# 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 demonstrates the relationship between interest rates and real output, in the goods and services market and the money market (also known as the assets market). The intersection of the "investmentsaving" (IS) and "liquidity preferencemoney supply" (LM) curves is the "general equilibrium" where there is simultaneous equilibrium in both markets.[1] Two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when the price level is fixed in the short-run; second, the IS–LM model shows why the aggregate demand curve shifts.[2] Hence, this tool is sometimes used not only to analyse the fluctuations of the economy but also to find appropriate stabilisation policies.[3]

The model was developed by John Hicks in 1937,[4] and later extended by Alvin Hansen,[5] as a mathematical representation of Keynesian macroeconomic theory. Between the 1940s and mid-1970s, it was the leading framework of macroeconomic analysis.[6] While it has been largely absent from macroeconomic research ever since, it is still the backbone of many introductory macroeconomics textbooks.[7]

## History

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.[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]

### LM curve

The money market equilibrium diagram.

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. 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 cash increases – the incentive will be to move into securities.

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 ${\displaystyle M/P=L(i,Y)}$, 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 i and the level Y of real income. The LM curve shows the combinations of interest rates and levels of real income for which 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.

By the above hypothesis, the graph indicates one of the major criticisms of deficit spending as a way to stimulate the economy: rising interest rates lead to crowding out – i.e., discouragement – of private fixed investment, which in turn may hurt long-term growth of the supply side (potential output).

Keynesians respond that deficit 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 upward 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 and 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; hence at the higher price level the level of aggregate demand is lower, so the aggregate demand curve is negatively sloped.

## References

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