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The '''IS/LM model''' is a mathematical model developed by [[John Hicks]] and [[Alvin Hansen]] in order to describe macroeconomic ideas proposed by [[John Maynard Keynes]] in his ''General Theory of Employment, Interest and Money''. The model describes an economy under autarky (a closed economy), while the more sophisticated [[Mundell-Fleming model]] takes into account international exchanges.  
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The '''IS-LM model''' is used in the teaching of [[macroeconomics]] to depict  the interaction of the factors determining the level of demand in an economy.


==The Model==
===The two markets===
The IS-LM model conceptualises the economy as consisting of two  [[market (economics)|market]] in one of which occurs all of the purchases of goods and services that happen throughout the country and in the other of which occurs all of the purchases of financial assets.  It shows how a country's national income  may be jointly  determined by the way people behave in the market for goods and services and the way they behave in the market for financial assets. In the market for goods, investment is taken to be the active element,  with consumption being determined passively as what remains of national income after deducting what is assumed to be the  more-or-less fixed proportion  that goes into saving. The financial assets market  is taken  to be made up on the one hand of money, which is non-interest-bearing, and on the other of all of those assets (such as stocks, bonds and savings certificates) which, in one way or another, can be considered to be  interest-bearing. The cost of holding money rather than interest-bearing assets is taken to be the interest payments that are thereby foregone, but people are taken to wish to hold a certain amount of money for day-to-day transactions.
[[Image:ISLM.png|right|250px]]
[[Image:ISLM.png|right|250px]]
The model presents simultaneously two curves, ''IS'' and ''LM'', in a graph in which the horizontal axis represents national income (Y) and the vertical axis represents the interest rate (i).


*''IS'' illustrates the relationship between the level of income (Y) and the interest rate (i) in the real sector (goods and services). Lower is the interest rate higher is investment and thus the income.
===Model structure===
*''LM'' describes the relationship between the level of income and the interest rate in the monetary market. Higher is the level of income, higher is the need for money and thus the interest rate.
In its graphical form the model is shown as a pair of intersecting curves relating the level of national income (on the horizontal axis) to the rate of interest (on the vertical axis).
* The I-S (investment-savings) curve depicts those combinations of interest rate and income that are consistent with the equality of investment and saving.
* The L-M (liquidity-money supply) curve shows, those combinations of interest rate and income that make the public just willing to hold a given quantity of money.


The intersection of the curves represents the general equilibrium for which both relationships are verified, that is to say the actual equilibrium of the economy.  
The shape of the I-S curve follows from the fact that a rise in interest rates tends to encourage saving and discourage investment, combined with  the assumption that the amount that people save rises and falls with income in an unchanging relationship (termed the "propensity to save").  Then for saving to be kept in line with investment, a rise in the interest rate must be accompanied by  fall in income so that the resulting  fall in investment is accompanied by the balancing fall in saving. Conversely, a fall in the interest rate would be associated with an increase in income. So the I-S curve has to fall from left to right.  


The IS/LM model is the most common macroeconomic model. It enables to understand easily the relationships between the real sector and the monetary market as well as the effects of monetary and fiscal policies. Yet its neglect of anticipations makes it obsolete to determine the actual efficiency of macroeconomic policies.
The shape of the L-M curve reflects two assumptions, one being the assumption that the quantity of money that the public wishes to hold in order to have it available for speculation falls as the interest rate rises, and the other being the assumption that the amount of money that is tied up in day-to-day transactions rises with a rise in national income. It follows  from those assumptions that, at a given level of the total [[money supply]], the process of reconciling the transactions demand with the speculative demand implies a positive association between national income and the rate of interest. So the L-M curve has to rise from left to right.  


== History ==
The way in which the  model  explains  the tendency for the economy to settle down to an [[economic equilibrium|equilibrium]] following a shock or a sudden change in behaviour,  can be examined in words by supposing that there is a reduction in the public's propensity to save, meaning that people spend more of their money on "consumption goods". That would prompt an increase in the supply of those goods, in the total income of those employed  in their production, and thus an increase in national income. However, that increase in expenditure and income would mean that more of the available money would be used as "transactions balances" reducing the amount available for  people to hold as cash reserves for speculative purposes. That would make people  willing to pay more in interest to restore their speculative reserves and the resulting rise in interest rates would stimulate saving and discourage investment and so check the growth in income. The implied assumption is that those adjustments take place instantaneously and without regard for expected developments.
=== Creation and rise ===


During the great depression, economists tried to find solutions to economic problems that classical economics seemed unable to explain. In his General Theory, Keynes tried to represent economic agents with simple rules. The consumption was simply linked to the income via a propensity to consume; investments were linked to the interest rates. On the monetary side, he gave up the classical concept of money neutrality and developed the assumption that money can be demanded for itself (speculative demand), depending on expectations about interest rates, and not only as a tool for transactions. Eventually, he argued that prices were rigid in a short-term view, while classical economics considered prices as the key adjustment variable. Keynes demonstrates that under those assumptions, monetary and fiscal authorities could have a powerful influence on economic activity.  
===Interpretation===
The model is widely used in the teaching of economics to discuss the relative effectiveness of [[fiscal policy]] and [[monetary policy]] as means of stabilising the economy.  


In 1937, John Hicks built the IS-LM model in order to translate those ideas in neoclassical terms. Some Keynesians saw his attempt as a simplification of Keynes vision but Keynes approved it.
The effect of using fiscal policy in the form of an increase in [[public expenditure]], as represented as the effect of a shift to the right of the I-S curve, is to produce an additional rise of national income, the magnitude of which depends upon the slope of the L-M curve at the point of intersection - the steeper it is, the smaller will be the additional increase in national income. The steepness of the L-M curve depends, in turn on two factors:
* the ''income elasticity of the demand for money'', (meaning the extent to which the demand for money for to finance transactions increases in response to a change in national income). The higher is the income elasticity, the  greater will be the interest rate increase need to bring the supply of money into equality with its supply and so the steeper will be the L-M curve.
* the ''interest elasticity of demand for money'' (meaning the extent to which the demand for money falls in response to an increase in interest rates).
The higher is the interest elasticity, the flatter will be the L-M curve.


An important extension of the IS-LM model was built by Robert Mundell (1963) and Marcus Fleming (1962) in the 1960's. The [[Mundell-Fleming model]] describes a small open economy with one more curve representing equilibriums of international exchanges.
The effect of using monetary policy by increasing the [[money supply]], as represented by a move to the right of the L-M curve, is to increase national income to an extent that depends upon the slope of the I-S curve at the point of intersection - the steeper is the I-S curve, the smaller will be the increase in national income. The slope of the I-S curve depends in turn upon:-
* the ''interest elasticity of investment'' (meaning the response of investment to a change of interest rates). The higher is that elasticity, the larger will be the increase in national income in response to a fall in interest rate so the flatter will be the I-S curve.


=== Decline ===
== The history of the model==
The model was first put forward in a 1937 lecture by Sir John Hicks, who presented it then as a way of illustrating the relationship between the [[Keynesian theory]] of [[macroeconomics]] and the previously orthodox "classical theory"
<ref>Hicks, J. R. (1937), "Mr. Keynes and the Classics - A Suggested Interpretation", ''Econometrica''[http://bbs.cenet.org.cn/uploadImages/20037191455699785.pdf]</ref>.


During the 1950’s and 1960’s microeconomic investigations on consumption and investment gave a better understanding of the IS slope. Milton Friedman developed the idea that the consumption level of household’s was mainly determined by a long-term expectation called the permanent income. Franco Modigliani life-cycle theory demonstrated that consumption was also related to age. Those two theories denied the effect of short-term policies on consumption, and thus the effects of the spending multiplier.
An important extension of the IS-LM model was built by Robert Mundell (1963) and Marcus Fleming (1962) in the 1960's. The [[Mundell-Fleming model]] describes a small open economy with one more curve representing equilibriums of international exchanges.
 
Such criticisms of keynesian ideas were not always criticisms of the IS/LM model. In fact, economists like Milton Friedman used the IS/LM framework to confute Keynesian economics.
 
The most severe criticisms of the IS/LM model came from the fact that it negligees private agents expectations about inflation. In fact, the model considers that short run is independent from long run. Yet expectations about the future have for example a direct impact on current wages which stimulates inflation and thus cancelled the positive effects of many macroeconomic policies described by the IS/LM model. In such cases, inflation remains the only effect and disturbs the coordination of private agents. The consequence of the rational expectations theory is that central banks of several industrial countries (the Federal Reserve and the European Central Bank for example) have been given independency and inflation control as their main objective. 
 
=== Nowadays ===
 
Nowadays IS/LM model is an obsolete tool : its neglect of expectations makes it inefficient to implement an efficient economic policy. Yet, along with its Mundell-Fleming extension, it remains the most common macroeconomic model taught to undergraduate students because of its pedagogical qualities.
 
== The model ==
=== Equilibriums in the real market : IS curve ===
 
“IS” stands for “[[investment]] and [[saving]]”. The IS curve represents all equilibriums for which total spending (consumption and investment) equals total output (income). This equation is equivalent to the equality between investment and saving, which is a basic accounting equation in a closed economy.
 
 
<center><math>Y=C+I</math></center>
 
Investment is a decreasing function of interest rate. Indeed, the interest rate represents the [[opportunity cost]] of an investment. Higher is the interest rate, higher must be the return on investment. It implies that when the interest rate is high many investments whose profitability would be low are not undertaken.
 
<center><math>Y=C+I(i)</math></center>
 
I is a decreasing function of i, and so is Y. Then ''IS'' is a decreasing curve.
 
=== Equilibriums in the monetary market : LM curve ===
 
“LM” refers to “Liquidity preference and money supply”. The LM curve represents all equilibriums where demand equals supply on the monetary market.
 
According to Keynes, people hold liquidities for two reasons.
 
*Citizens need cash for every day life transactions and because of uncertainty (they are cautious). Keynes calls those needs “transactions demand for money”. It is positively related to income (Y).
*When people want to save they must choose between securities (financial markets) and money. Money can be considered as an asset among others and its price is the interest rate. Keynes suggests that when the interest rate seems too low, speculators expect it to rise and thus "buy" (by selling financial assets for example) or borrow money. On the contrary, when they think that the interest rate is too high, speculators expect it to drop and sell money (by buying financial assets for example).   
 
So, according to Keynes, demand for money includes transactions demand (L1) and speculative demand (L2). In equilibrium we have the following relationship.
 
<center><math>\frac {M_o}{p}=L_1(Y)+L_2(i)\Leftrightarrow L_2(i)=\frac {M_o}{p}-L_1(Y)</math>
 
And since
 
<math>\begin{cases} L_2(i)\text{ is a decreasing function of }L_1(Y) \\ L_2\text{ is a decreasing function of }i \\ L_1\text{ is a increasing function of }Y \end{cases}\Leftrightarrow i \text{ is positively related to } Y</math>
 
then ''LM'' is a increasing curve.</center>
 
=== General equilibrium ===
 
The general equilibrium is given by the intersection of ''IS'' and ''LM''. The level of income and the interest rate can diverge from their equilibrium level only on a temporary basis. Indeed,
[[Image:ISLMequilibrium.png|right|250px]]
*If the interest rate and the income are situated at ''point A'', then it means that in the goods and services market, supply is insufficient to balance demand. Prices will rise and so will production. It also means that demand is insufficient to balance supply on the monetary market which will make the interest rate fall.
*At ''point B'', supply of goods and services is also insufficient and so is money supply. This combination implies a rise of both output and interest rate.
*At ''point C'', supply exceeds demand in the real market, and then companies must reduce their output. The lack of money make interest rate rise.
*At ''point D'', supply exceeds demand in both the real market and the monetary market. Both production and interest rate will drop.
 
 
== Analysis of macroeconomic policies ==
 
According to Keynes, the labour market is not a market among others. The demand of labour (that is to say the demand of corporations for workers) is not always determined by the level of wages, but also by the aggregate demand (C+I=Y). During a recession, the aggregate demand may be insufficient to require all production factors (capital and labour). In this case, the economy can be in equilibrium with persisting unemployment. In such a situation, the State can stimulate the economy with macroeconomic policies without creating inflationary tensions.
 
It can be noted that Keynes suggests implementing such measures in case of recession, while keynesian economists have then defended those policies as permanent regulation. 
 
 
===Slope of the curves===
 
[[Image:SlopLM.png|right|250px]]
The efficiency of macroeconomic policies is directly affected by the [[slope]] of LM and IS. For example, a [[liquidity trap]], which implies a flat ''LM'' curve, makes the monetary policy inefficient.
 
The liquidity trap occurs when interest rates would be so low that everyone would expect them to rise. In this case, an infinite speculative demand would actually make them reach a more realistic level. Keynes concludes that interest rates cannot fall under a certain level whatever the income Y. In this situation, LM is horizontal.
 
On the contrary, there is a level of interest rate for which speculators have lent all their money. There is no more saving to finance any expansion of the output. In this case, LM is vertical.
 
Between those extremes, expansions of the output are possible, but they increase the transactions demand for money and make interest rates rise.
 
The slope of ''IS'' reflects the interest rate elasticity of investment, and thus the impact of the variations of the interest rate on the output.
 
===Fiscal policy ===
{{main|Fiscal policy}}
A more detailed model can be made in order to understand the effects of government spending. In this model, G represents governmental spending, T taxes, C consumption of private agents and I investment of private agents.
 
<center><math>Y=C+I(i)+G-T</math>
 
If C is considered as a proportion of Y noted c, we obtain:
 
<math>Y=cY+I(i)+G-T</math><br>
<math>Y-cY=I(i)+G-T</math><br>
<math>(1-c)Y=I(i)+G-T</math><br>
<math>Y=(I(i)+G-T)/(1-c)</math></center>
 
 
The last equation implies that if the government increases its spending (G) without increasing tax revenues (T), by creating a deficit, then the effect on the national output will be 1/(1-c) times greater.  For example, if c=0,8, then an increase of 1 of G implies an increase of 1/(1-0,8)=5 of Y. This mechanism is known as the spending multiplier.
 
In a few words, the government can change the level of Y by reducing or expanding the budget deficit.


[[Image:ISLMfiscalexpansion.png|right|250px]]
==The limitations of the model==
In the case of a expansionary fiscal policy, the government increases its purchases or reduces taxes, which creates a budget deficit and makes Y rise as explained before. This deficit shifts the ''IS'' curve to the right (Y rises). It results in a new general equilibrium (E'). The output Y has become Y' while the interest rate has risen from i to i'. By the way of higher interest rates, such a policy is said to crowd-out private investment. According to keynesian economics, this negative effect can be exceeded by the positive effect of the spending multiplier at the following conditions :
During the 1950’s and 1960’s microeconomic investigations on consumption and investment gave a better understanding of the IS slope. [[Milton Friedman]] developed the idea that the consumption level of household’s was mainly determined by a long-term expectation a theory known as the [[permanent income hypothesis]]<ref>Friedman, Milton (1957). A Theory of the Consumption Function. Princeton Univ Press.</ref>. [[Franco Modigliani]] [[life-cycle theory]] demonstrated that consumption was also related to age. Those two theories denied short-term policies to have an important effect on consumption, and thus the effects of the [[spending multiplier]].
*The marginal propensity to consumption (c) is high. Higher is the marginal propensity to consumption, more important is the spending multiplier.
*the slope of the ''LM'' curve is low (important speculative demand for money). The importance of the speculative demand for money reduces the rise of interest rates linked to the expansion, and thus the crowding-out effect.
*and the slope of the ''IS'' curve is high (low interest rate elasticity of investment). Private investments are not very affected by the rise of interest rates.


===Monetary policy===
Such criticisms of Keynesian ideas were not always criticisms of the IS/LM model. In fact, economists like Milton Friedman used the IS/LM framework to confute Keynesian economics<ref>Bordo, Michael D. & Schwartz, Anna J. (2003), "IS-LM and Monetarism", National Bureau of Economic Research, p.18 [http://www.econ.ucdavis.edu/faculty/kdhoover/pdf/Hope/Bordo%20and%20Schwartz.pdf]</ref>. Yet Friedman rejected the paradigm of "general equilibrium" he viewed as characterized by "abstractness, generality, and mathematical elegance"<ref>Milton Friedman (1949 (1953)), , "The Marshallian Demand Curve" in ''Essays in Positive Economics'', Chicago: The University of Chicago Press, pp. 47-99.</ref>
{{main|Monetary policy}}


===Policy mix===
The most severe criticisms of the IS/LM model came from the fact that it neglects private agents' expectations. Modern macroeconomic models which take expectations into accounts can provide results opposite to those of IS/LM.  In fact, the model considers that short run is independent from long run. Yet expectations about the future have for example a direct impact on current wages which stimulates inflation and thus cancelled the positive effects of many macroeconomic policies described by the IS/LM model. In such cases, inflation remains the only effect and disturbs the coordination of private agents. The consequence of the rational expectations theory is that central banks of several industrial countries (the [[Federal Reserve]] and the [[European Central Bank]] for example) have been given independency and inflation control as their main objective.
{{main|Policy mix}}
==Limits==


===Neoclassical interpretation===
Not withstanding its limitations as a policy instrument, the model remains the most common macroeconomic model taught to undergraduate students because of its pedagogical qualities.


===Critics===
==References==
{{reflist}}[[Category:Suggestion Bot Tag]]

Latest revision as of 16:01, 30 August 2024

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The IS-LM model is used in the teaching of macroeconomics to depict the interaction of the factors determining the level of demand in an economy.

The Model

The two markets

The IS-LM model conceptualises the economy as consisting of two market in one of which occurs all of the purchases of goods and services that happen throughout the country and in the other of which occurs all of the purchases of financial assets. It shows how a country's national income may be jointly determined by the way people behave in the market for goods and services and the way they behave in the market for financial assets. In the market for goods, investment is taken to be the active element, with consumption being determined passively as what remains of national income after deducting what is assumed to be the more-or-less fixed proportion that goes into saving. The financial assets market is taken to be made up on the one hand of money, which is non-interest-bearing, and on the other of all of those assets (such as stocks, bonds and savings certificates) which, in one way or another, can be considered to be interest-bearing. The cost of holding money rather than interest-bearing assets is taken to be the interest payments that are thereby foregone, but people are taken to wish to hold a certain amount of money for day-to-day transactions.

ISLM.png

Model structure

In its graphical form the model is shown as a pair of intersecting curves relating the level of national income (on the horizontal axis) to the rate of interest (on the vertical axis).

  • The I-S (investment-savings) curve depicts those combinations of interest rate and income that are consistent with the equality of investment and saving.
  • The L-M (liquidity-money supply) curve shows, those combinations of interest rate and income that make the public just willing to hold a given quantity of money.

The shape of the I-S curve follows from the fact that a rise in interest rates tends to encourage saving and discourage investment, combined with the assumption that the amount that people save rises and falls with income in an unchanging relationship (termed the "propensity to save"). Then for saving to be kept in line with investment, a rise in the interest rate must be accompanied by fall in income so that the resulting fall in investment is accompanied by the balancing fall in saving. Conversely, a fall in the interest rate would be associated with an increase in income. So the I-S curve has to fall from left to right.

The shape of the L-M curve reflects two assumptions, one being the assumption that the quantity of money that the public wishes to hold in order to have it available for speculation falls as the interest rate rises, and the other being the assumption that the amount of money that is tied up in day-to-day transactions rises with a rise in national income. It follows from those assumptions that, at a given level of the total money supply, the process of reconciling the transactions demand with the speculative demand implies a positive association between national income and the rate of interest. So the L-M curve has to rise from left to right.

The way in which the model explains the tendency for the economy to settle down to an equilibrium following a shock or a sudden change in behaviour, can be examined in words by supposing that there is a reduction in the public's propensity to save, meaning that people spend more of their money on "consumption goods". That would prompt an increase in the supply of those goods, in the total income of those employed in their production, and thus an increase in national income. However, that increase in expenditure and income would mean that more of the available money would be used as "transactions balances" reducing the amount available for people to hold as cash reserves for speculative purposes. That would make people willing to pay more in interest to restore their speculative reserves and the resulting rise in interest rates would stimulate saving and discourage investment and so check the growth in income. The implied assumption is that those adjustments take place instantaneously and without regard for expected developments.

Interpretation

The model is widely used in the teaching of economics to discuss the relative effectiveness of fiscal policy and monetary policy as means of stabilising the economy.

The effect of using fiscal policy in the form of an increase in public expenditure, as represented as the effect of a shift to the right of the I-S curve, is to produce an additional rise of national income, the magnitude of which depends upon the slope of the L-M curve at the point of intersection - the steeper it is, the smaller will be the additional increase in national income. The steepness of the L-M curve depends, in turn on two factors:

  • the income elasticity of the demand for money, (meaning the extent to which the demand for money for to finance transactions increases in response to a change in national income). The higher is the income elasticity, the greater will be the interest rate increase need to bring the supply of money into equality with its supply and so the steeper will be the L-M curve.
  • the interest elasticity of demand for money (meaning the extent to which the demand for money falls in response to an increase in interest rates).

The higher is the interest elasticity, the flatter will be the L-M curve.

The effect of using monetary policy by increasing the money supply, as represented by a move to the right of the L-M curve, is to increase national income to an extent that depends upon the slope of the I-S curve at the point of intersection - the steeper is the I-S curve, the smaller will be the increase in national income. The slope of the I-S curve depends in turn upon:-

  • the interest elasticity of investment (meaning the response of investment to a change of interest rates). The higher is that elasticity, the larger will be the increase in national income in response to a fall in interest rate so the flatter will be the I-S curve.

The history of the model

The model was first put forward in a 1937 lecture by Sir John Hicks, who presented it then as a way of illustrating the relationship between the Keynesian theory of macroeconomics and the previously orthodox "classical theory" [1].

An important extension of the IS-LM model was built by Robert Mundell (1963) and Marcus Fleming (1962) in the 1960's. The Mundell-Fleming model describes a small open economy with one more curve representing equilibriums of international exchanges.

The limitations of the model

During the 1950’s and 1960’s microeconomic investigations on consumption and investment gave a better understanding of the IS slope. Milton Friedman developed the idea that the consumption level of household’s was mainly determined by a long-term expectation a theory known as the permanent income hypothesis[2]. Franco Modigliani life-cycle theory demonstrated that consumption was also related to age. Those two theories denied short-term policies to have an important effect on consumption, and thus the effects of the spending multiplier.

Such criticisms of Keynesian ideas were not always criticisms of the IS/LM model. In fact, economists like Milton Friedman used the IS/LM framework to confute Keynesian economics[3]. Yet Friedman rejected the paradigm of "general equilibrium" he viewed as characterized by "abstractness, generality, and mathematical elegance"[4]

The most severe criticisms of the IS/LM model came from the fact that it neglects private agents' expectations. Modern macroeconomic models which take expectations into accounts can provide results opposite to those of IS/LM. In fact, the model considers that short run is independent from long run. Yet expectations about the future have for example a direct impact on current wages which stimulates inflation and thus cancelled the positive effects of many macroeconomic policies described by the IS/LM model. In such cases, inflation remains the only effect and disturbs the coordination of private agents. The consequence of the rational expectations theory is that central banks of several industrial countries (the Federal Reserve and the European Central Bank for example) have been given independency and inflation control as their main objective.

Not withstanding its limitations as a policy instrument, the model remains the most common macroeconomic model taught to undergraduate students because of its pedagogical qualities.

References

  1. ↑ Hicks, J. R. (1937), "Mr. Keynes and the Classics - A Suggested Interpretation", Econometrica[1]
  2. ↑ Friedman, Milton (1957). A Theory of the Consumption Function. Princeton Univ Press.
  3. ↑ Bordo, Michael D. & Schwartz, Anna J. (2003), "IS-LM and Monetarism", National Bureau of Economic Research, p.18 [2]
  4. ↑ Milton Friedman (1949 (1953)), , "The Marshallian Demand Curve" in Essays in Positive Economics, Chicago: The University of Chicago Press, pp. 47-99.
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