LM Equation
The LM equation calculates the demand for money, and the equation is represented here:
L = k * Y - h * I
- L = Demand for Real Money
- k = Income Sensitivity of Demand for Real Money
- Y = Income
- h = Interest Sensitivity of Demand for Real Money
- i = Interest Rate
When we talk about real money, we aren't comparing real cash to Monopoly money. Instead, real money is adjusted for inflation. This tells us the true purchasing ability of money, or in essence, what your money can get you. The demand for money also depends on income. The more you make, the more you spend, or save in offshore accounts. It also depends on the interest rate, since people also leverage their money through investing.
We're subtracting the interest rate. As interest rates rise, people tend to invest their money.
The variables k (income sensitivity) and h (interest sensitivity) are modifiers that are added to income and the interest rates and will have value greater than zero. When talking about sensitivity in this case, we're talking about the likelihood of change.
LM Curve
Before we can map out the full LM curve, let's take a look at the demand for money, the L in the equation, in graph form. The LM equation can be used to create a straight line, much as the standard math formula (y = mx + b).
We'll put the interest rate on the y-axis, since this is the independent variable; we'll put L on the x-axis, since this is the demand for money. When interest rates go down, so does the demand for money. Again, we're talking about real money, not Monopoly money or pre-inflation dollars.
This graph is showing two sample calculations for L as plotted on the demand for money graph.
As national income increases, the demand curve shifts upward and outward, toward L on the graph. The size of the shift depends on the increase in income and the income sensitivity of the demand for money.
When the interest sensitivity for real money goes up, the slope of the demand curve is less steep. A small decrease in interest rates causes a larger increase in the demand for money.
There's one more thing to evaluate before we get to the full LM, and that is the money supply. In our example, we'll keep it simple and keep the money supply at a fixed rate. This means that it'll show up on the graph as a vertical line. In the following graphic, we've placed the money supply line on top of the demand for money graph:
Note the two circles and intersection points at interest points one and two. This indicates an equilibrium (remember, that means balanced) between demand and money supply at those points of interest.
Now that we have the building blocks set, let's look at the LM curve.
LM Curve on a Graph
On the left of our graph, we show the demand for money graph. We've now added a graph to show the demand for money against Y1 and Y2 income values. The dashed line crosses the money supply, and hits the first equilibrium interest rate at i1.
When the real interest rate goes up, real income goes up. In our graph above, we're showing two points where the money market is in equilibrium.
The LM line shifts to the right if any of the following conditions are met:
- Increase in money supply
- Increase in expected inflation rate
- Reduction of demand for money
Lesson Summary
The LM curve is a graphical representation of the equilibrium in the money market. L denotes liquidity and M equals money. Equilibrium is really just a fancy term for 'balance.' Demand for money is defined by the equation L = kY - hi, where L is the demand for inflation-adjusted money; k is income sensitivity of demand; Y is income; h is interest sensitivity of demand; and i is the interest rate. These factors affect the slope of the LM curve. For example, an increase in interest rates reduces the amount of money demanded, and an increase in income drives it up to the right.
