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Milds IS–LM model The IS curve moves to the right, causing higher interest rates (i) and expansion in the "real" economy (real GDP, or Y).

The IS–LM model, or Hicks–Hansen model, is a macroeconomic tool that shows the relationship between interest rates (ordinate) and assets market (also known as real output in goods and services market plus money market, as abscissa). The intersection of the "investmentsaving" (IS) and "liquidity preferencemoney supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets. Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when price level is fixed short-run; second, the IS–LM model shows why an aggregate demand curve can shift. Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.

The model was developed by John Hicks in 1937, and later extended by Alvin Hansen, as a mathematical representation of Keynesian macroeconomic theory. Between the 1940s and mid-1970s, it was the leading framework of macroeconomic analysis. While it has been largely absent from macroeconomic research ever since, it is still a backbone conceptual introductory tool in many macroeconomics textbooks. 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.

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• ✪ LM part of the IS-LM model | Macroeconomics | Khan Academy
• ✪ Government spending and the IS-LM model | Macroeconomics | Khan Academy
• ✪ IS/LM Introduction
• ✪ IS-LM Model Tutorial
• ✪ What shifts the IS or LM curves

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 first 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. 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".

Hicks later agreed that the model missed important points of Keynesian theory, criticizing it as having very limited use beyond "a classroom gadget", and criticizing equilibrium methods generally: "When one turns to questions of policy, looking towards the future instead of the past, the use of equilibrium methods is still more suspect." The first problem was that it presents the real and monetary sectors as separate, something Keynes attempted to transcend. In addition, an equilibrium model ignores uncertainty—and that liquidity preference only makes sense in the presence of uncertainty "For there is no sense in liquidity, unless expectations are uncertain." A shift in one of the IS or LM curves will cause a change in expectations, which shifts the other curve.

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.

Formation

The model is presented as a graph of two intersecting lines in the first quadrant.

The horizontal axis represents national income or real gross domestic product and is labelled Y. The vertical axis represents the real interest rate, r (or sometimes i). Since this is a non-dynamic model, there is a fixed relationship between the nominal interest rate and the real interest rate (the former equals the latter plus the expected inflation rate which is exogenous in the short run); therefore variables such as money demand which actually depend on the nominal interest rate can equivalently be expressed as depending on the real interest rate.

The point where these schedules intersect represents a short-run 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

IS curve represented by equilibrium in the money market and Keynesian cross diagram.

For the investment-saving curve, the independent variable is the interest rate and the dependent variable is the level of income. (Note that economic graphs often place the independent variable—interest rate, in this example—on the vertical axis while the dependent variable is measured with the horizontal axis.) The IS curve is drawn as downward-sloping with the interest rate r on the vertical axis and GDP (gross domestic product: Y) on the horizontal axis. The initials IS stand for "Investment and Saving equilibrium" but since 1937 have been used to represent the locus of all equilibria where total spending (consumer spending + planned private investment + government purchases + net exports) equals an economy's total output (equivalent to real income, Y, or GDP). To keep the link with the historical meaning, the IS curve can be said to represent the equilibria where total private investment equals total saving, where the latter equals consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus). In equilibrium, all spending is desired or planned; there is no unplanned inventory accumulation. The level of real GDP (Y) is determined along this line for each interest rate.

Thus the IS curve is a locus of points of equilibrium in the "real" (non-financial) economy. Each point on the curve represents the equilibrium between saving broadly defined and investment.

Given expectations about returns on fixed investment, every level of the real interest rate will generate a certain level of planned fixed investment and other interest-sensitive spending: lower interest rates encourage higher fixed investment and the like. Income is at the equilibrium level for a given interest rate when the saving that consumers and other economic participants choose to do out of this income equals investment (or, equivalently, when "leakages" from the circular flow equal "injections"). 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, this line represents the causation from falling interest rates to rising planned fixed investment (etc.) to rising national income and output.

The IS curve is defined by the equation

$Y=C\left({Y}-{T(Y)}\right)+I\left({r}\right)+G+NX(Y),$ where Y represents income, $C(Y-T(Y))$ represents consumer spending as an increasing function of disposable income (income, Y, minus taxes, T(Y), which themselves depend positively on income), $I(r)$ represents physical investment as a decreasing function of the real interest rate, G represents government spending, and NX(Y) represents net exports (exports minus imports) as a decreasing function of income (decreasing because imports are an increasing function of income).

LM curve

For the liquidity preference and money supply curve, the independent variable is "income" and the dependent variable is "the interest rate." The LM curve shows the combinations of interest rates and levels of real income for which the money market is in equilibrium. It is an upward-sloping curve representing the role of finance and money.

The LM function is the set of equilibrium points between the liquidity preference (or demand for money) function and the money supply function (as determined by banks and central banks).

Each point on the LM curve reflects a particular equilibrium situation in the money market equilibrium diagram, based on a particular level of income. In the money market equilibrium diagram, the liquidity preference function is simply the willingness to hold cash balances instead of securities. For this function, the nominal interest rate (on the vertical axis) is plotted against the quantity of cash balances (or liquidity), on the horizontal. The liquidity preference function is downward sloping. Two basic elements determine the quantity of cash balances demanded (liquidity preference) and therefore the position and slope of the function:

• 1) 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 (represented by Y, and also referred to as income). This is simply explained – as GDP increases, so does spending and therefore transactions, and therefore money balances needed to support the transactions. As GDP is considered exogenous to the liquidity preference function, changes in GDP shift the curve. For example, an increase in GDP will increase transactions which will increase the demand for money for given interest rates, and cause the liquidity preference curve to shift to the right.
• 2) 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.

The money supply function for this situation is plotted on the same graph as the liquidity preference function. The money supply is determined by the central bank decisions and willingness of commercial banks to loan money. Though the money supply is related indirectly to interest rates in the very short run, the money supply in effect is perfectly inelastic with respect to nominal interest rates (assuming the central bank chooses to control the money supply rather than focusing directly on the interest rate). 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 $M/P=L(i,Y)$ , 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. The LM curve shows the combinations of interest rates and levels of real income for which the money supply equals money demand – that is, for which the money market is in equilibrium.

For a given level of income, the intersection point between the liquidity preference and money supply functions implies a single point on the LM curve: specifically, the point giving the level of the interest rate which equilibrates the money market at the given level of income. Recalling that for the LM curve, the interest rate is plotted against real GDP (whereas the liquidity preference and money supply functions plot interest rates against the quantity of cash balances), 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 i1 to i2) and national income (from Y1 to Y2), 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 long-term 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 sub-model of larger models (especially the Aggregate Demand-Aggregate Supply model – the AD–AS model) which allow for a flexible price level. In the aggregate demand-aggregate 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.