Introduction
The IS-LM model is the foundational model used in New Keynesian Economics to try and predict what will happen to aggregate demand if economic conditions change. There are much more advanced versions of IS-LM in practice today, but I will just be explaining the most basic version. I will be assuming a closed economy (one that does not trade with foreigners) to simplify things.
Table of Contents
What are the Axes of the IS-LM Graph?
On the vertical axis we have the interest rate (r) and on the horizontal axes we have National Income (Y). The graph shows how the level of national income in a country is affected by the interest rate. This emphasises an implicit belief of New Keynesian Economics, that changes in the interest rate are an immensely powerful way of changing aggregate demand. This deeply rooted assumption at the heart of IS-LM has very little real-world evidence to support it.
What Does IS-LM Stand for?
IS-LM is supposed to represent two different ‘markets’:
- The ‘IS’ part stands for ‘Investment & Savings’, and this is meant to represent what is going on in the goods and services market. The curve is built on the idea that Business Investment decreases substantially if the interest rate goes up (because many projects are supposedly so marginal that business owners would realise that they can make more money leaving their money in the bank, earning a higher rate of interest than could be achieved from the long term profits of building a new factory). So, by ‘goods and services’ market, we more specifically mean Business Investments.
- The ‘LM’ part stands for ‘Liquidity & Money’, and this is meant to represent what is going on in the ‘market’ for real money balances. Again this isn’t a real marketplace, but is just a useful way of thinking about how the supply of and demand for money in its most liquid form (think cash or money in your bank’s current account) affects the interest rate. ‘Real Money Balances’ is the term given to describe how much cash (or other highly liquid assets) people want to hold at any given time.
Some Key Assumptions in the Short-Run
In New Keynesian Economics the short-run behaves very differently to the long run. The major change is that prices are fixed in the short-run but fully flexible in the long-run. The idea is that in the short-run prices do not have enough time to change. For example, firms will launch expensive advertising campaigns showing products retailing at a set price, if their costs go up, they probably won’t immediately pass that cost onto the customer in the form of higher prices. They may wait until their annual price review. In the IS-LM model I’ll be assuming that prices are completely fixed.
How does the IS-LM curve work?
Every point on the IS curve represents a point where a hypothetical interest rate produces a certain level of expenditure. You’ll see this expenditure referred to as National Income, which is just because total expenditure is the same as the total income that everyone receives in our closed economy.
Similarly, the LM curve represents in graphical form what the interest rate will be depending on the level of national income and the underlying demand for real money balances.
But there can only be one correct interest rate at any given time, and this must be an interest rate that lies on both the IS curve and the LM curve. To find this interest rate we just plot both the IS and LM curves onto one graph, and the point where they intersect will then tell us both the interest rate and the level of national income for the economy.
Deriving the IS-LM Curves
I will now go through a more detailed derivation of both the IS and LM curves. To help visualise what’s going on I’ve included some graphs.
IS Curve
The IS curve is based on two main ideas:
- That investment will change rapidly and substantially in response to interest rate changes
- That everyone plans the quantity of total expenditure they intend on making well in advance. This is called ‘planned expenditure’. For businesses this means getting the tricky job of forecasting how much to produce correct. If businesses have produced more stuff than people want to buy then they start to build up stock, so in response they must reduce their planned expenditure (by letting go of workers and producing less stuff). Businesses will have produced the correct amount of stuff when their plans are realised. This means that when their planned expenditure equals actual expenditure (i.e. they are basically selling everything they make) the economy will be in equilibrium.
The IS Curve Derived in Graphs
The derivation of the IS curve is most easily explained with the use of graphs. The first graph in this series is the ‘Investment Function’. This is just a rule (that could be expressed algebraically, though no one has produced a formula that accurately predicts Investment) showing how Investment changes in relation to the interest rate.
As you can see, higher interest rates lead to reduced amounts of Investment, which is in line with the New Keynesian view that business investment is strongly negatively correlated to the interest rate. Recall that Investment is one of the four spending components of national Income.
Planned expenditure is all of the expenditure that everyone is planning to make in for example the coming year. Therefor:
PE (Planned Expenditure) = C (consumption) + I (Investment) + G (Government Purchases)
We will now look at how planned expenditure is determined by the interest rate.
When planned expenditure equals actual expenditure, then firms are roughly selling everything they produce and are therefor considered to be at equilibrium (because New Keynesian Economists believe that people/businesses will always be content when their plans are realised). Graphically, a line where planned expenditure equals actual expenditure would be drawn as a 45-degree line. This line represents all the points where planned expenditure equals actual expenditure, and therefor the national income will be determined by where the planned expenditure lines intersect the 45-degree line.
So, in graph A we see that the lower interest rate r1 corresponds with a higher level of Investment. In graph B this means that the planned expenditure line e1 is higher than line e2 (which relates to r2, the higher interest rate). This is the mechanism New Keynesians believe happens when Interest rates change. The IS curve is just a summary of these two graphs, worked out by plotting every National income corresponding to a given interest rate.
The IS curve shows how total expenditure (national income) is affected by the interest rate.
LM Curve
The LM curve shows the imaginary market for real money balances. Remember real money balances basically means the amount of hard cash (coins, notes and money in your bank’s current account) that people want to hold at any given time. More formally, a real money balance is the money supply divided by the price level, or M/P. For our purposes we just need to remember that M/P means real money balances – and to think of this as the supply of liquid cash and deposits.
The LM Curve Derived in Graphs
Graph D is for the supply and demand of real money balances. Because we are looking at the short run prices are ‘fixed’, e.g. they cannot change. It is also conventionally assumed that the money supply is also fixed in the short run. As real money balances is just the money supply divided by the price level, then if both these variables are fixed we can say that the supply of real money balances is also fixed. More formally, where a horizontal line over a letter means it is fixed:
Supply of real money balances = M/P
Supply of real money balances = /
The demand for real money balances depends on two things, the interest rate and the level of national income. The higher the interest rate the lower the demand for real money balances (because people would like to earn the high interest rate by lending out their money). People also require real money balances (think cash in your bank account) for personal consumption. Higher levels of national income mean people will be consuming more and therefor spending more. To consume more, they will thus need higher real money balances.
In graph D the demand for real money balances is drawn for just one assumed level of national income. The shape of the demand curve is determined by the responsiveness of the demand for real money balances in relation to the interest rate. It is assumed that the demand curve will have this shape regardless of the level of national income, but if national income increases the demand curve will simply shift up or down as in graph E below.
In graph E we can see what happens when national income rises from Y1 up to Y2. There will be more transactions in the economy and so people will desire to hold more of their wealth as real money balances. The shape of the curve is still the same. As you can see, different levels of national income drive different interest rates. If we work out what the interest rate will be for every level of national income, then we can derive the LM curve from graph E.
The LM curve shows how national income changes the interest rate. Higher interest rates mean there is a greater demand for real money balances. A higher demand for real money balances is also (according to New Keynesians) associated with higher income levels.
Putting It All Together
We can now combine the IS and LM curves into a single graph. Remember that the IS curve represents all the points where planned expenditure equals actual expenditure and the goods and services market is said to be in equilibrium if located on this line. The LM curve represents all the points where the money market is in equilibrium, i.e. where the demand and the supply of real money balances are exactly equal thanks to the interest rate adjusting.
As the economy can only have one interest rate at any given time, this will be found where the IS and LM curves cross.
This produces the equilibrium interest rate as shown in graph G. This interest rate should alter investment enough to make sure that planned expenditure (all the stuff being produced) matches actual expenditure (all the stuff actually produced, but also all the stuff actually consumed). It will do this via influencing the amount businesses decide to invest on capital expenditure.
It is impossible to know which way this interest rate adjustment mechanism works. Does the interest rate change first because of businesses deciding to invest more/Less, and then this new interest rate affects the money market, or is it the other way around?. The IS-LM curve offers little insight into it’s internal mechanism which is part of what makes it so difficult to understand. If you’re still baffled by IS-LM then don’t be worried, it is unintuitive because it is quite simply wrong and full of contradictions, which we will discuss next.
IS-LM Criticisms
I’ve attempted to explain the IS-LM curve, but I do not advocate it as a useful economic tool. The main issues are:
- It assumes that Businesses will drastically alter their planned capital Investments (e.g. Building new factories or buying new machines) based on a small change in the interest rate. In reality there is huge uncertainty over every Long-term investment business make and so managers do not tend to commit to projects that have such an uncertain outcome that a marginal change in the interest rate would suddenly make the investment unprofitable
- The IS curve also assumes that businesses respond instantly to changes in the interest rate. However major Investment projects will have been committed to a long-time in advance, so money being spent on investment projects now was likely committed to a year ago.
- The LM curve focuses on the money market. It imagines a world where banks need depositor’s money to make loans to businesses. This seems believable but is a complete fiction. Modern banking is more sophisticated than this, but the short story is that banks do not use customer deposits to make loans to businesses. See more here.
There are other more general criticisms of the IS-LM framework, but the ones listed above are the most pertinent. New Keynesian Economics is the dominant economic school of thought, and it is built on the foundations of the IS-LM curve. Hopefully you can now both understand the IS-LM model, and also understand the fallacies it is built on.