CHAPTER 1

Monetary Policy

In Volume I of this book, we ignored the fact that people have a demand for money as well as for the goods that they use their money to buy. But people want to hold money to pay for their day-to-day transactions, and holding money incurs an opportunity cost measured by the return people could receive by using their money to buy interest-earning assets. Let’s call these assets “bonds.”

We can begin our discussion of the demand for money with an identity:

where M is the stock of money, V is the turnover rate of money, P is the price level, and Y is real income. In a fiat money system, money, having no intrinsic value, depends for its value entirely on its scarcity, and it is the government that controls the amount of money in existence. In the United States, the Federal Reserve System controls the money supply through purchases and sales of financial instruments, originally short-term government securities, and nowadays, long-term private securities, for example, mortgages as well.

If Y equals $2 million, P equals 1, and M equals $1 million, then V must equal 2, which means that every dollar is spent twice, on average, in the course of a year’s production. Under the principles developed so far in this book, V is some fixed amount and Y is determined by the flow of resources into production and is independent of the level of M. Thus a given percentage change in M would bring about an equal percentage change in P:

or

According to the reasoning of Volume I, Chapter 5, if the real interest rate r is 5% and if the price level is growing at 4%, then the nominal interest rate R will be 9%. From that chapter, we know that there will be no effect on the real interest rate due to changes in the inflation rate as long as the perceptions of the suppliers of financial capital are aligned with the perceptions of investors and as long as both are aligned with the actual inflation rate. Thus, there will be no effect on real economic activity because of a rise or fall in the inflation rate or, therefore, in the nominal interest rate.

But that analysis does not take into account the fact that people have a demand for money and that their demand for money varies with the cost of holding it. Money is the most liquid of all assets. It also offers a zero yield from holding it. Because money pays no interest, the opportunity cost of holding it is R, the nominal interest rate, which, in equilibrium, equals the real interest rate plus the rate of inflation.

People have a choice between holding their financial assets in the form of cash and holding them in the form of assets that yield a return, R. People will want to hold more money the greater their real income and the lower the nominal return on income-earning assets.

Our Eve in the earlier chapter held only income-earning assets. But she will also want to hold some of her assets in the form of cash. The question is what determines the utility-maximizing mix of cash and income-earning assets.

In the forgoing example, nominal income was $2 million, and people held half of it, $1 million, in cash. Now let’s modify our assumption, noted earlier, that V is fixed in value. Let k = 1/V, where k is the fraction of their nominal income that people want to hold in the form of cash. We can specify a demand equation for money, in which the demand for money varies positively with k, P, and Y:

and, in equilibrium,

In equilibrium, the supply of money equals the demand for money, and the demand for money equals kPY. The supply of money, we assume, is determined by the Federal Reserve. The question is how k, P, and Y adjust to bring the demand for money into line with the supply of money, given that the Fed determines the supply of money.

Let’s assume, for now, that Y is fixed. That means we are left with the need to consider how P and k adjust to changes in M. In Volume I, Chapter 5, we showed how the nominal interest rate would adjust to changes in expected inflation, but we omitted any consideration of the determinants of expected inflation. Here we provide for a theory of expected inflation by writing:

where is expected inflation and is the growth of the money supply. In Table 1.1, we assume that the nominal interest rate, R, equals the sum of the real rate and expected inflation, per the earlier chapter:

In Table 1.1, the money supply grows by 5% annually in years 2 through 4 and then grows by 6% from year 5 on (column 2). As a consequence of the increased growth of M, expected inflation rises from 5 to 6% (column 4), and the nominal interest rises from 10 to 11% (column 6). This induces people to hold a larger share of their assets as bonds and a smaller share as cash. Thus, k falls (we assume) from 50 to 40% (column 9), which is to say that velocity rises from 2 to 2.5. The fall in k, combined with the resulting spike in inflation, brings the demand for money into line with the supply of money (column 10).

So far, we don’t allow for any “real” effects (real income remains fixed at $2 million). Money appears to be “neutral” with respect to the “real” economy, which implies that real income, Y, remains fixed.

Yet, there is a real effect resulting from the fact that the decision to hold a smaller fraction of an investment portfolio in cash will impose a real cost. That cost is miniscule in comparison to GDP, but it is a cost nevertheless. To see why it is a cost, consider a person who is paid $10,000 on the first of every month. If the nominal interest rate were zero, it would cost nothing to keep the whole amount in cash. Over the course of a month, the person’s average cash balance would be $5,000. His k would equal 0.5 and the velocity of money would be 2.

Table 1.1 Increase in the growth of M causing a rise in R

But suppose that the nominal interest rate rises to 5%. Now the cost of keeping money in cash is the 5% return that the person would receive by putting money in bonds. The individual might then decide to keep only half of the $10,000 in cash for the first two weeks of the month, putting the other half in bonds for that two-week period. After two weeks, the individual would then convert the bonds he held for the first two weeks into cash to finance his remaining expenditures for that month. His cash balance would then equal only $2,500 (= 0.5 × 0.5 × $10,000), on average, over the course of the month. His velocity would equal 4.

To continue the example, suppose that the nominal interest rate rose to 10%. The individual might decide to keep only 1/4 of his monthly paycheck in cash, leaving the rest in bonds. He would hold only $1,250 (= 0.5 × 0.5 × 0.5 × $10,000) in cash, on average over the course of the month. His k would fall from 1/4 to 1/8 and his V would rise from 4 to 8.

In this last example, the individual puts 3/4 of his paycheck in bonds when he is paid on the first of the month, leaving 1/4 (= $2,500) in his checking account. He spends that amount by the end of the first week and then converts another $2,500 from bonds into cash in order to pay for his second week of expenses, leaving $5,000 in bonds. This continues until the end of the fourth week when he has converted all of his bonds into cash. See Figure 1.1.

What this tells us is that a rising nominal interest rate induces the individual to go back and forth from bonds to cash very frequently, an exercise that comes at a cost in terms of the individual’s time and any fees he has to pay to go from cash to bonds and again into cash. Yet there is no compensating rise in the real return if the real interest rate remains unchanged, that is, if the rise in R results only from rising inflation. Essentially, what the individual does is move in and out of cash more frequently in order to protect himself from rising inflation.

This is what Table 1.1 illustrates: the fact that if prices are driven by expectations of monetary growth, the only effect of an increase in the growth of the money supply is to raise the rate of inflation and the nominal interest rate, and to impose costs in the form of cash management costs. Expected inflation varies with the observed growth in M. Actual inflation, recorded in column (12) equals the percentage change in the price level, P. P, in turn, equals MV/Y.

Figure 1.1 Example of average cash holdings

Now let’s consider another possibility: that P would remain fixed as M rose. In Table 1.2, we consider a one-time rise in M, from $1 million to $1.050 million. Because both P and k are assumed to be fixed, Y must rise to bring the demand for money into line with the supply of money.

Another possibility is that the rise in M would cause a fall in R, and therefore r, since prices are assumed to be constant (see Figure 1.2). There we show the demand for money as inversely related to the nominal interest rate. People use their extra cash in part to buy bonds, driving up the price of bonds. Bond yields fall and, with them, R (which is a composite of bond yields).¹ The fall in R causes people to feel comfortable holding a larger share of their portfolios and of the incomes in cash. Thus, k rises, and V falls.

The fall in R is important, insofar as, with prices fixed, r must equal R and will also, therefore, fall. As we saw in Volume I, Chapter 5, a fall in r reduces the cost of capital, leading to an increase in the capital stock and positive net investment. With the fall in the cost of capital and rise in the capital stock, Y also rises. Tables 1.2 and 1.3 illustrate how the goal of increasing Y motivates the adoption of an expansive monetary policy. In Table 1.2, the increase in the money supply works directly on Y without any change in R. In Table 1.3, the increase in the money supply works on Y through the resulting reduction in r and rise in the capital stock.

Table 1.2 Increase in M causing a rise in Y

Figure 1.2 Rise in the money supply

To summarize: If the money supply rises, as in these examples, people will find themselves involuntarily holding more money than they wish to hold, given k, P, and Y. In the scenario explored in Table 1.1, where Y is assumed to be constant, people try to spend down their new cash holdings and, in the process, drive up the price level. The resulting rise in R induces people to hold a smaller share of their assets in the form of cash, with some resulting increase in the cost of asset management. As k falls, V rises.

If P and k are fixed (Table 1.2), then Y must rise to bring people’s demand for cash balances into line with supply. Alternatively (or in addition), R might fall, causing k to rise and through the resulting fall in r, causing Y to rise. Tables 1.2 and 1.3 are descriptive.

Finally, it is necessary to consider an autonomous rise in k, which is motivated by perhaps a precaution against an expected fall in Y. Table 1.4 illustrates this possibility. There M and Y are assumed to be constant, so that the effect of the rise in k is a fall in P. Table 1.5 assumes that P is fixed, so that the impact is solely on Y. In this scenario, a precautionary rise in k ends up being a self-fulfilling prophesy.

Table 1.3 Increase in M causing a fall in R

Table 1.4 Increase in k and a fall in P

Table 1.5 Increase in k and a fall in Y

Table 1.6 Increase in M and no change in PY

Table 1.6 illustrates still another possibility: that the Fed will increase M to no avail, since k will rise and velocity will fall, thus leaving real GDP unchanged. The rise in M just brings about a rise in k.

When M falls, r, P, Y, and k move in a direction the opposite of that illustrated in Tables 1.1 through 1.5. When k falls, the results are the opposite of the ones provided in Tables 1.5 and 1.6.

Let’s see how monetary policy has been conducted in recent years. From Figure 1.3, we see that the money supply, defined as “M1” (currency and demand deposits), rose modestly (at an annual rate of 5%) from 1980 to 2009. Then it rose by 22% from the fourth quarter of 2007 to the third quarter of 2009. After rising sharply for several years, velocity fell by 18% from the fourth quarter of 2007 to the third quarter of 2009 (see Figure 1.4). For the same period, the federal funds rate was kept near zero. From this evidence, it is possible to conclude that Federal Reserve policy was only weakly expansive over the course of the Great Contraction.

Figure 1.3 M1, 1980–2017

Source: Board of Governors of the Federal Reserve System.

Figure 1.4 Velocity of M1, 1980–2017

Source: Board of Governors of the Federal Reserve System.

APPENDIX A

Implications of Tax Policy for Monetary Policy

Any change in tax policy has implications for monetary policy. If a cut in the corporate income tax, for example, leads to an increase in real GDP, the Federal Reserve has to consider whether it should accommodate the resulting fall in prices or expand the money supply so as to keep prices from falling.

A more complex example would involve the substitution of a tax on consumption for the existing federal income tax. Suppose, in considering this possibility that all income is labor income and that all production goes for either government or personal consumption. Suppose also that all production is pizza production, that pizza sells for $1.00 a slice, and that pizza producers make 1,000 slices. Government collects taxes through an income tax of 20%. So we have

Consumers receive $1,000 in before-tax income but must pay $200 to the government in taxes, which the government uses to buy 200 slices of pizza, leaving the remaining 800 for individual consumption. Let’s also put some values to the equation of exchange:

If the money supply is $500, velocity must be 2, so that the left-hand side of (A1.2) matches up with the right-hand side.

Finally, we assume that workers are paid $10 per hour and that they produce 10 slices of pizza for every hour worked. Thus labor income is

so that pizza workers work 100 hours to produce 1,000 slices of pizza. Each worker’s after-tax wage rate is $8 per hour.

Now suppose the government decides to replace the income tax with a consumption tax and with the intention of raising enough revenue to continue buying its 200 slices of pizza. The government must impose a tax on consumption that permits it to continue diverting 200 pizza slices from individual to government consumption. But what happens to the price of pizza?

Almost everyone would say that the price of pizza will rise by the amount of the sales tax. So if the government wants to be able to buy 20% of the pizza output, the sales tax rate must be 25%. The price of pizza before the sales tax is imposed remains at $1.00. With a 25% sales tax, the price rises to $1.25. Total wages remain at $1,000 and now workers get to put that entire $1,000 in their pockets. But with nominal output now equal to $1,250, that $1,000 buys only 800 ((=$1,000/$1,250) × 1,000) slices, just as before. Government collects $250 (= 0.20 × $1,250) in tax revenue, with which it buys the remaining 200 slices.

Because PY now equals $1,250, MV must also equal $1,250. And, if V is constant, it can happen only if government expands M by 25% to $625.

Suppose, alternatively, that government does not expand M at all. Then, because V and Y are assumed to remain constant, price can’t change either.

Thus, something must happen to wages. Specifically, the wage rate has to fall by 20% to $8 per hour. Recall that there is no income tax now, so hourly take-home pay would also equal $8, just as it did before, under the income tax. Now also the price of pizza, exclusive of the sales tax, falls to $0.80. (If workers receive only $8 per hour to make 10 slices of pizza, the firm can cover the costs of producing those 10 slices by collecting only $0.80 for every slice sold.) If a 25% sales tax is imposed on pizza, the price to the consumer will remain at $1.00 (= 1.25 × $.80). Given that their wages now equal $800, workers can, once again, buy 800 of the 1,000 slices produced. Government collects $.20 in revenue for each slice sold and, given that 1,000 slices are sold, it collects $200 in revenue that it uses to buy 200 slices.

So we have two scenarios: (1) Prices rise by 25%, as enabled by a 25% increase in the money supply. Or (2) prices remain constant, as made necessary by the fact that the money supply is kept unchanged, in which event wages fall by 20%. More generally, the extent to which the switch from an income to a sales tax results in a rise in the price level depends on the degree to which the Fed wants to “accommodate” the imposition of the sales tax by permitting the money supply to rise. The greater the increase in the money supply, the greater the increase in prices and the smaller the decrease in wages that must take place in order to keep real output from changing. However it turns out, government consumes the same amount of pizza as it did under the income tax.

It is necessary to go into this detail in that one approach to tax reform that gets a lot of attention is to junk existing federal taxes in favor of a national sales tax. It is useful to consider the possible implementation of this idea because it presents an example of the interdependence between monetary policy and tax policy, or more generally, between monetary policy and any policy change that would give rise to large-scale adjustments in prices and/or wages.

In a sense, in the forgoing example, the Fed has to choose between two, equally problematical ways to adjust to the policy change considered here. If it accommodates the change by permitting prices to rise, it will reduce the real value of government bonds held by the public. If it does not accommodate the change, then it will be necessary for workers to accept nominal wage cuts, which they might resist (to their own detriment).

The adoption of a flat tax softens, but does not eliminate, this dilemma. Because a flat tax necessitates an increase in the tax rate on labor income, it would push down after-tax nominal wages unless the Fed accommodated by expanding M and letting the resulting rise in prices bring about the necessary reduction in real after-tax wages.

The lesson for the Fed is that if, for example, it aims to keep the inflation rate at a certain level, then it has to consider how changes in tax policy and in other policies require it to take into account how accommodation of those policy changes can affect prices.

¹ Suppose a borrower sells a bond for $1,000 that will be redeemed for $1,050 a year later. The yield is 5%. But suppose the bond rises in price to $1,025. A person who buys the bond for $1,050 now gets a yield of 2.4% (= 1,050/1,025 – 1) when the bond matures.