Money Market Equilibrium: Supply, Demand, and Interest Rates

The Theory of Liquidity Preference

John Maynard Keynes developed the theory of liquidity preference to explain the factors that determine the interest rate in the short run. The theory posits that the interest rate adjusts to balance the supply of and demand for the economy's most liquid asset: money.

The Supply of Money

First, let's consider the supply of money. We distinguish between the nominal money supply ($M$), which is the total amount of currency and deposits, and real money balances ($M/P$), which measure the purchasing power of the money supply. For instance, if the nominal money supply is $1000 and a loaf of bread costs $2, the real money supply is 500 loaves of bread.

In our model, we assume the central bank has direct control over the nominal money supply, $M$. We also make the simplifying assumption, common in short-run analysis, that the aggregate price level, $P$, is fixed. Therefore, the supply of real money balances, $M/P$, is also fixed and determined exogenously by the central bank.

Because the central bank sets the money supply without regard to the interest rate, the real money supply curve is a vertical line.

The Demand for Money

Now, why do people choose to hold money? Money is the most liquid asset, meaning it can be used directly for transactions. However, holding wealth as money comes with an opportunity cost: you forgo the interest you could have earned by holding interest-bearing assets, such as bonds.

The interest rate ($r$) is the opportunity cost of holding money.

• When the interest rate is high, people are less willing to hold their wealth as idle cash and will prefer to buy bonds to earn a higher return. The quantity of money demanded is therefore low.
• When the interest rate is low, the opportunity cost of holding money is small, so people are more willing to hold cash for convenience. The quantity of money demanded is therefore high.

This inverse relationship means the money demand curve is downward-sloping.

The other key determinant of money demand is the level of national income ($Y$). When income is higher, people are making more purchases, so they need to hold more money to facilitate these transactions. Thus, an increase in income shifts the money demand curve to the right.

The video below provides a good economic intuition for the determinants of money demand.

Equilibrium in the Money Market

Just like in any other market, equilibrium is found where the supply curve intersects the demand curve. The equilibrium interest rate is the rate at which the quantity of real money balances supplied is exactly equal to the quantity of real money balances demanded.

What happens if the interest rate is not at this equilibrium? The market adjusts.

• If $r>r_{equilibrium}$: There is an excess supply of money. People are holding more money than they wish to at such a high interest rate. They will attempt to convert this excess money into interest-bearing assets by purchasing bonds. This increased demand for bonds drives bond prices up. As we learned in the previous lesson, an increase in a bond's price leads to a decrease in its yield. The interest rate will fall until it reaches the equilibrium level.

• If $r<r_{equilibrium}$: There is an excess demand for money. People want to hold more money than is available. To get more cash, they will sell their interest-bearing assets, like bonds. This increased supply of bonds drives bond prices down, causing their yields to rise. The interest rate will rise until it reaches the equilibrium level.

This adjustment mechanism ensures that the interest rate always gravitates toward the level that balances money supply and money demand.

Calculating the Equilibrium Interest Rate

With your background, you'll find the process of calculating the equilibrium interest rate straightforward. It simply involves setting the equation for money supply equal to the equation for money demand and solving for the interest rate, $r$.

A typical linear money demand function might look like this:

where $k$ and $h$ are positive parameters indicating the sensitivity of money demand to income ($Y$) and the interest rate ($r$), respectively. For a given level of income, this simplifies to $(M/P{)}^d=a-br$, where $a$ is a constant incorporating income and $b$ is the interest sensitivity.

The following video provides a complete numerical example, walking through the calculation of the equilibrium interest rate and analyzing the effects of a change in monetary policy.

Let's summarize the core calculation from the video.

• Money Supply: $M=1000$, $P=2$. So, Real Money Supply $(M/P{)}^s=1000/2=500$.
• Money Demand: $(M/P{)}^d=1000-100r$.

To find the equilibrium, we set supply equal to demand:

Solving for $r$:

The equilibrium interest rate is 5%.

Practice Problems

To solidify your understanding, let's work through another problem. The resource below provides a set of solved problems that will be useful. We'll focus on the first part of Question 3.

Solution Walkthrough:
Setting money supply equal to money demand:

Now, we solve for $r$:

The equilibrium interest rate is 25%. This exercise demonstrates how robust the equilibrium-finding method is, regardless of the specific numbers or functional forms.

Conclusion

In this lesson, we have constructed the workhorse model of the money market based on Keynes's theory of liquidity preference. You are now able to explain and calculate how the interaction between the supply of and demand for money determines the economy's equilibrium interest rate.

Key Takeaways:

• The money market consists of a fixed, vertical money supply (controlled by the central bank) and a downward-sloping money demand.
• Money demand is inversely related to the interest rate, which represents the opportunity cost of holding money.
• The interest rate adjusts to ensure equilibrium, where $M^s=M^d$. If there is an excess supply of money, people buy bonds, and the interest rate falls. If there is an excess demand for money, people sell bonds, and the interest rate rises.
• Calculating the equilibrium interest rate is an algebraic exercise of setting the money supply and demand equations equal to each other and solving for $r$.
• Changes in the money supply, the price level, or national income will shift the curves and lead to a new equilibrium interest rate.

We've focused on how a given money supply ($M$) affects the interest rate. But how does a central bank's action, like buying bonds, translate into a change in the overall money supply? Our next lesson will delve into the mechanics of money creation within the banking system. We will introduce the money multiplier, which explains how an initial change in reserves can lead to a much larger final change in the total money supply.