The IS-LM Framework – Part 2
The IS-LM framework – Part 1
I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to complete the text during 2013 (to be ready in draft form for second semester teaching). Comments are always welcome. Remember this is a textbook aimed at undergraduate students and so the writing will be different from my usual blog free-for-all. Note also that the text I post is just the work I am doing by way of the first draft so the material posted will not represent the complete text. Further it will change once the two of us have edited it.
NOTE: Randy and I discussed at length how much mainstream analysis we would include in the textbook. Clearly, we have a responsibility to provide students with an understanding of the tools that are used in the profession including those that are frequently referred to in the policy debate.
As you will see from the Table of Contents (information below), I think we have been fairly generous in how much of the mainstream material, which we see as having no analytical veracity or policy relevance, we have included.
This Chapter is about IS-LM analysis, a framework we also reject outright. However, during the current crisis, it has been used by notable economists who have held it out as an approach that still has relevance. In that vein we have decided to include it as a separate chapter even though, at first, we had excluded it from the book.
However, we don’t go the next step and derive and utilise the full AD-AS model that flows from the IS-LM approach and is the main organising framework for the orthodox exposition.
The homePage for the Textbook is now available but the material is still being added and the site won’t be fully functional for some months yet. We have nearly agreed on the Table of Contents, which defines the order of exposition of the pedagogy. You can find the site at http://www.mmtonline.net and the Table of Contents is available there.
Note I still haven’t finished the British-IMF Case Study but the sequencing needs for a class that is using the book this semester requires I get the IS-LM Chapter completed first – over the next couple of weeks.
Chapter 16 – The IS-LM Framework
16.1 Introduction
Soon after the publication of Keynes’s General Theory, British economist J.R. Hicks published an article that attempted to integrate the insights he felt were useful in the General Theory with those of the so-called “Classics” that Keynes had opposed. We discussed the debate between Keynes and the Classics in Chapter 15.
The so-called Neo-classical synthesis that emerged and dominated macroeconomic thinking, particularly the textbook expositions, was built on the work of J.R. Hicks and his IS-LM model (see box for more discussion).
The IS and LM curves are the equilibrium relationships pertaining, respectively, to the product (goods) market (investment = saving) and the money market (demand for money (liquidity preference) equals money supply).
The representation of the goods market equilibrium in terms of simple equality between investment and saving reflected the historical period that the model was developed – the simplifying assumption was that we would gain essential insights into income determination by assuming a closed economy without government.
The IS equation was subsequently extended to allow for the impact of governments and net exports on aggregate demand.
The income-expenditure model we considered in Chapter 12 allowed the interest rate to impact on investment and hence aggregate demand and output in the goods market. The interest rate was considered to be determined by the equality of money demand and supply in the money market.
The IS-LM approach thus was built on the interdependence of the equilibrium states in the two markets. The general IS-LM approach showed how the equilibrium solution for output (employment) and the interest rate was simultaneous. We needed to know what the interest rate was to solve the level of income and the level of income to solve the interest rate.
In an analytical sense, there were two unknowns – output and the interest rate – and two equations to allow us to solve the unknowns.
The IS-LM model is an early example of a general equilibrium model that remains fashionable in mainstream economics.
16.2 The LM Curve
We assume that the price level is constant. The IS-LM model allows us to introduce price level changes but at present we are operating in real terms.
Money market equilibrium requires that the demand for money equal the supply. We use the term money demand to refer to the willingness to hold cash balances as part of a wealth portfolio.
The demand for money – or as Keynes called it – the liquidity preference – is a function of the level of income and the interest rate.
Three motives have been identified for holding liquid balances (money) in preference to other assets:
- Transactions motive – people need money to engage in daily transactions. Thus the demand for liquidity will be some proportion of total national income.
- Precautionary motive – at times major events occur that need to be resolved through transactions – for example, maintaining a cash balance to pay for engine repairs on a car. This motive also tends to vary with national income as the higher is the level of economic activity, the higher are the overall transactions.
- Speculative motive – Keynes contribution, which we considered in Chapter 15 was to highlight that money is not simply a means of exchange. People used money in times of uncertainty over movements in interest rates. They have a choice between holding money which earns no interest return or purchasing an interest-bearing asset, which has less liquidity. Keynes juxtaposed the decision to hold money or bonds. If the interest rate is expected to rise, the price of bonds falls and capital losses would be expected. So at lower interest rates more people would prefer to hold money than take a chance that they would lose should they invest in bonds. Alternatively, if the interest rate falls, the price of bonds rises and capital gains would be enjoyed. At higher interest rates, more people will form the view that rates will fall rather than rise and the liquidity preference will be lower.
The other way of thinking about the impact of interest rates is to realise that the opportunity cost of holding money rises when interest rates are higher because holding money negates the alternative of holding an interest-earning asset.
Figure 16.1 shows the liquidity preference function for a range of income levels. The nominal rate of interest is on the vertical axis and the volume of money demand is on the horizontal axis.
The money demand curve (L) is downward sloping with respect to the interest rate and shifts outwards at higher income levels (Y1 < Y2).
The higher is the interest rate, the lower will be the demand for liquidity, other things equal. However, at any interest rate, the higher is the level of national income, the higher will be the demand for money.
The money demand curve is smooth and non-linear because of diversity of opinion. For example, as interest rates rise, wealth holders progressively form the view that they have reached their maximum. Eventually everybody adopts the same expectation.
The money supply (Ms) is assumed to be controlled by the central bank via the monetary base and the money multiplier determines the quantity of money supplied for a given base.
We can thus capture that assumption as a vertical line. The intersection of the money demand and money supply curves determines the interest rate.
This is faithful to Keynes departure from the Classics who considered the interest rate to mediate saving and investment (that is, a real variable). Keynes noted that the nominal interest rate was a monetary variable determined by the demand for liquity and the supply of money available.
Figure 16.1 Money Market Equilibrium
If the national income level was Y0 then the intersection of the relevant liquidity preference function and the money supply line would generate an interest rate of i0 – Point A.
What would happen if income rose to Y1?
At the current interest rate i0 there would now be an excess demand for liquidity (measured by the segment AB) and this would lead to the interest rate rising until the excess demand was eliminated at C (i1) given that the money supply would be fixed.
What would happen if the central bank increased the money supply?
If the national income level was Y0 then the intersection of the relevant liquidity preference function and the money supply line would generate an interest rate of i0 – Point A.
What would happen if income rose to Y1?
At the current interest rate i0 there would now be an excess demand for liquidity (measured by the segment AB) and this would lead to the interest rate rising until the excess demand was eliminated at C (i1) given that the money supply would be fixed.
What would happen if the central bank increased the money supply?
Figure 16.2 shows the impact of an increase in the money supply from Ms1 to Ms1.
At national income level Y0 and Ms1, the interest rate is i0 and the money market is in equilibrium at Point A.
If the money supply rises to Ms2 then there is an excess supply of money at i0 (measured by the segment AB) and the interest rate would drop until is reached i2 – Point D, where the demand for money is again equal to the money supply.
You can also see that if we start at Point A and the national income level rose to Y1 the interest rate could be held constant at i0 if the central bank accommodates the increased demand for money at the higher income level by increasing the money supply to Ms2.
We are now in a position to derive the LM curve which shows all combinations of income and interest rates that are consistent with money market equilibrium.
Figure 16.3 shows the derivation of the LM curve. From the money market diagram, the Points A, B and C represent equilibirium states where money demand equals money supply for different levels of income.
Each equilibrium point is thus a unique combination of income and interest rates.
We can translate this understanding to a new graph (right-hand panel) where national income (Y) is on the horizontal axis and the interest rate (i) is on the vertical axis.
If we trace the respective equilibrium points across into the income-interest space diagram we get a series of points that are consistent with money market equilibrium.
The intersection of all those points is the LM curve.
Figure 16.3 The LM Curve
| Advanced material: John Hicks on his IS-LM Framework John Richard Hicks – was a British economist who “invented” the IS-LM general equilibrium macroeconomic framework. In his 1937 article published in Econometrica – Mr. Keynes and the “Classics”; A Suggested Interpretation – Hicks sought to provide an interpretation of Keynes’ General Theory within a single diagram – the IS-LL model. As the model became popularised and standard macroeconomic textbook fare, the terminology became IS-LM to describe the product market equilibrium (IS) and the money market equilibrium (LM). The IS-LM model was designed to demonstrate how the determination of total real output was dependent on the interdependent outcomes in the product and money markets. Hicks said he “invented a little apparatus” (the IS-LM framework) to bring together Keynesian and Classical economics into an integrated model. By the 1970s, Hicks started to sign his academic papers John Hicks rather than J.R. Hicks, which reflected his growing sense of rejection of his earlier work. In 1975, to formalise is transition away from his earlier views, he wrote (Page 365):
The issue was that he began to realise that the static equilibrium IS-LM model left out the key contribution of Keynes – the importance of time and endemic uncertainty. For example, in the IS-LM model the current flow of investment is meant to be sensitive to interest rate changes in the same period, which is one way in which the money market outcome influences the product market equilibrium. But investment in any period is largely pre-determined by decisions made in previous periods. In 1980, Hicks wrote that he rejected the way in which is little aparatus had been deployed by economists and the policy interpretations they had drawn from it. He said (1980: 139):
By way of conclusion, he wrote (1980: 152-153):
The last point was telling. While the intersection of given IS and LM curves might reflect conditions now, the other points on the respective curves are what John Hicks called “theoretical constructions” (1980: 149) and “surely do not represent, make no claim to represent, what actually happened”. References: Hicks, J.R. (1937) ‘Mr. Keynes and the “Classics”; A Suggested Interpretation’, Econometrica, 5(2), April, 147-159. JSTOR link Hicks, John (1975) ‘Revival of Political Economy: The Old and the New’, The Economic Record, The Economic Society of Australia, 51(135), September, 365-67. Hicks, John (1980)'”IS-LM”: An Explanation’, Journal of Post Keynesian Economics, 3(2): 139–154. JSTOR link |
Conclusion
PART 2 next week – manipulation of the LM curve and the derivation of the IS curve.
Saturday Quiz
The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:
That is enough for today!
(c) Copyright 2013 Bill Mitchell. All Rights Reserved.
I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to complete the text during 2013 (to be ready in draft form for second semester teaching). Comments are always welcome. Remember this is a textbook aimed at undergraduate students and so the writing will be different from my usual blog free-for-all. Note also that the text I post is just the work I am doing by way of the first draft so the material posted will not represent the complete text. Further it will change once the two of us have edited it.
Previous Parts to this Chapter:
Chapter 16 – The IS-LM Framework
[PREVIOUS MATERIAL HERE IN PART 1]Figure 16.3 shows the derivation of the LM curve. From the money market diagram, the Points A, B and C represent equilibrium states where money demand equals money supply for different levels of income.
Each equilibrium point is thus a unique combination of income and interest rates.
We can translate this understanding to a new graph (right-hand panel) where national income (Y) is on the horizontal axis and the interest rate (i) is on the vertical axis.
If we trace the respective equilibrium points across into the income-interest space diagram we get a series of points that are consistent with money market equilibrium.
The intersection of all those points is the LM curve.
Figure 16.3 The LM Curve
Note that at interest rate, i0, the LM curve is flat and becomes steeper at higher interest rates. What does that mean? The horizontal segment of the LM curve relates to the presence of the liquidity trap, which was named by English economist Dennis Robertson, who in the 1930s, worked closely with J.M. Keynes at Cambridge University.
The liquidity trap arises at some minimum interest rate (which could be zero) where everybody forms the view that the only direction for interest rates is up. The equivalent expectation is that everybody considers that capital losses will be incurred on bond portfolios because when interest rates rise, bond prices fall.
The result is that once interest rates reach this minimum level, all people will prefer to hold any new money in the form of cash instead of bonds.
In Chapter 15 of the The General Theory of Employment, Interest and Money, Keynes said (1936: 207):
There is the possibility … that, after the rate of interest has fallen to a certain level, liquidity-preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest … Moreover, if such a situation were to arise, it would mean that the public authority itself could borrow through the banking system on an unlimited scale at a nominal rate of interest.
As we will see when we consider policy analysis within the IS-LM framework, the existence of a liquidity trap renders monetary policy ineffective as a counter-stabilising tool.
Monetary policy is characterised in this framework as the central bank manipulating the money supply and when the interest rate is at i0 in Figure 16.3, increasing the money supply would have no impact on interest rates or the price of bonds. In other words, monetary policy changes cannot alter the level of national income.
In a liquidity trap, a rise in the money supply leads to an equal rise in the demand for money and as a result the interest rate does not change. We will consider this in more detail later in the Chapter.
The LM curve is upward sloping at higher levels of income because as national income rises the demand for money increases and at each given money supply, the interest rate has to rise to ration the excess money demand and retain money market equilibrium.
The slope of the LM curve is steeper:
- The more sensitive the demand for money (transactions and precautionary motives) is to national income changes. Thus, small changes in national income lead to large changes in excess money demand at a given money supply level. The rise in interest rates to restore money market equilibrium, other things equal, has to be larger as a consequence.
- The less sensitive the speculative demand for money is to changes in interest rates. Thus, for a given excess demand for money, the interest rate increase that is required to restore money market equilibrium is larger.
While the horizontal LM curve (liquidity trap case) is one extreme, the other extreme is sometimes referred to as the Classical Case, which describes a vertical LM curve.
The Classical case arises from a demand for money function which is not sensitive to the interest rate. In other words, money is considered to be a means of exchange only and the speculative demand for money (which renders the overall demand for money sensitive to interest rates) is ignored.
In these cases, the demand for money shifts outwards when income rises and inwards when it fall. As a consequence there is only one national income level consistent with money market equilibrium for a given money supply and the LM curve is vertical.
In the Appendix to this Chapter we derive an analytical solution to the IS-LM framework for advanced studies, which show the impact of these two sensitivities (elasticities).
Shifts in the LM curve arise from changes in the money supply. Refer back to Figure 16.2, which showed that for a given money demand curve, interest rates fall when the money supply rises. The reasoning was that at a given money market equilibrium combination of interest rates and income, a rise in the money supply generates an excess supply of money, which requires interest rates to fall to stimulate the demand for money sufficiently to absorb the extra money.
In terms of the LM curve, this means that at higher levels of money supply, equilibrium interest rates will be lower at each income level which translates into a shift outwards in the LM. The opposite occurs when the money supply falls.
The LM curve can also shift if there is an autonomous change in liquidity preference, which means the money demand rises (falls) at each income level depending on whether the preference for liquidity rises (falls).
For example, if people become more pessimistic about the future they may use increased cash holdings as a haven from uncertainty. This will lead to an outward shift in the money demand curve so that for a given money supply, interest rates will be higher at each income level.
16.3 The IS curve
The IS curve shows all combinations of interest rates and income where the product (goods) market is in equilibrium. So unlike the simple income-expenditure model we developed in Chapter 12, the IS curve framework requires us to incorporate information about the money market (interest rates) in our understanding of equilibrium in the product market.
In Chapter 12 we developed the real expenditure model of income determination. From the National Accounting framework we know that total expenditure (E) in the domestic economy in any particular period can be expressed as:
(16.1) E = C + I + G + (X – M)
Equation (16.1) is identical to Equation (12.2). As it stands, Equation (16.1) is an accounting statement by dint of the definitions and sources of aggregate spending.
The equilibrium level of national income (Y) is determined by aggregate expenditure, such that Y = E. The task of Chapter 12 was then to understand the behaviour of each of the expenditure components in Equation (16.1) and theorise how they interact to determine national income.
At that stage we assumed that firms in aggregate plan a fixed volume of investment spending in each period. We were concerned at that stage of the text in tracing out the implications of changes in autonomous (exogenous) components of expenditure (investment, government, exports etc) on national income via the multiplier process.
However, in Chapter 2, we develop a more detailed model of investment spending, which allows us to take into account the impact on capital formation of changes in interest rates.
As a preview, we assume that rather than being exogenous, total investment spending is influenced, in part, by expectations of future economic conditions and the interest rate.
Business firms are continually forming expectations about future output. Firms have to make resource commitments (working capital, labour etc) well in advance of realisation (sales) and so the scale of production at any point in time reflects the guesses they make in a highly uncertain world.
Further, for given expectations about future sales and revenue, a firm’s investment decisions will also be influenced by the cost of capital goods, which, in turn, will be affected by the interest rate.
If interest rates rise, the cost of funds necessary to invest in new capital equipment rises and so marginal projects (relative to expected revenue) may become unprofitable. In other words, investment is likely to be an inverse function of the interest rate, other things being equal.
In other words, we might hypothesise that total investment is given as:
(16.2) I = b1 – b2i
where b1 is an autonomous component of investment and b2 is the interest-rate sensitivity of investment to interest rate changes.
The higher is b2, the more investment will decline (rise) for a given interest rate rise (fall).
The IS-LM framework retains the insight of Keynes that planned savings is a positive function of national income. A more detailed analysis of the General Theory would also reveal that Keynes considered that the interest rate might also influence consumption spending (via wealth impacts). Further, the purchase of consumer durables such as white goods, which might require access to consumer credit).
However, for now, to keep the argument simple, we assume that the interest rate only impacts on investment.
In Chapter 12. we assumed that firms in the economy are quantity-adjusters and so prices are fixed in the short-term. Figure 12.8 brought together the 450 aggregate supply curve with the aggregate demand curve (E). It showed that equilibrium national income occurs when the Aggregate Demand Function cuts the 450 line.
At this point, the aggregate demand expectations formed by the firms, which motivated their decisions to supply – Y* – are consistent with the planned expenditure – E* – by consumers, firms, government and the external economy.
Figure 16.4 augments Figure 12.8 by adding in the impact of Equation (16.2) – that is, allowing investment to be inversely impacted by interest rate changes.
Figure 16.4 Product market equilibrium and interest rate changes
[#28.4:451]
The total expenditure curve, E = C + I + G + NX is drawn from a given interest rate. The lower the interest rate (i0 < i1), the higher in investment (and total spending) at all income levels. As a consequence, the total expenditure curve shifts upwards.
When interest rates rise, the total expenditure curve would shift downwards, other things equal.
Point A in Figure 16.4 shows the product market equilibrium associated with an interest rate of i0. So we know that the combination of income level, Y*0 and interest rate level, i0 is an equilibrium combination in the product market.
What happens if the interest rate was to rise to i1? Total investment would decline at all income levels and the total expenditure curve would shift downward from E0 to E1.
The excess supply at the prior income level leads firms to cut back output and employment and national income falls. A new product market equilibrium occurs when E*1 = Y*1.
So the combination of income level, Y*1 and interest rate level, i1 is an equilibrium combination in the product market.
We thus have two combinations of interest rates and income levels which are consistent with product market equilibrium. Clearly we could trace out the impact of many interest rate changes and thus many equilibrium combinations of interest rates and income.
The IS curve is the line that joins all the equilibrium combinations of interest rates and national income. Figure 16.5 shows this derivation.
Figure 16.5 The derivation of the IS curve
GRAPH TO COME.
Conclusion
PART 3 next week – Policy Analysis and Critique
Saturday Quiz
The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:
Monday’s Blog
I am going to be in some very remote locations for the next three days (Kakadu National Park) and I might not get to file a blog on Monday. We will see.
That is enough for today!
(c) Copyright 2013 Bill Mitchell. All Rights Reserved.
The IS-LM Framework – Part 3
I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to complete the text during 2013 (to be ready in draft form for second semester teaching). Comments are always welcome. Remember this is a textbook aimed at undergraduate students and so the writing will be different from my usual blog free-for-all. Note also that the text I post is just the work I am doing by way of the first draft so the material posted will not represent the complete text. Further it will change once the two of us have edited it.
Previous Parts to this Chapter:
Chapter 16 – The IS-LM Framework
[PREVIOUS MATERIAL HERE IN PARTS 1 and 2]We thus have two combinations of interest rates and income levels which are consistent with product market equilibrium. Clearly we could trace out the impact of many interest rate changes and thus many equilibrium combinations of interest rates and income.
The IS curve is the line that joins all the equilibrium combinations of interest rates and national income. Figure 16.5 shows this derivation.
Figure 16.5 The derivation of the IS curve
Point A is one product equilibrium where the interest rate is i0 and total expenditure is E0 generating total national income of Y0.
In the right-hand panel where the interest rate is on the vertical axis and national income is on the horizontal axis, point A shows the combination of the interest rate and income which produce the product market equilibrium shown in the left-hand pane.
If interest rates fell to i1, total expenditure rises to E1 as a result of the higher investment expenditure, which leads to a rise in national income via the expenditure multiplier. Point B shows the new product market equilibrium at (i1, Y1).
We could examine the impact of any number of interest rate changes on product market equilibrium in the left panel and subsequently map these points into the right panel. The result would be the IS curve.
The IS curve therefore is a series of points corresponding to equilibrium combinations of national income and interest rates in the product market.
It is clear that in the IS-LM framework, the money market impacts on the product market through the impact of interest rate changes on investment. The change in income results from the initial response of investment to an interest rate change then being multiplied through the expenditure system via induced consumption and leakages to taxation and imports.
In other words, the total change in income that follows a change in the interest rate depends on the values of the expenditure multiplier and the sensitivity of investment to interest rate changes.
What factors will shift the IS curve? First, any increase (decrease) in autonomous spending shifts IS up (down) because for a given interest rate, the equilibrium level of national income rises (falls) when autonomous spending rises (falls).
The magnitude of the shift up or down in the IS resulting from a rise (fall) in autonomous spending is determined by the magnitude of the change in autonomous spending and the size of the expenditure multiplier.
For a given change in autonomous spending, the shift in the IS curve will be larger the larger is the value of the expenditure multiplier.
The slope of the IS curve represents this overall sensitivity of national income to interest rate changes. The larger is the expenditure multiplier and the larger is the sensitivity of investment to interest rate changes the flatter the IS curve.
This is because for a given change in interest rates, the initial response of investment spending will be larger the more responsive it is to the cost of capital, other things being equal.
In turn, a given change in investment will generate a larger (smaller) change in national income the larger (smaller) is the value of the expenditure multiplier.
If current period investment is very unresponsive to a change in the current interest rate then the IS curve will be very steep. It is argued by economists who consider time to be an important consideration in economic analysis that investment spending plans are based on expectations of future revenue streams that were formed in past periods.
The current period’s flow of investment spending reflects these past decisions. The time it takes to evaluate different projects, design the appropriate necessary capital equipment, source funding and then implement the capital infrastructure suggests that current investment spending will be relatively insensitive to current changes in interest rates.
We discuss this topic more in Chapter 22.
It should be clear from this discussion that changes in the tax rate (t), which impact on the value of the expenditure multiplier will also impact on the slope of the IS curve. For example, a rise in the tax rate will cause the IS curve to become steeper because it reduces the value of the expenditure multiplier – a larger leakage from the expenditure system.
Similarly, a rising saving propensity or propensity to import, which mean that there are larger leakages from the expenditure system each time income changes, will lead to a steeper IS curve.
16.4 General Equilibrium in the IS-LM framework
The intention of the IS-LM framework is to bring the product market and money market outcomes into a single diagram so that we can simultaneously determine the equilibrium value of national income and the interest rate. In doing so, it recognises the interdependency between these markets, a point that Keynes demonstrated clearly.
What happens in one market impacts on the other market, which then leads to feedback loops and new equilibrium outcomes in each.
The IS-LM framework thus conceives of a general equilibrium defined as the interest rate and income level that generates simultaneous equilibrium in the both the product and money markets.
In a graphical form, this equilibrium position corresponds to the intersection of the IS and LM curves. In the Advanced Material Box we derive the algebra corresponding to this general equilibrium.
Figure 16.6 shows the IS-LM solution for equilibrium income and interest rates, Y*, i*. Two things are worth noting. The vertical green line at YFE, denotes a full employment national output level. In other words, at this output level all available labour and capital are being productively deployed.
The IS-LM joint equilibrium thus can occur at levels of income which are below full employment in the labour market. This is consistent with Keynes’ insight that the capitalist monetary system has a tendency to reach under-full employment steady states which need to be shocked by policy interventions.
At Y* and i*, business firms are selling as much as they expected to sell and have no incentive to expand production and employment. The desire for liquidity by firms and households are also being full met by the available supply of money.
This under-full employment equilibrium can be reached at interest rates above the minimum rate, where the economy enters a liquidity trap.
Figure 16.6 General IS-LM Equilibrium
| Advanced material: The IS-LM algebra The formal IS-LM model for a simplified open economy begins with the following relationships. Product Market
Product Market Equilibrium The product market equilibrium can be solved as a relationship between GDP (Y) and the interest rate (i) given the autonomous spending aggregates and the value of the multiplier. Substituting Equations (2) to (7) into (1) we get: (10) Y = C0 + cY – ctY + I0 – bi + G + X – mY Rearranging gives the equation for the IS curve: (11) Y = α(A– bi) where α = 1/(1 – c(1 – t) + m), the expenditure multiplier and A is the autonomous spending component, C0 + I0 + G + X. The slope of the IS curve is given by αb, so the larger the multiplier (α) and the sensitivity of investment to interest rates (b), the flatter will be the slope because the response of national income to a given interest rate will be larger. Money Market Equilibrium The money market equilibrium is given by the equality of money supply and money demand. (12) Ms = kY – hi Which produces the LM curve where Y is a function of i: (13) Y = (1/k)Ms + (h/k)i The slope of the LM curve is given by (h/k), so the larger the sensitivity of the demand for money to interest rates (h) and the smaller the sensitivity to income (k), the flatter will be the slope because for a small change in interest rates, a much larger change in national income will be required to maintain the equality between the demand for money and the given money supply. Equation (13) can also be written with i as a function of Y: (14) i = (k/h)Y – (1/h)Ms General Equilibrium A state of general equilibrium in this context is defined as the interest rate and income level that generates simultaneous equilibrium in the both the product and money markets. This equilibrium position corresponds to the intersection of the IS and LM curves. To solve for the equilibrium level of national income we can substitute Equation (14) into the IS curve equation (11) to give: (15) Y = α[A- (b/h)(kY – Ms)] Solving for equilibrium Y gives: (16) Equation (16) indicates that equilibrium income is determined by autonomous spending (A), which includes the fiscal policy parameter (G) and the money supply (Ms). We use the solution in Equation (16) to solve for the equilibrium interest rate: (17)
Equation (17) tells us that the equilibrium interest rate is determined by autonomous spending (A) and the money supply (Ms). Some economists use Equation (15) to define a fiscal policy multiplier, which indicates the change in national income for a given change in government spending, if the money supply is held constant. The fiscal policy multiplier is given by the coefficient on autonomous spending A in Equation (15). You will note that this is different to the expenditure multiplier, α because it takes into account the interest rate impacts of rising income on investment spending that emanate from the shifts in the demand for money in the money market. The simple expenditure multiplier is derived on the assumption that interest rates do not change when national income rises. Similarly, a monetary policy multiplier can be derived, which shows the increase in national income for a given change in the money supply, if government spending and tax rates are held constant. This is given by the coefficient on Ms in Equation (15). Note though that this assumes that monetary policy is conducted through the central bank exercising its assumed control over the money supply. This is one of the flaws of the IS-LM framework when applied to the real world – the central bank does not have control over the money supply and the assumed money multiplier does not exist in any form other than as an ex post, non-causal accounting statement. |
Conclusion
PART 4 next week – Complete Chapter POLICY ANALYSIS IN THE CONTEXT OF THE CURRENT CRISIS (HOW THE IS-LM IS BEING USED BY SOME TO ANALYSE THE CRISIS), PIGOU AND KEYNES EFFECTS AND CRITIQUE OF FRAMEWORK.
Saturday Quiz
The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:
That is enough for today!
(c) Copyright 2013 Bill Mitchell. All Rights Reserved.
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