The IS-LM (Investment Savings-Liquidity preference Money supply) model focuses on the equilibrium of the market for goods and services, and the money market. It basically shows the relationship between real output and interest rates.

It was developed by John R. Hicks, based on J. M. Keynes’ “General Theory”, in which he analysed four markets: goods, labour, credit and money. This model, firstly named IS-LL, appeared in his article “Mr. Keynes and the Classics: a Suggested Interpretation”, published in 1937 in the journal Econometrica.

In order to understand how this model works, we’ll first see how the IS curve, which represents the equilibrium in the goods market, is defined. Then, the LM curve, which represents the equilibrium in the money market. Finally, we’ll analyse how the equilibrium is reached.

IS curve: the market for goods and services

In a closed economy, the equilibrium condition in the market for goods is that production (Y), is equal to the demand for goods, which is the sum of consumption, investment and public spending. This relationship is called IS. If we define consumption (C) as C = C(Y-T) where T corresponds to taxes, the equilibrium would be given by:

Y = C (Y- T) + I + G

We consider that investment is not constant, and we see that it depends mainly on two factors: the level of sales and interest rates. If the sales of a firm increase, it will need to invest in new production plants to raise production; it is a positive relation. With regard to interest rates, the higher they are, the more expensive investments are, so that the relationship between interest rates and investment is negative. The new relationship is expressed as follows (where i is the interest rate):

Y = C (Y- T) + I (Y, i) + G

If we keep in mind the equivalence between production and demand, which determines the equilibrium in the market for goods, and observe the effect of interest rates, we obtain the IS curve. This curve represents the value of equilibrium for any interest rate.

An increasing interest rate will cause a reduction in production through its effect on investment. Therefore, the curve has a negative slope. The adjacent graph shows this relationship. 

LM curve: the market for money

The LM curve represents the relationship between liquidity and money. In a closed economy, the interest rate is determined by the equilibrium of supply and demand for money: M/P=L(i,Y) considering M the amount of money offered, Y real income and i real interest rate, being L the demand for money, which is function of i and Y.

The equilibrium of the money market implies that, given the amount of money, the interest rate is an increasing function of the output level. When output increases, the demand for money raises, but, as we have said, the money supply is given. Therefore, the interest rate should rise until the opposite effects acting on the demand for money are cancelled, people will demand more money because of higher income and less due to rising interest rates.

The slope of the curve is positive, contrary to what happened in the IS curve. This is because the slope reflects the positive relationship between output and interest rates.

IS-LM model

At any point of these curves the equilibrium condition in the corresponding market is true, but only at the point where the two curves intersect, both equilibrium conditions are satisfied. We can see this intersection in the following graph:

The IS and LM curves undertake changes due to many factors, such as different kinds of economic policies. These variations will explain the changes in the values of production and of interest rates taking place in the economies.
For instance, if there is an increase in government spending, which is considered a fiscal policy, the IS curve will shift to the right, as seen in the graph in the left. This happens because more government spending means more production for any interest rate. This shift, as seen in the adjacent graph, will consequently change the equilibrium from point E₁ to point E₂, with a greater level of output, but also at greater interest rates.

On the other hand, if we consider a monetary policy, such as an increase in the money supply, the curve that shifts will be the LM curve, as seen in the graph in the right. An increase in the money supply will decrease the interest rate, shifting the LM curve to the right, thus increasing output.

Monetarists’ views on the IS-LM model:

Monetarists greatly criticized the IS-LM model, highlighting some different views regarding the elasticity (and therefore the slope) of both curves. In their opinion, the LM curve is very inelastic, while the IS curve is very elastic. The most important thing we derive from these different views is the different consequences and effectiveness of expansionary fiscal and monetary policies.

Monetarists argue that monetary policies are more effective. Take the same example as before, an increase in the money supply. This will shift the LM curve to the right, displacing the equilibrium from E₁ to E₂ in the figure below. However, monetarists consider also two other effects: direct and indirect wealth effect. The first one, also known as Pigouvian effect, considers that, because of the increase in money supply, people will consume more, shifting the IS curve and changing the equilibrium to point E₃. The second one considers that, because of the initial drop in the equilibrium interest rates, people will invest more, thus shifting even more the IS curve and changing the equilibrium to point E₄.

Now, monetarists are more sceptic than Keynesians about fiscal policy. This is because, as seen in the figure below, the initial shift of the IS curve (from point E₁ to point E₂) will be partly offset by a second shift of the same curve. This, known as crowding-out, happens because the increase in government spending increases interest rates, which decreases the attractiveness of investment. Therefore, the more the government spends, the less private capital will be invested, which moves the equilibrium from point E₂ to E₃. Also, because of higher output, money demand increases, which shifts the LM curve to the left, to point E₄.

Both views have a great army of researchers and professors defending them, as part of the modern division on such matters into two main doctrines: New Keynesian Economics and New Classical Macroeconomics. All the effects presented here must be taken into consideration when analysing the IS-LM model. However, it must be noted that some of these conclusions change when considering an open economy, which is analysed by the IS-LM-BoP or Mundell-Fleming model.

John R. Hicks, in his article “Mr. Keynes and the Classical; a Suggested Interpretation”, published in 1937 in the journal Econometrica, developed a model known as IS-LL, which will later become IS-LM. The purpose of the article was to compare classical economists’ view on the goods and money market, with Keynes’ views.
In a few words, Hicks would assume Keynes’ innovations (possibility of frictional unemployment, the impact of animal spirits on investment, as well as money illusion effects) to take place in the short run, while classical views (such as full employment, perfect competition and the ability of the economy to re-equilibrate itself without government intervention) to be valid on the long run.
Hicks starts with the following assumptions, which we will maintain:

-he considers the short period;

-the quantity of physical equipment is fixed;

-homogeneous labor;

-depreciation can be neglected;

-rate of money wages (w) can be taken as given;

-quantity of money (M) is given;

-price level of goods equals their marginal cost.

(For the sake of simplicity, we will not consider differences between investment and consumption goods, nor the differences on the distribution of income.)

He also defines the following variables, which we will reformulate according to the level of simplicity we are aiming at:

-Y: total income;

-M: money quantity (which is given);

-I: investment;

-S: savings;

-i: rate of interest.

By uniting both classical and Keynesian views, Hicks writes the following three equations:

-M(Y,i) : we see that money quantity depends on both total income and the rate of interest;

-I(i) : investment depends on the rate of interest;

-I=S(Y) : investment must equal savings, which depend on total income.

From these three equations, we can see the relation between total income and the rate of interest in both markets:

-money market: since the money quantity is given, the LL curve (blue) will slope upwards, because an increase in income usually raise the demand for money (people need cash to consume goods) and an increasing rate of interest tend to lower money demand (the explanation of this can be made from two different angles: people will rather save more money since the interest rate is higher, therefore will spend less and demand less cash; or people are less willing to borrow money from banks, to spend it or invest it, because of the higher rate of interest);

-goods market: the IS curve (green) shows the relation between income and interest needed to make savings equal to investment. It slopes downwards because the lower the interest, the more people will invest, and therefore the higher will the total income be.

Income and the rate of interest are therefore determined where the IS and LL curves intersect (point P).

This model (more precisely, the IS-LM) is used nowadays to show the effect of diverse economic policies on a closed economy, and served as a starting point for the later Mundell-Fleming model, which helps understand their effects on an open economy.