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IS–LM model, or Hicks–Hansen model, is a twodimensional macroeconomic tool that shows the relationship between interest rates and assets market (also known as real output in goods and services market plus money market). The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets.^{[1]} Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when the price level is fixed in the shortrun; second, the IS–LM model shows why an aggregate demand curve can shift.^{[2]} Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.^{[3]}
The model was developed by John Hicks in 1937^{[4]} and was later extended by Alvin Hansen,^{[5]} as a mathematical representation of Keynesian macroeconomic theory. Between the 1940s and mid1970s, it was the leading framework of macroeconomic analysis.^{[6]} While it has been largely absent from macroeconomic research ever since, it is still a backbone conceptual introductory tool in many macroeconomics textbooks.^{[7]} By itself, the IS–LM model is used to study the short run when prices are fixed or sticky and no inflation is taken into consideration. But in practice the main role of the model is as a path to explain the AD–AS model.^{[2]}
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Introduction to IS LM model

ISLM Model Tutorial

IS/LM Introduction
Transcription
We've already studied the IS curve in some detail and just a bit of a review here, it's just relating real interest rates to real GDP. Let me just write that as Y, real GDP. The relationship, there's 2 ways we've viewed it; one is real interest rates driving investment which drives real GDP or I should say real interest rates driving planned investments which drives real GDP. If you have a high real interest rate then you're not going to have as much plan investment and if you looked at our Keynesian cross, it's pretty clear that if you don't have as high planned investment you will not have as high of a GDP or high of a real GDP. Similarly, if you have a lower real interest rate you'll have more planned investment and then you will have a higher real GDP. Our IS curve looks like this. Our IS curve is downward sloping. It's easier for me to draw a dotted line. Right over there is our IS curve, stands for investment savings curve. This right here is taking it much more from the investment side, how real interest rates drive investment. You could also view it from the other angle. You could view how real GDP drives savings which drives interest rates. That interpretation, at low levels of GDP you have less savings. That's essentially there is less excess capital to go around and so it is scarce. The price of that is expensive and the price of money is interest rates and if we're dealing in real terms, real interest rates and so it would be high. If you have higher GDP and everything else is held constant, if government spending is held constant, consumer spending will go up but it won't go up as high as GDP. You're going to have more savings, there's more stuff to lend around and so the price that's asked for lending that money will go down and that price is real interest rates. These are two ways of viewing it. This is the savings driven way and this is the real interest rates driving investment. So that's why it's called the IS curve, investment savings curve. Now, what I want to talk about is the LM curve, LM. Let me draw a little line over here although I'm going to plot it on top of this so that we can start thinking about the equilibrium level of real interest rate and real GDP. The LM curve, LM stands for liquidity preference money supply. Liquidity preference money supply. Liquidity preference, it sounds like a fancy thing but it's actually a very basic, it's a very basic idea. This is, if we hold real money constant and when I talk about real money. Let me clarify here. If I talk about real money, we're talking about the amount of money in supply if we adjust for something like inflation. You could measure real money, in the U.S. you could measure it as base money or maybe the total amount of federal reserve notes or M0. You could measure it as M0 divided by the CPI. Maybe M0 goes up but if the CPI goes up by the same amount, by the same percentage then you're not going to have a change in real money. If M0 goes up without prices increasing then real money has gone up. If M0 stays constant but prices have increased then real money has gone down. All liquidity preference is describing is if we assume this is constant at any given level here, assume constant, then the more economic activity that there is the more demand that there is for that money and so there will be higher real interest rates. People will be willing to pay higher prices for that money in real terms. All it's saying is if you have very, let's start over here, if you have a lot of economic activity people will want to hold currency so that they can have transactions so they have some flexibility. The money itself is going to be circulating much, much more. There's going to be higher demand for that money. If there's higher demand for that money people will either be willing to pay more for access to that money or you're going to have to pay them more for them to give you their money because they really want that liquidity. They really want that access to their money. And the price of money is interest rates. For the LM curve, when we think about liquidity preference, holding real money constant, high levels of GDP, a lot of economic activity, people want to have currency, demand for currency is high so the price is currency is high which is real interest rates and so we would have real interest rates high due to liquidity preference. On the other side of that, if you have low economic activity people might say, "Well, there's not as much demand for currency, "there's fewer transactions going on." And so you will have to pay someone less to part with their money or if someone's willing to pay less in order to get access to money. So at low levels of GDP, according to liquidity preference, you're going to have lower real interest rates. Our LM curve looks something like this, this is IS in this dotted line yellow and our LM curve looks something like that. When you plot these two constraints against each other the IS is telling us a relationship between real interest rates driving investment and how that affects GDP or how real GDP affects savings affecting real interest rates. It's a different constraint that what liquidity preference is telling us. This is how much people as things get better and better, more and more economic activity, people want to hold more money. These two different constraints, now you take them both into consideration, you end up with an equilibrium point. There is going to be 1 point that meets both constraints and this is the point at which the economy is at equilibrium Real interest rates and real GDP. Now, let's think about what would happen if the federal reserve decided to print, if we'd take a U.S. focus, if the Central Bank or the federal reserve decides to print more money? By this definition up here of our real money in the very short term, especially when we put our Keynesian hat on, we assume in the very short term prices are sticky. This, in the very short term, this doesn't change much. If this goes up then real money goes up especially in the short term. Real money goes up. If real money goes up, you're essentially increasing the supply of real money. Anytime you increase the supply of real money at any given level of demand, people are going to want to pay less for it. So what you're going to have happening is, so at any given level of GDP there's now more money there. The price of that money is going to be less, the prices of real interest rate. If the federal reserve, if the central bank prints money and real money increases, we're assuming in the very short term that prices don't change because they're sticky so real money has gone up, the price of that real money will go down at any given level of GDP. That would shift the LM curve down and so we can start to see what would that do to our equilibrium interest rates and level of GDP. In that situation, real interest rates, the equilibrium real interest rates clearly went down. We also see, based on this model, some expansion of GDP.
History
The IS–LM model was introduced at a conference of the Econometric Society 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.^{[4]}^{[8]} Hicks, who had seen a draft of Harrod's paper, invented the IS–LM model (originally using the abbreviation "LL", not "LM"). He later presented it in "Mr. Keynes and the Classics: A Suggested Interpretation".^{[4]}
Although generally accepted as being imperfect, the model is seen as a useful pedagogical tool for imparting an understanding of the questions that macroeconomists today attempt to answer through more nuanced approaches. As such, it is included in most undergraduate macroeconomics textbooks, but omitted from most graduate texts due to the current dominance of real business cycle and new Keynesian theories.^{[9]} For a contemporary and alternative reinvention of the ISLM approach that uses Keynesian Search Theory, see Roger Farmer's work on the ISLMNAC model, part of his broader research agenda which studies how beliefs independently influence macroeconomic outcomes.^{[10]}^{[11]}
Formation
The point where the IS and LM schedules intersect represents a shortrun equilibrium in the real and monetary sectors (though not necessarily in other sectors, such as labor markets): both the product market and the money market are in equilibrium. This equilibrium yields a unique combination of the interest rate and real GDP.
IS (investment–saving) curve
The IS curve shows the causation from interest rates to planned investment to national income and output.
For the investment–saving curve, the independent variable is the interest rate and the dependent variable is the level of income. The IS curve is drawn as downwardsloping with the interest rate r on the vertical axis and GDP (gross domestic product: Y) on the horizontal axis. The IS curve represents the locus where total spending (consumer spending + planned private investment + government purchases + net exports) equals total output (real income, Y, or GDP).
The IS curve also represents the equilibria where total private investment equals total saving, with saving equal to consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus). The level of real GDP (Y) is determined along this line for each interest rate. Every level of the real interest rate will generate a certain level of investment and spending: lower interest rates encourage higher investment and more spending. The multiplier effect of an increase in fixed investment resulting from a lower interest rate raises real GDP. This explains the downward slope of the IS curve. In summary, the IS curve shows the causation from interest rates to planned fixed investment to rising national income and output.
The IS curve is defined by the equation
where Y represents income, represents consumer spending increasing as a function of disposable income (income, Y, minus taxes, T(Y), which themselves depend positively on income), represents business investment decreasing as a function of the real interest rate, G represents government spending, and NX(Y) represents net exports (exports minus imports) decreasing as a function of income (decreasing because imports are an increasing function of income).
LM (liquiditymoney) curve
The LM curve shows the combinations of interest rates and levels of real income for which the money market is in equilibrium. It shows where money demand equals money supply. For the LM curve, the independent variable is income and the dependent variable is the interest rate.
In the money market equilibrium diagram, the liquidity preference function is the willingness to hold cash. The liquidity preference function is downward sloping (i.e. the willingness to hold cash increases as the interest rate decreases). Two basic elements determine the quantity of cash balances demanded:
 Transactions demand for money: this includes both (a) the willingness to hold cash for everyday transactions and (b) a precautionary measure (money demand in case of emergencies). Transactions demand is positively related to real GDP. As GDP is considered exogenous to the liquidity preference function, changes in GDP shift the curve.
 Speculative demand for money: this is the willingness to hold cash instead of securities as an asset for investment purposes. Speculative demand is inversely related to the interest rate. As the interest rate rises, the opportunity cost of holding money rather than investing in securities increases. So, as interest rates rise, speculative demand for money falls.
Money supply is determined by central bank decisions and willingness of commercial banks to loan money. Money supply in effect is perfectly inelastic with respect to nominal interest rates. Thus the money supply function is represented as a vertical line – money supply is a constant, independent of the interest rate, GDP, and other factors. Mathematically, the LM curve is defined by the equation , where the supply of money is represented as the real amount M/P (as opposed to the nominal amount M), with P representing the price level, and L being the real demand for money, which is some function of the interest rate and the level of real income.
An increase in GDP shifts the liquidity preference function rightward and hence increases the interest rate. Thus the LM function is positively sloped.
Shifts
One hypothesis is that a government's deficit spending ("fiscal policy") has an effect similar to that of a lower saving rate or increased private fixed investment, increasing the amount of demand for goods at each individual interest rate. An increased deficit by the national government shifts the IS curve to the right. This raises the equilibrium interest rate (from i_{1} to i_{2}) and national income (from Y_{1} to Y_{2}), as shown in the graph above. The equilibrium level of national income in the IS–LM diagram is referred to as aggregate demand.
Keynesians argue spending may actually "crowd in" (encourage) private fixed investment via the accelerator effect, which helps longterm growth. Further, if government deficits are spent on productive public investment (e.g., infrastructure or public health) that spending directly and eventually raises potential output, although not necessarily more (or less) than the lost private investment might have. The extent of any crowding out depends on the shape of the LM curve. A shift in the IS curve along a relatively flat LM curve can increase output substantially with little change in the interest rate. On the other hand, an rightward shift in the IS curve along a vertical LM curve will lead to higher interest rates, but no change in output (this case represents the "Treasury view").
Rightward shifts of the IS curve also result from exogenous increases in investment spending (i.e., for reasons other than interest rates or income), in consumer spending, and in export spending by people outside the economy being modelled, as well as by exogenous decreases in spending on imports. Thus these too raise both equilibrium income and the equilibrium interest rate. Of course, changes in these variables in the opposite direction shift the IS curve in the opposite direction.
The IS–LM model also allows for the role of monetary policy. If the money supply is increased, that shifts the LM curve downward or to the right, lowering interest rates and raising equilibrium national income. Further, exogenous decreases in liquidity preference, perhaps due to improved transactions technologies, lead to downward shifts of the LM curve and thus increases in income and decreases in interest rates. Changes in these variables in the opposite direction shift the LM curve in the opposite direction.
Incorporation into larger models
By itself, the IS–LM model is used to study the short run when prices are fixed or sticky and no inflation is taken into consideration. But in practice the main role of the model is as a submodel of larger models (especially the Aggregate DemandAggregate Supply model – the AD–AS model) which allow for a flexible price level. In the aggregate demandaggregate supply model, each point on the aggregate demand curve is an outcome of the IS–LM model for aggregate demand Y based on a particular price level. Starting from one point on the aggregate demand curve, at a particular price level and a quantity of aggregate demand implied by the IS–LM model for that price level, if one considers a higher potential price level, in the IS–LM model the real money supply M/P will be lower and hence the LM curve will be shifted higher, leading to lower aggregate demand as measured by the horizontal location of the IS–LM intersection; hence at the higher price level the level of aggregate demand is lower, so the aggregate demand curve is negatively sloped.
Introduction of the new full equilibrium (FE) component: The IS–LM–FE model
Sir John Hicks, a Nobel laureate, created the model in 1937 as a graphical representation of the ideas introduced by John Maynard Keynes in his influential 1936 book, The General Theory of Employment, Interest, and Money. ^{[12]} In his original IS–LM model, Hicks assumed that the price level was fixed, reflecting John Maynard Keynes' belief that wages and prices do not adapt quickly to clear markets.
The introduction of an adjustment to Hicks' loose assumption of a fixed price level requires allowing the price level to change. Allowing the price level to change necessitates the addition of a third component, the full equilibrium (FE) condition.^{[12]} When this component is added to the IS–LM model, a new model called IS–LM–FE emerges. The IS–LM–FE model is widely used in cyclical fluctuations analysis, forecasting, and macroeconomic policymaking.^{[12]} There are many advantages to using the IS–LM–FE model as a framework for both classical and Keynesian analyses: First, rather than learning two different models for classical and Keynesian analyses, a single model can be used for both.^{[12]} Second, using a single framework highlights the many areas of agreement between the Keynesian and classical approaches while also emphasizing the differences between them. Furthermore, since various versions of the IS–LM–FE model (along with its ideas and terminology) are frequently used in economic and macroeconomic policy analyses, studying this framework will help to understand and engage in contemporary economic debates. Three approaches are used when analyzing this economic model: graphical, numerical, and algebraic.
Reinventing ISLM: the ISLMNAC model
In the ISLMNAC model, the longrun effect of monetary policy depends on the way people form beliefs.^{[13]} Roger Farmer and Konstantin Platonov study a case they call 'persistent adaptive beliefs' in which people believe, correctly, that shocks to asset values are permanent. The important innovation in this work is a model of the labor market in which there can be a continuum of longrun steady state equilibria.
See also
References
 ^ Gordon, Robert J. (2009). Macroeconomics (Eleventh ed.). Boston: Pearson Addison Wesley. ISBN 9780321552075.
 ^ ^{a} ^{b} Mankiw, N. Gregory (2012). Macroeconomics (Eighth ed.). New York: Worth Publishers. ISBN 9781429240024.
 ^ Sloman, John; Wride, Alison (2009). Economics (Seventh ed.). Prentice Hall. ISBN 9780273715627.
 ^ ^{a} ^{b} ^{c} Hicks, J. R. (1937). "Mr. Keynes and the 'Classics': A Suggested Interpretation". Econometrica. 5 (2): 147–159. doi:10.2307/1907242. JSTOR 1907242.
 ^ Hansen, A. H. (1953). A Guide to Keynes. New York: McGraw Hill. ISBN 9780070260467.
 ^ Bentolila, Samuel (2005). "Hicks–Hansen model". An Eponymous Dictionary of Economics: A Guide to Laws and Theorems Named after Economists. Edward Elgar. ISBN 9781843760290.
 ^ Colander, David (2004). "The Strange Persistence of the ISLM Model" (PDF). History of Political Economy. 36 (Annual Supplement): 305–322. CiteSeerX 10.1.1.692.6446. doi:10.1215/0018270236suppl_1305. S2CID 6705939.
 ^ Meade, J. E. (1937). "A Simplified Model of Mr. Keynes' System". Review of Economic Studies. 4 (2): 98–107. doi:10.2307/2967607. JSTOR 2967607.
 ^ Mankiw, N. Gregory (May 2006). "The Macroeconomist as Scientist and Engineer" (PDF). p. 19. Retrieved 20141117.
 ^ Farmer, Roger E. A.; Platonov, Konstantin (2019). "Animal spirits in a monetary model" (PDF). European Economic Review. 115: 60–77. doi:10.1016/j.euroecorev.2019.02.005. S2CID 55928575.
 ^ Farmer, Roger E. A. (20160902). "Reinventing ISLM: The ISLMNAC model and how to use it". Vox EU. Retrieved 20201001.
 ^ ^{a} ^{b} ^{c} ^{d} Acemoglu, Daron; David I. Laibson; John A. List (2018). Macroeconomics (Second ed.). New York. ISBN 9780134492056. OCLC 956396690.
 ^ Farmer, Roger E. A. (2012). "Confidence, crashes, and animal spirits" (PDF). The Economic Journal. 122 (559): 155–172. doi:10.1111/j.14680297.2011.02474.x. S2CID 16986435.
Further reading
 Ackley, Gardner (1978). "The 'IS–LM' Form of the Model". Macroeconomics: Theory and Policy. New York: Macmillan. pp. 358–383. ISBN 9780023002908.
 Barro, Robert J. (1984). "The Keynesian Theory of Business Fluctuations". Macroeconomics. New York: John Wiley. pp. 487–513. ISBN 9780471874072.
 Darby, Michael R. (1976). "The Complete Keynesian Model". Macroeconomics. New York: McGrawHill. pp. 285–304. ISBN 9780070153462.
 Farmer, Roger E. A. (2012). "Confidence, crashes, and animal spirits" (PDF). The Economic Journal. 122 (559): 155–172. doi:10.1111/j.14680297.2011.02474.x. S2CID 16986435.
 Farmer, Roger E. A.; Platonov, Konstantin (2019). "Animal spirits in a monetary model" (PDF). European Economic Review. 115: 60–77. doi:10.1016/j.euroecorev.2019.02.005. S2CID 55928575.
 Farmer, Roger E. A. (20160902). "Reinventing ISLM: The ISLMNAC model and how to use it". Vox EU. Retrieved 20201001.
 Dernburg, Thomas F.; McDougall, Duncan M. (1980). "Macroeconomic Equilibrium: The Level of Economic Activity". Macroeconomics (Sixth ed.). New York: McGrawHill. pp. 53–229. ISBN 9780070165342.
 Keiser, Norman F. (1975). "The RealGoods and Monetary Spheres". Macroeconomics (Second ed.). New York: Random House. pp. 231–260. ISBN 9780394319223.
 Krugman, Paul (20111009). "ISLMentary". The New York Times. Retrieved 20201001.
 Leijonhufvud, Axel (1983). "What is Wrong with IS/LM?". In Fitoussi, JeanPaul (ed.). Modern Macroeconomic Theory. Oxford: Blackwell. pp. 49–90. ISBN 9780631131588.
 Mankiw, N. Gregory (2013). "Aggregate Demand I+II". Macroeconomics (Eighth international ed.). London: Palgrave Macmillan. pp. 301–352. ISBN 9781464121678.
 Sawyer, John A. (1989). "A Model from Keynes's General Theory". Macroeconomic Theory. New York: Harvester Wheatsheaf. pp. 62–95. ISBN 9780745005553.
 Smith, Warren L. (1956). "A Graphical Exposition of the Complete Keynesian System". Southern Economic Journal. 23 (2): 115–125. doi:10.2307/1053551. JSTOR 1053551.
 Vroey, Michel de; Hoover, Kevin D., eds. (2004). The ISLM model: Its Rise, Fall, and Strange Persistence. Durham: Duke University Press. ISBN 9780822366317.
 Young, Warren; Zilberfarb, BenZion, eds. (2000). ISLM and Modern Macroeconomics. Recent Economic Thought. Vol. 73. Springer Science & Business Media. ISBN 9780792379669.
External links
 Krugman, Paul. There's something about macro – An explanation of the model and its role in understanding macroeconomics.
 Krugman, Paul. ISLMentary – A basic explanation of the model and its uses.
 Wiens, Elmer G. IS–LM model – An online, interactive IS–LM model of the Canadian economy.