Chapter 10: The Monetary Policy and Aggregate Demand Curves

Preview

At the height of the financial crisis in December 2008, the Federal Open Market Committee of the Federal Reserve announced a surprisingly bold policy decision that sent markets into a frenzy. The committee lowered the federal funds rate, the interest rate charged on overnight loans between banks, by seventy-five basis points (0.75 percentage point), moving the federal funds rate almost all the way to zero. The whole world wondered if this bold move would jolt the economy out of recession. Would it boost stock market values? Would it trigger higher inflation?

The short-run model of the aggregate economy that we are building step by step will allow us to analyze how a central bank’s policy decisions affect the economy. We start this chapter by explaining why monetary policy makers set interest rates to rise when inflation increases, leading to a positive relationship between real interest rates and inflation, which is called the monetary policy (MP) curve. Then, using the MP curve with the IS curve we developed in the preceding chapter, we derive the aggregate demand curve, a key element in the aggregate demand-aggregate supply model framework used in the rest of this book to discuss short-run economic fluctuations.

The Federal Reserve and Monetary Policy

Central banks throughout the world use a very short-term interest rate on safe debt as their primary policy tool. In the United States, the Federal Reserve conducts monetary policy via its setting of the federal funds rate, the interest rate at which banks lend to each other overnight. For example, after the FOMC meeting of September 17-18, 2013, the Federal Reserve issued a statement that read, “[the] Committee decided to keep the target range for the federal funds rate at 0 to ¼ percent.”

The Federal Reserve controls the federal funds rate by varying the liquidity it provides to the banking system. When the Fed provides more liquidity, banks have more money to lend to each other, and this excess liquidity causes the federal funds rate to fall. When the Fed drains liquidity from the banking system, banks have less to lend, and the shortage of liquidity leads to a rise in the federal funds rate. How the Federal Reserve sets the federal funds rate is discussed in more detail at the end of this chapter, but for now it is enough to know that the Federal Reserve has the ability to set the federal funds rate at whatever level it chooses.

Recall from Chapter 2 that the real interest rate, $r$ , is the nominal interest rate, $i$ minus expected inflation, $π^{e}$ :

$r = i - π^{e}$

Changes in nominal interest rates can change the real interest rate only if actual and expected inflation remain unchanged in the short run. Here is where sticky prices, which we discussed in Chapter 8, enter the picture. When prices are sticky, changes in monetary policy will not have an immediate effect on inflation and expected inflation. As a result, when the Federal Reserve lowers the federal funds rate, real interest rates fall; and when the Federal Reserve raises the federal funds rate, real interest rates rise.

It is important to note that although the Federal Reserve can determine the real interest rate in the short run, it is not able to control the real interest rate in the long run. In the long run, prices are flexible. Recall from Chapter 4 that the real interest rate in the long run is determined by the interaction of saving and investment and not by the central bank. Indeed, we will see that the aggregate demand-aggregate supply model comes to exactly the same conclusion when analyzing the economy in the long run.

The Monetary Policy Curve

We have now seen how the Federal Reserve can control real interest rates in the short run. The next step in our analysis is to examine how monetary policy reacts to inflation. The monetary policy (MP) curve indicates the relationship between the real interest rate set by the central bank and the inflation rate. We can write this relationship as follows:

$r = \overset{r}{ˉ} + λπ (1)$

where $\overset{r}{ˉ}$ is the autonomous (exogenous) component of the real interest rate set by the monetary policy authorities, which is unrelated to the current level of the inflation rate or to any other variable in the model, and where $λ$ is the responsiveness of the real interest rate to the inflation rate.

To make our discussion of the monetary policy curve more concrete, Figure 10.1 shows an example of a monetary policy curve $M P$ in which $\overset{r}{ˉ} = 1.0$ and $λ = 0.5$ :

$r = 1.0 + 0.5 π (2)$

At point A, where inflation is at $1%$ , the Federal Reserve sets the real interest rate at $1.5%$ ; at point B, where inflation is at $2%$ , the Fed sets the real interest rate at $2%$ ; and at point C, where inflation is at $3%$ , the Fed sets the real interest rate at $2.5%$ . The line going through points A, B, and C is the monetary policy curve $M P$ , and it is upward-sloping, indicating that monetary policy raises real interest rates when the inflation rate rises.

Figure 10.1: The Monetary Policy Curve
The upward slope of the MP curve indicates that the central bank raises real interest rates when inflation rises because monetary policy follows the Taylor principle.

The Taylor Principle: Why the Monetary Policy Curve Has an Upward Slope

To see why the MP curve has an upward slope, we need to recognize that central banks seek to keep inflation stable. In order to stabilize inflation, monetary policy makers follow the Taylor principle, named after John Taylor of Stanford University, in which they raise nominal rates by more than any expected rise in inflation, so that real interest rates rise when there is a rise in inflation, as the MP curve suggests. John Taylor and many other researchers have found that monetary policy makers tend to follow the Taylor principle in practice.

To see why monetary policy makers follow the Taylor principle, in which higher inflation results in higher real interest rates, consider what would happen if monetary policy makers instead allowed the real interest rate to fall when inflation rose. In this case, an increase in inflation would lead to a decline in the real interest rate, which would increase aggregate output, which would in turn cause inflation to rise further, which would cause the real interest rate to fall further, increasing aggregate output further. Schematically:

$π ↑\Rightarrow r ↓\Rightarrow Y ↑\Rightarrow π ↑\Rightarrow r ↓\Rightarrow Y ↑\Rightarrow π ↑$

The result would be that inflation would continually keep rising and spin out of control. Indeed, this is exactly what happened in the 1970s, when the Federal Reserve did not raise nominal interest rates by as much as inflation rose, so that real interest rates fell. Inflation accelerated to over $10%$ .

Shifts in the MP Curve

In common parlance, the Federal Reserve is said to “tighten” monetary policy when it raises real interest rates, and to “ease” it when it lowers real interest rates. It is important, however, to distinguish between changes in monetary policy that shift the monetary policy curve, which we call autonomous changes, and changes driven by the Taylor principle, which are reflected as movements along the monetary policy curve. Such changes are called automatic adjustments to interest rates.

Central banks may make autonomous changes to monetary policy for various reasons. They may wish to change the inflation rate from its current value. For example, to lower inflation, they could increase $\overset{r}{ˉ}$ by one percentage point and so raise the real interest rate at any given inflation rate, an action that we will refer to as an autonomous tightening of monetary policy. This autonomous monetary tightening would shift the monetary policy curve upward by one percentage point from $M P_{1}$ to $M P_{2}$ in Figure 10.2, thereby causing the economy to contract and inflation to fall. Or, the banks may have information unrelated to inflation that suggests interest rates must be adjusted to achieve good economic outcomes. For example, if the economy is going into a recession, monetary policy makers will want to lower real interest rates at any given inflation rate, an autonomous easing of monetary policy, in order to stimulate the economy and prevent inflation from falling. This autonomous easing of monetary policy would result in a downward shift of the monetary policy curve, say by one percentage point, from $M P_{1}$ to $M P_{3}$ in Figure 10.2.

Movements Along the MP Curve Versus Shifts in the Curve

A stumbling block for many students in understanding the aggregate demand-aggregate supply $(A D / A S)$ framework that we will be studying in coming chapters is the distinction between shifts in the $M P$ curve versus movements along the $M P$ curve. Movements along the $M P$ curve—that is, movements from point A to B to C in Figure 10.1—should be viewed as a central bank’s normal response (also known as an endogenous response) of raising interest rates when inflation is rising. Thus we can think of a movement along the $M P$ curve as a rise in the interest rate as inflation rises, which is an automatic response of the central bank to a change in inflation. Such a response does not involve a shift in the $M P$ curve.

On the other hand, when the central bank raises interest rates at a given level of the inflation rate, that is, $\overset{r}{ˉ}$ rises in Equation 1, this is not an automatic response to higher inflation, but is rather an autonomous tightening of monetary policy that shifts the $M P$ curve up, from $M P_{1}$ to $M P_{2}$ in Figure 10.2.

The distinction between autonomous monetary policy changes and movements along the monetary policy curve is illustrated by the following two Policy and Practice cases, which outline the monetary policy actions taken by the Federal Reserve during the period from 2004 to 2006, and the actions taken in the fall of 2007, at the onset of the 2007-2009 financial crisis.

Policy and Practice: Movements Along the MP Curve – The Rise in the Federal Funds Rate Target, 2004-2006
Fears of deflation—i.e., fears that inflation could turn negative—led the Federal Reserve to commit to keeping the federal funds rate at the very low level of $1%$ from June of 2003 to June of 2004. However, with the economy growing rapidly, inflationary pressures began to rise, and the FOMC decided at its June 2004 meeting to increase the federal funds rate by $\frac{1}{4}$ of a percentage point. Furthermore, the FOMC made this process an automatic one, raising the federal funds rate by exactly the same amount at every subsequent FOMC meeting through June of 2006 (see Figure 10.3). These monetary policy actions were clearly movements along the MP curve, similar to the movements from point A to B to C in Figure 10.1.

Policy and Practice: Shifts in the MP Curve – Autonomous Monetary Easing at the Onset of the 2007-2009 Financial Crisis
When the financial crisis started in August 2007, inflation was rising and economic growth was quite strong. A movement along the MP curve should have suggested that the Fed continue to raise interest rates, but instead the Fed did the opposite: it began an aggressive lowering of the federal funds rate, despite the rising inflation rate, as shown in Figure 10.3. The Fed thus shifted the monetary policy curve downward, from $M P_{1}$ to $M P_{3}$ , as shown in Figure 10.2. The Fed pursued this autonomous monetary policy easing because the negative shock to the economy caused by the disruption to financial markets (more about this in Chapter 15) indicated that, despite the currently high inflation rates, the economy was likely to weaken in the near future, and the inflation rate would fall. Indeed, this is exactly what came to pass, with the economy going into recession in December 2007, and the inflation rate falling sharply after July 2008.

The Aggregate Demand Curve

We are now ready to derive the relationship between the inflation rate and aggregate output when the goods market is in equilibrium. This relationship is shown graphically by the aggregate demand curve. The MP curve we developed earlier in the chapter demonstrates how central banks respond to changes in inflation with changes in interest rates, in line with the Taylor principle. The IS curve we developed in Chapter 9 showed that changes in interest rates, in turn, affect equilibrium output. With these two curves, we can now link the quantity of aggregate output demanded with the inflation rate, given the public’s expectations of inflation and the stance of monetary policy. The aggregate demand curve is central to the aggregate demand and supply analysis we develop further in the next two chapters, which allows us to explain short-run fluctuations in both aggregate output and inflation.

Deriving the Aggregate Demand Curve Graphically

Using the hypothetical MP curve from Equation 2, we know that when the inflation rate rises from $1%$ to $2%$ to $3%$ , real interest rates rise from $1.5%$ to $2%$ to $2.5%$ . We plot these points in panel (a) of Figure 10.4 and connect them to form the MP curve. In panel (b), we graph the IS curve described in Equation 13 of Chapter 9 $(Y = 12 - r)$ . As the real interest rate rises from $1.5%$ to $2%$ to $2.5%$ , the equilibrium moves from point 1 to point 2 to point 3, and aggregate output falls from $10.5$ trillion to $10$ trillion to $9.5$ trillion. In other words, as real interest rates rise, consumption, investment, and net exports decline, leading to a decline in aggregate demand. Panel (c) demonstrates that as inflation rises from $1%$ to $2%$ to $3%$ , the equilibrium moves from point 1 to point 2 to point 3, and aggregate output falls from $10.5$ trillion to $10$ trillion to $9.5$ trillion.

The line that connects the three points in panel (c) is the aggregate demand curve, $A D$ , and it indicates the level of aggregate output corresponding to each of the three real interest rates consistent with equilibrium in the goods market for any given inflation rate. The aggregate demand curve has a downward slope, because a higher inflation rate leads the central bank to raise real interest rates, thereby lowering planned spending and hence lowering the level of equilibrium aggregate output.

By using some algebra (see the box, “Deriving the Aggregate Demand Curve Algebraically”), the $A D$ curve in Figure 10.4 can be written numerically as follows:

$Y = 11 - 0.5 π (3)$

Deriving the Aggregate Demand Curve Algebraically
To derive the numerical AD curve, we start by taking the numerical IS curve, Equation 13 from the preceding chapter:

$Y = 12 - r$

We then substitute in for $r$ from the numerical MP curve in Equation 2, $r = 1.0 + 0.5 π$ , to yield

$Y = 12 - (1.0 + 0.5 π) = (12 - 1) - 0.5 π = 11 - 0.5 π$

as in the text.

Similarly, we can derive a more general version of the AD curve using the algebraic version of the IS curve from Equation 12 in Chapter 9,

$Y = [\overline{C} + \overline{I} - d \overline{f} + \overline{G} + \overline{N X} - m p c \times \overline{T}] \times \frac{1}{1 - m p c} - \frac{c + d + x}{1 - m p c} \times r$

and then substitute in for $r$ from the algebraic MP curve in Equation 1, $r = \overline{r} + λπ$ , to yield the more general AD curve:

$Y = [\overline{C} + \overline{I} - d \overline{f} + \overline{G} + \overline{N X} - m p c \times \overline{T}] \times \frac{1}{1 - m p c} - \frac{c + d + x}{1 - m p c} \times (\overline{r} + λπ) (4)$

Factors That Shift the Aggregate Demand Curve

Movements along the aggregate demand curve describe how the equilibrium level of aggregate output changes as the inflation rate changes. When factors other than the inflation rate change, however, the aggregate demand curve can shift. We first review the factors that shift the IS curve, and then consider the factors that shift the $A D$ curve.

Shifts in the IS Curve. We saw in Chapter 9 that six factors cause the IS curve to shift. It turns out that these same factors cause the aggregate demand curve to shift as well:

Autonomous consumption expenditure
Autonomous investment spending
Government purchases
Taxes
Autonomous net exports
Financial frictions

We examine how changes in these factors lead to a shift in the aggregate demand curve in Figure 10.5.

Suppose that inflation is at $2.0%$ and so the MP curve shows that the real interest rate is at $2.0%$ in Figure 10.5 panel (a). The $I S_{1}$ curve in panel (b) then shows that the equilibrium level of output is at $\$ 10 $t r i l l i o na tp o in t$ A_1 $, w hi c h cor r es p o n d s t o an e q u i l ib r i u m l e v e l o f o u tp u t o f$ $10 $t r i l l i o na tp o in t$ A_1 $o n t h e$ AD_1$ curve in panel (c).

Now suppose there is a rise in, for example, government purchases by $\$ 1 $t r i l l i o n . P an e l (b) s h o w s t ha tw i t h t h e in f l a t i o n r a t e an d r e a l in t er es t b o t hh e l d co n s t an t a t$ 2.0% $, t h ee q u i l ib r i u mm o v es f r o m p o in t$ A_1 $t o p o in t$ A_2 $, w i t h o u tp u t r i s in g t o$ $12.5 $t r i l l i o n, so t h e I S c u r v es hi f t s t o t h er i g h t f r o m$ IS_1 $t o$ IS_2 $. T h er i se in o u tp u tt o$ $12.5 $t r i l l i o nm e an s t ha t, h o l d in g in f l a t i o nan d t h er e a l in t er es t r a t eco n s t an t, t h ee q u i l ib r i u min p an e l (c) a l so m o v es f r o m p o in t$ A_1 $t o p o in t$ A_2 $, an d so t h e A D c u r v e a l sos hi f t s t o t h er i g h t f r o m$ AD_1 $t o$ AD_2$.

Figure 10.5 shows that any factor that shifts the IS curve shifts the aggregate demand curve in the same direction. Therefore, “animal spirits” that encourage a rise in autonomous consumption spending or planned investment spending, a rise in government purchases, a fall in taxes, a fall in financial frictions, or an autonomous rise in net exports—all of which shift the IS curve to the right—will also shift the aggregate demand curve to the right. Conversely, a fall in autonomous consumption spending, a fall in planned investment spending, a fall in government purchases, a rise in taxes, a rise in financial frictions, or an autonomous fall in net exports will cause the aggregate demand curve to shift to the left.

Shifts in the MP Curve. We now examine what happens to the aggregate demand curve when the MP curve shifts. Suppose the Federal Reserve decides to autonomously tighten monetary policy by raising the real interest rate by one percentage point at any given level of the inflation rate because it is worried about the economy overheating. At an inflation rate of $2.0%$ , the real interest rate rises from $2.0%$ to $3.0%$ in Figure 10.6. The MP curve shifts up from $M P_{1}$ to $M P_{2}$ in panel (a). Panel (b) shows that when the inflation rate is at $2.0%$ , the higher interest rate results in the equilibrium moving from point $A_{1}$ to point $A_{2}$ on the IS curve, with output falling from $\$ 10 $t r i l l i o n t o$ $9 $t r i l l i o n . T h e l o w er o u tp u t o f$ $9 $t r i l l i o n occ u r s b ec a u se t h e hi g h er r e a l in t er es t r a t e l e a d s t o a d ec l in e in co n s u m pt i o n, in v es t m e n t, an d n e t e x p or t s, w hi c h l o w er s a g g r e g a t e d e man d . T h e l o w er o u tp u t o f$ $9 $t r i l l i o n t h e n d ecr e a ses t h ee q u i l ib r i u m o u tp u tl e v e l f r o m p o in t$ A_1 $t o p o in t$ A_2 $in p an e l (c), an d so t h e A D c u r v es hi f t s t o t h e l e f t f r o m$ AD_1 $t o$ AD_2$.

Our conclusion from Figure 10.6 is that an autonomous tightening of monetary policy—that is, a rise in the real interest rate at any given inflation rate—shifts the aggregate demand curve to the left. Similarly, an autonomous easing of monetary policy shifts the aggregate demand curve to the right.

We have now derived and analyzed the aggregate demand curve—an essential element in the aggregate demand and supply framework that we examine in the next two chapters. We will use the aggregate demand curve in this framework to determine both aggregate output and inflation, as well as to examine events that cause these variables to change.

The Money Market and Interest Rates

Earlier in the chapter, we gave only a very brief description of how the Federal Reserve sets the federal funds rate. At this point we will go into more detail, to describe how the Federal Reserve sets this nominal interest rate by analyzing the market for money using the liquidity preference framework, which determines the equilibrium nominal interest rate by equating the supply and demand for money.

Liquidity Preference and the Demand for Money

John Maynard Keynes developed a theory of money demand that he described as liquidity preference theory – hence the name of the framework – that carefully distinguishes between nominal quantities and real quantities. The nominal quantity of money is in terms of units of currency, like $\$ 50 $bi l l i o n . L i q u i d i t y p r e f er e n ce t h eor y, h o w e v er, e x amin es t h e d e man df or m o n ey in t er m so f t h er e a l g oo d s an d ser v i ces i t c anb u y . S o, f or e x am pl e, i f t h e p r i ce l e v e l d o u b l e d, t h es am e$ $50$ billion would buy only half as many goods. Keynes reasoned that when people decide how much money they want to hold (demand), they consider real money balances, the quantity of money in real terms.

In this model, demand for real money balances depends on real income, $Y$ , and the nominal interest rate, $i$ . We present Keynes’ liquidity preference theory in equation form as follows:

$M^{d} / P = L (i, Y) (5)$

We refer to Equation 5 as the liquidity preference function. The minus sign below $i$ means that as the nominal interest rate, $i$ rises, the demand for real money balances falls; the plus sign below $Y$ means that as income, $Y$ , rises, the demand for real money balances also rises. (See the chapter appendix for further discussion of Keynesian and other theories of money demand, as well as the empirical evidence on money demand.)

Why would the demand for real money balances have a negative relationship with the nominal interest rate $i$ ? The intuition for this relationship is provided by the concept of opportunity cost that you learned about in your principles of economics course. Recall that opportunity cost is the amount of income forgone (sacrificed) by holding money rather than alternative assets such as bonds. In Keynes’s analysis, money earns little, if any, interest, since it is held as currency or in checking accounts. The opportunity cost of holding money is $i$ , the nominal interest paid on bonds. As the interest rate $i$ rises, it becomes more costly to hold money instead of bonds – that is, the opportunity cost rises – and the quantity of money demanded falls. Note that the demand for real money balances is related to the nominal interest rate $i$ , while spending decisions are related to the real interest rate.

Real money balances are positively related to income for two reasons:

As income rises, households and firms conduct more transactions and so keep more money on hand to make purchases.
Higher incomes make households and firms wealthier, and the wealthy tend to hold larger quantities of all financial assets, including money.

Demand Curve for Money

The first step in our analysis is to use the liquidity preference function to obtain a demand curve that shows the relationship between the quantity demanded of real money balances and the interest rate when we hold all other economic variables, such as income, constant by treating their values as given. Because our analysis is for the short run, we will assume that prices are sticky and so the price level is fixed in the short run at $\overline{P}$ . Referring to Figure 10.7, suppose that for a given level of income, at an interest rate of $i_{1}$ , the quantity of real money balances that people want to hold is $M_{1} / \overline{P}$ , which we mark as point A. As the liquidity preference function shows, lower interest rates encourage firms and households to desire higher quantities of real money balances, since the opportunity cost of holding money falls. When the interest rate falls to $i^{*}$ , the quantity of real money balances demanded rises to $\overline{M} / \overline{P}$ , marked as point E. As the rate falls to $i_{2}$ and the opportunity cost of money declines further, the quantity of real money balances demanded rises again to $M_{2} / \overline{P}$ , at point D. Connecting these points—A, E, and D—creates the demand curve for real money balances, MD, in Figure 10.7. It slopes downward, since lower interest rates increase the quantity of real money balances demanded, all else being equal.

Supply Curve for Money

A central bank, such the Federal Reserve in the United States, can fix the money supply close to any level it desires by buying or selling government securities in open market operations, which we described in Chapter 5. Imagine that the Fed buys $\$ 1 $bi l l i o n o f g o v er nm e n t sec u r i t i es (b o n d s) f r o mbank s . T h e F e d p a y s f or t h e b o n d s b y d e p os i t in g$ $1$ billion into accounts that banks must maintain at the central bank. These deposits, which we refer to as reserves, represent increased liquidity in the banking system. Flush with additional liquidity from higher reserves, banks loan out more money to their customers, increasing bank deposits. Since these deposits are included in the money supply, as we saw in Chapter 5, the open market purchase leads to an increase in liquidity and the money supply. Similar reasoning leads to the conclusion that an open market sale of government securities leads to a decrease in liquidity and a decrease in the money supply.

If the Fed can fix the money supply at the level $\overline{M}$ , and the price level is also fixed in the short run at $\overline{P}$ , then the quantity of real money balances supplied, $M^{s} / P$ , is fixed at $\overline{M} / \overline{P}$ regardless of the interest rate. Thus the supply curve showing the quantity of real money balances supplied at each level of the nominal interest rate is a vertical line, shown in Figure 10.7 as the line $M S$ .

Equilibrium in the Money Market

As the supply and demand analysis you learned in your principles course tells us, market equilibrium occurs when the amount people are willing to buy (quantity demanded) at a given price equals the amount supplied (quantity supplied) at a given price. In the money market, equilibrium occurs when the quantity of real money balances demanded equals the quantity of real money balances supplied:

$\frac{M ^{d}}{P} = \frac{M ^{s}}{P} (6)$

In Figure 10.7, equilibrium occurs at point E (for “equilibrium”), where the demand and supply curves, $M D$ and $M S$ , intersect at an interest rate of $i^{*}$ . Figure 10.7 demonstrates the tendency of interest rates to return to the equilibrium rate $i^{*}$ when rates are too high or too low.

Response to Excess Supply. Once people have satisfied their demand for real money balances, they want to put any additional money into alternative assets like bonds or interest-bearing bank accounts. This condition of excess supply of money occurs when the interest rate is higher than the equilibrium level. At the rate $i_{1}$ in Figure 10.7, the quantity of real money balances supplied (point B) is greater than the quantity demanded (point A). As excess money pours into alternative assets, banks and bond issuers will realize they can pay lower rates of interest and still attract the same number of customers. As the downward arrow shows, the issuers of these assets will continue lowering interest rates to the equilibrium level $i^{*}$ , at which point the excess supply of real money balances is eliminated.

Response to Excess Demand. When people want to hold more money than is available, they will sell alternative assets like bonds and withdraw from interest-bearing bank accounts until they replenish their desired level of real money balances. This scenario of excess demand for money occurs when the interest rate is below the equilibrium interest rate $i^{*}$ . In Figure 10.7, when the rate is at $i_{2}$ , the quantity demanded at point D exceeds the quantity supplied at point C. People will pull money from bonds and bank accounts, inducing banks and bond issuers to raise the interest rates they offer to acquire new sources of funds. Rates will keep rising until they reach the equilibrium level $i^{*}$ , at which point the excess demand for money is eliminated.

Changes in the Equilibrium Interest Rate

We can now use the supply and demand framework for the money market to analyze why interest rates change. To avoid confusion, remember the distinction between movements along a demand (or supply) curve and shifts in a demand (or supply) curve. When the quantity demanded changes as a result of a change in the interest rate, there is a movement along the demand curve, such as the change in the quantity demanded when we move from point A to E to D in Figure 10.7. A shift in the demand (or supply) curve, by contrast, occurs when the quantity demanded (or supplied) changes at each given interest rate in response to a change in some other factor besides the interest rate. When a change to one of these factors shifts the supply or demand curve, there will be a new equilibrium value for the interest rate.

Factors That Shift the Demand Curve. The liquidity preference function in Equation 5 states that the nominal interest rate $i$ and real income $Y$ determine demand for real money balances. As we’ve just seen in Figure 10.7, changes in $i$ do not shift the demand curve; they instead lead to movement along the demand curve. A change in $Y$ does shift the demand curve, since the quantity of real money balances demanded changes at any given interest rate. Figure 10.8 illustrates this effect. When income rises, demand for money increases from point $A_{1}$ on the initial demand curve to point $A_{2}$ at the same level of interest rates. At another level of interest rates, demand for money increases from point $B_{1}$ on the initial demand curve to point $B_{2}$ . Continuing this reasoning for every point on the initial demand curve $M D_{1}$ , we can see that the demand curve shifts to the right from $M D_{1}$ to $M D_{2}$ .

With the supply of money balances set at $\overline{M} / \overline{P}$ and the supply curve stable at $M S$ , the rightward shift of the demand curve moves the new equilibrium to point 2 at the intersection of the $M D_{2}$ curve with the supply curve $M S$ . As you can see, the equilibrium interest rate rises from $i_{1}$ to $i_{2}$ . Thus, when income rises (holding other variables, such as the price level and the quantity of money, constant), interest rates will rise.

Factors That Shift the Supply Curve. The quantity supplied of real money balances, $M^{s} / P$ , can change, shifting the supply curve, for either of two reasons: 1) the quantity of money supplied by the Federal Reserve, $M^{s}$ , changes, or 2) the price level, $P$ , changes.

If the Federal Reserve increases the money supply from $\overline{M}_{1}$ to $\overline{M}_{2}$ , with the price level fixed at $\overline{P}$ , the quantity of real money balances supplied rises at any given interest rate. The supply curve then shifts to the right from $M S_{1}$ to $M S_{2}$ in panel (a) of Figure 10.9. The equilibrium moves from point 1 down to point 2, where the $M S_{2}$ supply curve intersects with the demand curve $M D$ , and the equilibrium interest rate falls from $i_{1}$ to $i_{2}$ . When the money supply increases (holding other economic variables constant), interest rates will decline.

If, holding the money supply constant, the price level rises from $\overline{P}_{1}$ to $\overline{P}_{2}$ , the quantity supplied of real money balances, $M^{s} / P$ , falls at any given interest rate. The supply curve then shifts to the left from $M S_{1}$ to $M S_{2}$ in panel (b) of Figure 10.9, and the equilibrium moves from point 1 up to point 2, with the equilibrium interest rate rising from $i_{1}$ to $i_{2}$ . When the price level rises (holding the supply of money and other variables constant), interest rates will rise.

Figure 10.9: Response to Shifts in the Supply Curve
In panel (a), when the money supply rises, the supply curve shifts to the right from $M S_{1}$ to $M S_{2}$ as a result of the change in quantity supplied at all interest rates. Equilibrium moves from point 1 to point 2 and the interest rate falls from $i_{1}$ to $i_{2}$ . In panel (b), when the price level rises, the supply curve shifts to the left from $M S_{1}$ to $M S_{2}$ as a result of the change in quantity supplied at all interest rates. Equilibrium moves from point 1 to point 2 and the interest rate rises from $i_{1}$ to $i_{2}$ .

Chapter 10 Appendix: The Demand for Money

In this appendix, we will journey deeper into the intricate world of money demand, exploring the pioneering ideas of John Maynard Keynes and subsequent developments, including portfolio theories. We’ll also cast a critical eye on the empirical evidence, examining how well these theories hold up in the real world.

Keynesian Theories of Money Demand: The Birth of Liquidity Preference

Imagine a world before modern economic thought, where the prevailing wisdom, the quantity theory, held that the speed at which money circulated (velocity) was more or less a constant. Then, in 1936, John Maynard Keynes, with his seminal work The General Theory of Employment, Interest and Money, threw a magnificent wrench into that assumption. He didn’t just tweak the existing view; he revolutionized it, introducing a concept he called liquidity preference. This theory proposed that people hold money for three distinct, yet interconnected, reasons: the transactions motive, the precautionary motive, and the speculative motive. Let’s unpack each of these.

The Transactions Motive: Money as a Medium of Exchange

At its core, the quantity theory recognized that we hold money because it’s the grease that makes the wheels of commerce turn. We need it to buy our morning coffee, pay rent, or purchase a new book. Keynes initially agreed with this intuitive idea, suggesting that the amount of money we hold for these everyday transactions is proportional to our income. The more we earn, the more we spend, and thus, the more money we need readily available.

However, even Keynes and subsequent economists recognized a crucial evolving factor: payment technology. Think about it: credit cards, digital wallets, instant electronic transfers – these are like magical shortcuts that allow us to make purchases without physically holding cash. As these technologies advance, our need to hold physical or even checkable deposits for transactions could decline significantly relative to our income. This has led to decades of speculation about a “cashless society,” an intriguing vision that, while slowly unfolding, hasn’t yet fully materialized. The allure of physical cash, it seems, holds a persistent charm!

The Precautionary Motive: Our Financial Safety Net

Life, as we know, is full of surprises! What if a fantastic opportunity suddenly arises, like that Wii entertainment system you’ve been eyeing, now on sale for a whopping 25% off? Or what if an unexpected expense crops up, like a car repair? Keynes brilliantly observed that people don’t just hold money for planned transactions; they also keep a certain amount as a cushion against the unforeseen. This is the precautionary motive.

Much like the transactions motive, Keynes argued that the desire for these “just in case” balances would also be proportional to income. The wealthier you are, or the higher your income, the larger your buffer against life’s little (or big) curveballs might be. It’s like having an emergency fund, but in a more liquid form.

The Speculative Motive: Betting on the Future of Interest Rates

Here’s where Keynes truly broke new ground. He introduced the idea that people also hold money as a store of wealth, driven by what he called the speculative motive. Think about it: money, in Keynes’s definition, often includes currency (which yields no interest) and checking accounts (which typically offer very low interest). What’s the cost of holding this non-interest-bearing asset? It’s the opportunity cost – the interest you could have earned if you had invested that money in an alternative, interest-bearing asset, like a bond. We represent this opportunity cost by the nominal interest rate on bonds, $i$ .

Keynes’s genius lay in recognizing this inverse relationship:

As the interest rate $i$ rises, the opportunity cost of holding money increases. Suddenly, holding idle cash feels more “expensive” because you’re foregoing more potential earnings from bonds.
Therefore, as $i$ rises, the quantity of money demanded for speculative purposes falls. People shift their wealth from non-interest-bearing money to higher-yielding bonds.

This is a crucial insight, suggesting that our demand for money is not just about transactions but also about our strategic decisions regarding wealth allocation.

Synthesizing the Three Motives: The Liquidity Preference Function

Bringing these three motives together, Keynes formulated what he called the liquidity preference function. It elegantly captures the idea that our demand for real money balances is influenced by both our income and the prevailing interest rates.

Let $M^{d}$ represent the nominal quantity of money demanded and $P$ represent the price level. The demand for real money balances, $\frac{M ^{d}}{P}$ , can be expressed as:

\frac{M ^{d}}{P} = L (i, Y) (1)

This equation tells us two fundamental things:

The demand for real money balances ( $\frac{M ^{d}}{P}$ ) is negatively related to the nominal interest rate ( $i$ ). As $i$ goes up, $L (i, Y)$ goes down.
The demand for real money balances ( $\frac{M ^{d}}{P}$ ) is positively related to real income ( $Y$ ). As $Y$ goes up, $L (i, Y)$ goes up.

Later Keynesian economists, including the brilliant Nobel laureate James Tobin, expanded on this. They showed that even the transactions and precautionary demands for money, not just the speculative demand, are also negatively related to interest rates. Why? Because holding even transaction balances ties up funds that could be earning interest elsewhere. If interest rates are high enough, people will find ways to economize on their cash holdings, even for daily needs.

An incredibly powerful implication of Keynesian theories is that velocity is not constant. If the demand for money is sensitive to interest rates, then velocity, the speed at which money circulates, must also fluctuate. Let’s see how:

We start with the liquidity preference function (1):

\frac{M ^{d}}{P} = L (i, Y)

To find velocity, recall the quantity theory identity: $M V = P Y$ . We can rewrite this as $V = \frac{P Y}{M}$ . To link this to our money demand function, we first express the reciprocal of the real money demand:

Step 1: Take the reciprocal of the liquidity preference function. \frac{P}{M ^{d}} = \frac{1}{L ( i , Y )}

Now, knowing that in money market equilibrium, the quantity of money demanded ( $M^{d}$ ) must equal the actual money supply ( $M$ ), we can substitute $M$ for $M^{d}$ :

Step 2: Substitute M for M^{d} assuming money market equilibrium. \frac{P}{M} = \frac{1}{L ( i , Y )}

To arrive at velocity, $V = \frac{P Y}{M}$ , we need to multiply both sides of our equation by real income $Y$ :

Step 3: Multiply both sides by real income Y to isolate velocity. (\frac{P}{M}) \cdot Y = (\frac{1}{L ( i , Y )}) \cdot Y

Rearranging the terms on the left side to match the definition of velocity:

Step 4: Rearrange the terms on the left side. \frac{P Y}{M} = \frac{Y}{L ( i , Y )}

Thus, we arrive at the expression for velocity:

V = \frac{P Y}{M} = \frac{Y}{L ( i , Y )} (2)

This equation reveals the dramatic shift in understanding. If the interest rate $i$ goes up, people want to hold less money (i.e., $L (i, Y)$ declines). If they’re holding less money for a given level of income and prices, it means each unit of money is being used more frequently – it’s circulating faster! Therefore, velocity ( $V$ ) rises.

Because interest rates are constantly fluctuating, Keynesian theories fundamentally challenged the classical quantity theory’s assertion that nominal income is primarily determined by movements in the money supply. Instead, they suggested a more dynamic, and perhaps less predictable, relationship.

Portfolio Theories of Money Demand: Money as Just One Asset Among Many

Expanding on Keynes’s insights, portfolio theories of money demand offer an even broader framework. They view an individual’s decision to hold money not in isolation, but as part of a larger strategy: how much of each asset do I want to hold in my overall financial portfolio? Money is simply one asset in a diverse collection that might also include bonds, stocks, real estate, and other forms of wealth.

The Four Pillars of Portfolio Theory

Portfolio theory provides a powerful lens through which to analyze the demand for any asset, including money. It identifies four key determinants:

Wealth: Imagine you suddenly become wealthier – perhaps you inherit a fortune or your investments soar. You now have more resources to distribute across various assets. Naturally, the demand for most assets, including money, tends to increase with wealth. You have a larger pie to slice.
Expected Return: This is all about opportunity. If Asset A is expected to yield a higher return than Asset B (after accounting for their current prices), you’ll likely want to hold more of Asset A, relative to Asset B. The demand for an asset is positively related to its expected return relative to other assets.
Risk: Most of us are inherently risk-averse. We prefer a sure thing over a gamble, given the same expected return. If an asset is perceived as riskier than alternatives, we’ll demand less of it. So, the demand for an asset is negatively correlated with its risk relative to other assets.
Liquidity: How quickly and easily can you transform an asset into spendable cash without losing significant value? That’s liquidity. Being able to access your funds instantly makes an asset more desirable. Thus, the demand for an asset is positively correlated with its liquidity relative to other assets.

Connecting Portfolio Theory to Keynesian Liquidity Preference

The beauty of portfolio theory is that it not only reinforces Keynes’s conclusions but also provides a deeper rationale. Let’s revisit the Keynesian determinants:

Income and Wealth: Portfolio theory readily explains why the demand for real money balances is positively related to income. Income and wealth tend to move hand-in-hand; higher income often means higher wealth. With more wealth, people have more resources to allocate, and a portion of that will naturally go into holding more money.
Interest Rates: How does portfolio theory explain the negative relationship between interest rates and money demand?
- When interest rates rise, the expected return on money (currency yields 0%, checking accounts very little) remains largely unchanged.
- However, the expected return on alternative assets, like bonds, increases.
- Therefore, money’s expected return relative to bonds goes down.
- Suddenly, bonds become more attractive, making money less desirable. The opportunity cost of holding money becomes higher, prompting a shift away from money and into bonds.

So, portfolio theory doesn’t just parrot Keynes; it gives us a richer understanding of the underlying economic choices.

Other Factors That Affect the Demand for Money: A Broader Horizon

Portfolio theory allows us to zoom out even further, revealing several other crucial factors that can influence our demand for money, beyond just income and interest rates:

Wealth (again, but with a nuance!): While portfolio theory says higher wealth means more money demand, this effect is often small when income is held constant. Why? Because as wealth grows substantially, people tend to diversify. They might put a small fraction into highly liquid money, but a larger portion will go into interest-bearing assets with similar risk and liquidity profiles, like money market mutual funds, which aren’t typically counted in narrow definitions of money like M1. Indeed, currency and checkable deposits are sometimes called “dominated assets” because you can often find other assets that pay higher returns and are just as safe.
Risk: Money is often considered one of the least risky assets in nominal terms. A dollar is always a dollar (unless there’s a revolution!). Bank deposits, especially with deposit insurance, are also very safe.
- Risk of other assets: However, risk is always relative. If the stock market suddenly becomes very volatile, money (being nominally safe) becomes relatively less risky compared to stocks. This increased relative safety can drive up the demand for money.
- Inflation risk: Here’s a twist! While money is safe in nominal terms, its real return (nominal return minus expected inflation) can become highly unpredictable if inflation itself is highly variable. If inflation risk rises, money becomes relatively more risky in real terms, making it less desirable. People might then shift to “inflation hedges” like Treasury Inflation Protected Securities (TIPS), gold, or real estate, whose real returns are less eroded by inflation variability.
Liquidity of other assets: What if other assets become more liquid? Over recent years, financial innovation has brought us money market mutual funds (which often allow check writing), and home equity lines of credit that can function almost like checking accounts. As these alternatives become increasingly liquid, the relative liquidity of traditional money (currency, checkable deposits) falls. This makes money less unique in its liquidity, leading to a decrease in the demand for it.

Summary: The Seven Influencers of Money Demand

Our journey through Keynesian and portfolio theories reveals a sophisticated landscape. The demand for money is not a simple function but a dynamic interplay of seven key factors. For quick reference, let’s consolidate them:

TABLE 10A1.1 FACTORS THAT DETERMINE THE DEMAND FOR MONEY

Variable	Change in Variable	Money Demand Response	Reason
Interest rates	$↑$	$↓$	Opportunity cost of money rises
Income	$↑$	$↑$	Higher transactions, higher wealth
Payment technology	$↑$	$↓$	Less need for money in transactions
Wealth	$↑$	$↑$	More resources to put into money (though small)
Risk of other assets	$↑$	$↑$	Money relatively less risky, more desirable
Inflation risk	$↑$	$↓$	Money relatively more risky (in real terms), less desirable
Liquidity of other assets	$↑$	$↓$	Money relatively less liquid, less desirable

Empirical Evidence on the Demand for Money: Theory Meets Reality

The real test of any theory is how well it explains the world around us. For money demand, two critical questions have dominated empirical research, questions that cut to the heart of whether the quantity of money truly is the primary determinant of aggregate spending:

Is the demand for money sensitive to changes in interest rates?
Is the money demand function stable over time?

Interest Rates and Money Demand: Is There a Floor?

Recall that if interest rates don’t affect money demand, then velocity is more likely to be constant and predictable. In that scenario, the quantity theory holds sway, suggesting a direct link between the money supply and aggregate spending. However, the more sensitive money demand is to interest rates, the more unpredictable velocity becomes, and the less clear that link appears.

There’s even an extreme scenario: the liquidity trap. This is a fascinating concept where the demand for money becomes ultrasensitive to interest rates. Imagine a situation where interest rates are so low (effectively zero) that people expect them to only go up. If rates go up, bond prices fall. So, instead of holding bonds, people would rather hold money, even at zero interest, to avoid capital losses on bonds and to seize future opportunities when rates rise. In a liquidity trap, a change in the money supply would have no effect on interest rates because people are willing to hold any amount of new money supplied without demanding a higher return. Consequently, conventional monetary policy loses its direct punch on aggregate spending.

What does the evidence say? For decades, when nominal interest rates were above zero, the data consistently showed that money demand is sensitive to interest rates, though not extremely so. There was little historical evidence for a true liquidity trap.

However, recent history, particularly in the aftermath of the 2008 financial crisis and during periods of very low inflation, has brought us face-to-face with a modified version of the liquidity trap. When nominal interest rates hit their effective lower bound of zero (or very close to it), they truly cannot go lower. In this unique situation, the demand for money does become effectively flat. People are indifferent between holding cash and holding assets that pay zero interest. Indeed, this is precisely the scenario the United States has experienced in recent years, prompting central banks like the Federal Reserve to resort to nonconventional monetary policies (like quantitative easing) to stimulate the economy, as their traditional interest-rate tools lose their efficacy.

Stability of Money Demand: A Shifting Landscape?

If the money demand function, like our Equation (1), is unstable—meaning it shifts unpredictably over time, as Keynes himself believed—then velocity will also be unpredictable. This instability undermines the tight link between the quantity of money and aggregate spending, further challenging the quantity theory. The stability of the money demand function is also a critical compass for central banks: Should they target interest rates or the money supply to guide monetary policy? An unstable money demand function implies that the money supply provides less reliable information about the future course of the economy.

Until the early 1970s, empirical evidence strongly supported a stable money demand function, providing a firm foundation for monetary policy based on money supply targets. However, everything changed after 1973. The rapid march of financial innovation – the introduction of new financial instruments and ways to make payments, blurring the lines of what “money” even means – led to substantial and unpredictable shifts in estimated money demand functions.

This instability has profound implications:

It calls into question the adequacy of our theoretical models and empirical analyses of money demand. The world became more complex than our models could easily capture.
For monetary policy, it meant that velocity became much harder to predict. If you can’t predict how fast money circulates, simply controlling the quantity of money doesn’t guarantee a predictable impact on the economy.
Consequently, monetary policymakers have increasingly shifted their focus. Instead of primarily targeting the money supply, they now tend to think of monetary policy in terms of setting interest rates, as reflected in concepts like the monetary policy curve.

In essence, the instability of money demand has led to a significant downgrading of the focus on the money supply in the actual conduct of monetary policy. While money remains a vital concept, its role as a precise policy lever has been challenged by the dynamism of financial markets and human behavior.

And so, we conclude our exploration of money demand. We’ve moved from simple transactions to complex portfolio choices, from stable relationships to unpredictable shifts. The demand for money is not a static concept but a living, breathing aspect of economic life, constantly evolving with technology, expectations, and risk. What questions does this raise for you? What further mysteries of money would you like to unravel? The journey of discovery is far from over!

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