The LM Curve Derived & Explained
By Steve Bain
The LM curve introduces money-market equilibrium points to the short-run Keynesian economic model and, together with the IS curve, it completes the important IS-LM Model.
In my previous posts about Keynesian economics I had focused entirely on the goods/services market, and for details on that see the links at the bottom of the page, but the money-market also plays a central role in macroeconomics which we now need to understand.
As with so many markets in economics it's easiest and best to start with a simple supply and demand analysis. The demand for money is a complicated topic of study because it has many different uses. Money-supply is also complicated when we consider how money is created i.e. by both the central-bank (which controls the monetary base) and the high street banks (which control the creation of credit).
Analysis of these complications forms much of the body of economic theory, but we don't need to delve too deeply into those complications on this page.
The task here is to describe a basic model of the money-market in order to complete our Keynesian model of short-run demand management.
As always, keep in mind that this model assumes that there is spare capacity in the economy such that output can be expanded without causing any rise in the price level (see my page about aggregate-supply for clarity on that).
The Demand for Money
In the diagram above the demand for money is shown via the downward sloping L curve, whilst the supply is shown via the vertical M/S line. This might not look like a typical supply and demand model, not least because the axes are labelled differently from the usual price and quantity measures, but look again.
The price of money is the interest that must be paid for holding it (if it is borrowed money), or the interest that must be foregone for holding it (i.e. the lost interest earnings that could have been made by investing the money).
Similarly, the supply of money is simply the nominal money-supply divided by the price-level (M/P). The price-level is important here, because rising prices erode the real money-supply by reducing its purchasing power. People demand money for many reasons, but their demand is for real money balances with a given level of purchasing power.
In the diagram, the supply of money is vertical with a fixed purchasing power when the price level is stable and the supply of nominal money is fixed.
As with other supply and demand models, equilibrium in the money market is reached at the intersection of the two curves, which gives an interest rate of R as shown.
The LM Curve Derived
The diagram above shows what happens in the money-market after an increase in national income/output i.e. an expansion in the goods market. With more goods and services being bought and sold there will be an increase in demand for money to facilitate those purchases, and so the demand for money curve shifts from L1 to L2 as illustrated in the left side of the diagram.
The extra demand for money, given the fixed supply of it, causes an increase in the interest rate from R1 to R2, because lenders will now be able to extract a higher price for their money since demand for it has increased.
You might wonder how an increase in income could have come about in the first place since that requires more spending on goods and services but the money-supply is fixed, so how can there have been any extra spending? This can be facilitated by an increase in the 'velocity' of exchange i.e. an increase in the rate at which the existing money stock circulates around the economy.
In reality, of course, the high street banks would be able to create more money in this scenario by simply extending credit lines via the money-multiplier process, but in this model we assume that the central-bank intervenes in the market by raising the base rate of interest (sometimes called the 'bank rate') to whatever level is necessary to hold the money-supply constant.
The central-bank can achieve this by selling bonds at a reduced price (and thus a higher yield or implied interest rate) in order to draw money out of the system to offset the creation of extra credit by the high-street banks.
On the right-side of the diagram, the LM curve is derived by connecting the money-market to national income/output. The curve shows all points at which equilibrium is achieved in the money-market at varying levels of national income. The slope of the LM curve depends on the responsiveness of money-demand to national income, and to the interest rate.