the intermediate level) about the short-run effects of monetary and fiscal policy. If one were to teach IS-MP to undergrads, I would prefer to do it as an supplement, rather than a substitute, for IS-LM.
My favorite of these approaches is to think of IS-LM as a way to reconcile two seemingly incompatible views about what determines interest rates. One view says that the interest rate is determined by the supply of and demand for savings – the “loanable funds” approach. The other says that the interest rate is determined by the tradeoff between bonds, which pay interest, and money, which doesn’t, but which you can use for transactions and therefore has special value due to its liquidity – the “liquidity preference” approach. (Yes, some money-like things pay interest, but normally not as much as less liquid assets.)
The IS–LM analysis is simply a more detailed look at what lies behind aggregate demand. It decomposes aggregate demand into its two constituent markets—money and goods. The money market is summarized in the LM curve, the goods market in the IS curve. The advantages of the analysis are that it allows us to look at the two markets separately, to examine the determination of interest rates, and to distinguish clearly between fiscal and monetary policy. It is a very useful tool for short-run analysis of the economy.
A point that I would like to make is that the marginal propensity of consumption is a measure of the degree of confidence the consumers experience. In other words, if the consumers are very confident in a bright future, what should they do? Consume. Hence, for the same level of disposable income (output minus taxes) they consumer a higher proportion (increase in little c). Consumer sentiment or consumer confidence is one of the most important variables in the economy because they have a direct effect on consumption patterns. You can think of movements in little c as movements in that consumer sentiment (a higher degree of confidence reduces savings, in the same way little c does).
The LM curve, "L" denotes Liquidity and "M" denotes money, is a graph of combinations of real income, Y, and the real interest rate, r, such that the money market is in equilibrium (i.e. real money supply = real money demand).
The IS curve describes the combination of interest rates and output that clear the goods and services market in the short run. The goods and services market is said to clear when spending by consumers, firms, the government (and foreigners if an open economy) on goods and services equals the production of goods and services. The basic equation for the IS curve in a closed economy is closely related to the national income accounting identity Y = C+I+G, where Y is GDP.
The Keynesian theory takes many of the elements used in the Classical theory, but adds to them the premise that prices do not clear markets in the short run. Instead, prices have a life of their own, with the price level or its rate of change subject to considerable inertia (think of a runaway truck, if you like metaphors). This sounds plausible on the face of it, and we've often argued that (say) adjustments in the labor market might take some time. What makes this theory interesting, however, is not that the premise is plausible, but that this one modification changes some of the theory's short-run predictions in dramatic ways.
The IS/LM model was born at the Econometric Conference held in Oxford during September, 1936. Roy Harrod, John R. Hicks, and James Meade all presented papers describing mathematical models attempting to summarize John Maynard Keynes' General Theory of Employment, Interest, and Money. Hicks, who had seen a draft of Harrod's paper, invented the IS/LM model (originally using LL, not LM). He later presented it in "Mr. Keynes and the Classics: A Suggested Interpretation".