Which Of The Following Rates Of Growth In The Money Supply

11.1 The Quantity Theory of Money

Learning Objectives

After yous have read this section, you should be able to answer the following questions.

1. What is the quantity theory of money?
2. What is the classical dichotomy?
3. According to the quantity theory, what determines the inflation rate in the long run?

We begin by presenting a framework to highlight the link between money growth and inflation over long periods of time.The framework complements our word of inflation in the short run, contained in Chapter ten "Agreement the Fed". The quantity theory of moneyA relationship amidst money, output, and prices that is used to study inflation. is a human relationship among money, output, and prices that is used to study aggrandizement. Information technology is based on an accounting identity that tin can be traced dorsum to the round menstruation of income. Among other things, the circular flow tells us that

nominal spending = nominal gdp (GDP).

The "nominal spending" in this expression is carried out using money. While money consists of many unlike assets, you can—as a metaphor—think of money as consisting entirely of dollar bills. Nominal spending in the economy would and then have the form of these dollar bills going from person to person. If in that location are not very many dollar bills relative to total nominal spending, and then each bill must exist involved in a large number of transactions.

The velocity of moneyNominal Gdp divided by the money supply. is a measure of how quickly (on average) these dollar bills change hands in the economy. It is calculated by dividing nominal spending by the money supply, which is the full stock of money in the economy:

$$\text{velocity of money}=\frac{\text{nominal spending}}{\text{coin supply}}=\frac{\text{nominal Gross domestic product}}{\text{coin supply}}\text{.}$$

If the velocity is high, then for each dollar, the economy produces a big corporeality of nominal GDP.

Using the fact that nominal GDP equals real GDP × the price level, we encounter that

$$\text{velocity of coin}=\frac{\text{toll level × real GDP}}{\text{money supply}}\text{.}$$

And if we multiply both sides of this equation by the money supply, we get the quantity equationAn equation stating that the supply of coin times the velocity of money equals nominal Gdp. , which is one of the almost famous expressions in economics:

coin supply × velocity of coin = price level × real Gross domestic product.

Allow us see how these equations piece of work by looking at 2005. In that yr, nominal GDP was nigh $13 trillion in the United states. The corporeality of money circulating in the economic system was almost $6.5 trillion.In Chapter ix "Money: A User'due south Guide", we discussed the fact that at that place is no simple single definition of money. This figure refers to a number chosen "M2," which includes currency and also deposits in banks that are readily accessible for spending. If this coin took the grade of 6.5 trillion dollar bills changing easily for each transaction that nosotros count in Gdp, then, on boilerplate, each bill must accept changed hands twice during the year (13/6.5 = 2). Then the velocity of money was 2 in 2005.

The Classical Dichotomy

So far, we have but written a definition. There are two steps that have us from this definition to a theory of inflation. Showtime we use the quantity equation to requite us a theory of the cost level. And then nosotros examine the growth rate of the price level, which is the inflation rate.

In macroeconomics we are e'er careful to distinguish between nominal and real variables:

• Nominal variablesA variable defined and measured in terms of coin. are divers and measured in terms of money. Examples include nominal Gdp, the nominal wage, the dollar price of a carton of milk, the price level, then forth. (Most nominal variables are measured in monetary units, but some are just numbers. For example, the nominal interest rate tells you lot how many dollars you lot will obtain adjacent yr for each dollar you invest in an nugget this twelvemonth. Information technology is thus measured as "dollars per dollar," so it is a number.)
• All variables not defined or measured in terms of money are real variablesA variable defined and measured in terms other than money, ofttimes in terms of existent Gross domestic product. . They include all the variables that nosotros divide by a toll alphabetize in order to right for the effects of inflation, such equally real GDP, real consumption, the capital stock, the real wage, so forth. For the sake of intuition, you can call back of these variables as being measured in terms of units of (base year) GDP (and so when we talk about real consumption, for instance, you can call back virtually the actual consumption of a packet of goods and services by a household). Real variables also include the supply of labor (measured in hours) and many variables that have no specific units but are merely numbers, such equally the velocity of money or the capital letter-to-output ratio of an economy.

Prior to the Bang-up Depression, the dominant view in economics was an economic theory chosen the classical dichotomyThe dichotomy that real variables are determined independently of nominal variables. . Although this term sounds imposing, the idea is not. According to the classical dichotomy, real variables are determined independently of nominal variables. In other words, if you have the long list of variables used by macroeconomists and write them in two columns—real variables on the left and nominal variables on the right—and then you can figure out all the existent variables without needing to know whatsoever of the nominal variables.

Post-obit the Bang-up Low, economists turned instead to the aggregate expenditure modelThe relationship betwixt planned spending and output. to better understand the fluctuations of the aggregate economy. In that framework, the classical dichotomy does not agree. Economists all the same believe the classical dichotomy is important, but today economists think that the classical dichotomy only applies in the long run.

The classical dichotomy can exist seen from the following thought experiment. Start with a state of affairs in which the economy is in equilibrium, meaning that supply and demand are in balance in all the dissimilar markets in the economy. The classical dichotomy tells us that this equilibrium determines relative prices (the price of one good in terms of some other), not absolute prices. We tin understand this consequence by thinking about the markets for labor, goods, and credit.

Effigy eleven.ii "Labor Market Equilibrium" presents the labor market equilibrium. On the vertical centrality is the existent wage considering households and firms brand their labor supply and demand decisions based on real, not nominal, wages. Households want to know how much boosted consumption they tin can get by working more than, whereas firms want to know the cost of hiring more labor in terms of output. In both cases, information technology is the existent wage that determines economical choices.

Figure 11.two Labor Market Equilibrium

Now retrieve nearly the markets for appurtenances and services. The demand for any practiced or service depends on the existent income of households and the real price of the practiced or service. Nosotros tin can summate existent prices by correcting for inflation: that is, by dividing each nominal price by the aggregate price level. Household demand decisions depend on real variables, such as existent income and relative prices.If you lot have studied the principles of microeconomics, retrieve that the budget constraint of a household depends on income divided past the toll of one skilful and on the price of i good in terms of another. If at that place are multiple appurtenances, the budget constraint tin be determined by dividing income by the toll level and by dividing all prices by the aforementioned toll level. The same is true for the supply decisions of firms. We take already argued that labor demand depends on only the real wage. Hence the supply of output as well depends on the existent, not the nominal, wage. More generally, if the firm uses other inputs in the production process, what matters to the firm's conclusion is the price of these inputs relative to the price of its output, or—more by and large—relative to the overall price level.If you have studied the principles of microeconomics, the condition that cost equals marginal cost is used to narrate the output decision of a house. What matters then is the price of the input, relative to the price of output.

What about credit markets? The supply and demand for credit depends on the real interest rate. This means that those supplying credit think virtually the return they receive on making loans in real terms: although the loan may be stated in terms of money, the supply of credit actually depends on the real return. The aforementioned is true for borrowers: a loan contract may stipulate a nominal interest rate, but the existent interest rate determines the toll of borrowing in terms of goods. The supply of and need for credit is illustrated in Figure 11.3 "Credit Market Equilibrium".

Figure 11.3 Credit Marketplace Equilibrium

The credit market equilibrium occurs at a quantity of credit extended (loans) and a existent interest rate where the quantity supplied is equal to the quantity demanded.

The classical dichotomy has a key implication that we can study through a comparative statics exercise. Recollect that in a comparative statics exercise we examine how the equilibrium prices and output change when something else, outside of the marketplace, changes. Here we ask: what happens to existent GDP and the long-run price level when the money supply changes? To find the answer, we begin with the quantity equation:

money supply × velocity of money = toll level × real GDP.

Previously nosotros discussed this equation equally an identity—something that must be true by the definition of the variables. At present we plow information technology into a theory. To do so, we make the assumption that the velocity of money is fixed. This means that whatever increase in the money supply must increase the left-hand side of the quantity equation. When the left-hand side of the quantity equation increases, then, for any given level of output, the toll level is college (equivalently, for any given value of the price level, the level of real GDP is higher).

What and then changes when we modify the money supply: output, prices, or both? Based on the classical dichotomy, we know the reply. Real variables, such as real GDP and the velocity of money, stay constant. A change in a nominal variable—the money supply—leads to changes in other nominal variables, simply real variables do non change. The fact that changes in the money supply accept no long-run effect on existent variables is chosen the long-run neutrality of moneyThe fact that changes in the money supply accept no long-run effect on real variables. .

How does this view of the furnishings of budgetary policy fit with the monetary transmission machineryA machinery explaining how the actions of a fundamental depository financial institution affect amass economic variables, in detail real Gdp. ?Come across Chapter 10 "Understanding the Fed". The monetary manual mechanism explains that the monetary authority affects aggregate spending past changing its target involvement rate.

• The budgetary authority changes interest rates.
• Changes in interest rates influence spending on durables past firms and households.
• Changes in spending influence aggregate spending through a multiplier effect.

Retrieve that the monetary authority changes involvement rates through open up-market operations. If it wants to heave aggregate spending, information technology does so by cutting interest rates, and it cuts interest rates past purchasing government bonds with money. An interest rate cutting is equivalent to an increment in the supply of money, so the monetary transmission mechanism besides teaches the states that an increment in the supply of coin leads to an increase in aggregate spending.There is one difference, unimportant here, which is that the monetary manual mechanism does not necessarily suppose that the velocity of money is abiding. The monetary transmission mechanism is useful when we want to understand the short-run furnishings of monetary policy. When studying the long run, it is easier to work with the quantity equation and to call up most budgetary policy in terms of the supply of money rather than involvement rates.

Finally, a reminder: in the short run, the neutrality of money does not concord. This is because in the brusk run nosotros assume stickiness of nominal wages and/or prices. In this case, changes in the nominal money supply will lead to changes in the real money supply. With sticky wages and/or prices, the classical dichotomy is cleaved.

Long-Run Inflation

We now use the quantity equation to provide us with a theory of long-run inflation. To exercise so, we employ the rules of growth rates. One of these rules is as follows: if yous have two variables, x and y, and then the growth rate of the product (x × y) is the sum of the growth rate of x and the growth charge per unit of y. Nosotros tin can apply this to the quantity equation:

money supply × velocity of money = price level × real GDP.

The left side of this equation is the production of two variables, the money supply and the velocity of coin. The right side is as well the production of two variables. So we obtain

growth rate of the money supply + growth charge per unit of the velocity of money = inflation charge per unit + growth charge per unit of output.

We take used the fact that the growth rate of the price level is, past definition, the inflation rate.

Nosotros continue to presume that the velocity of money is a abiding.In fact, the velocity of money might as well grow over time as a issue of developments in the financial sector. Saying that the velocity of coin is abiding is the same as saying that its growth charge per unit is zero. Using this fact and rearranging the equation, we observe that the long-run inflation rate depends on the difference between how rapidly the money supply grows and how rapidly output grows:

inflation rate = growth rate of money supply − growth rate of output.

The long-run growth charge per unit of output does not depend on the growth charge per unit of the money supply or the inflation rate. Nosotros know this because long-run output growth depends on the aggregating of capital, labor, and technology. From our word of labor and credit markets, equilibrium in these markets is described past real variables. Equilibrium in the labor market depends on the real wage and not on any nominal variables. Likewise, equilibrium in the credit market tells u.s. that the level of investment does not depend on nominal variables. Since the capital stock in any period is simply the accumulation of past investment, we know that the stock of capital is besides independent of nominal variables.

Therefore at that place is a direct link between the coin supply growth rate and the aggrandizement rate. The classical dichotomy teaches us that changes in the money supply do non affect the velocity of money or the level of output. It follows that any changes in the growth rate of the money supply will prove up one-for-i as changes in the aggrandizement charge per unit. Nosotros say more than almost monetary policy later, simply detect that there are immediate implications for the bear of monetary policy:

• In a growing economic system, there are more transactions taking place, then there is typically a need for more money to facilitate those transactions. Thus some growth of the money supply is probably desirable to match the increased income.
• If the monetary authorities want a stable price level—zilch inflation—in the long run, then they should try to set the growth charge per unit of the money supply equal to the (long-run) growth rate of output.
• If the budgetary authorities want a low level of inflation in the long run, then they should aim to take the money supply grow just a little fleck faster than the growth rate of output.

Keep in heed that this is simply a theory. The quantity equation holds every bit an identity. But the assumption of constant velocity and the statement that long-run output growth is independent of money growth are assertions based on a body of theory. We now expect at how well this theory fits the facts.

Key Takeaways

1. The quantity theory of coin states that the supply of money times the velocity of money equals nominal GDP.
2. According to the classical dichotomy, existent variables, such as real GDP, consumption, investment, the real wage, and the existent interest rate, are determined independently of nominal variables, such every bit the coin supply.
3. Using the quantity equation along with the classical dichotomy, in the long run the aggrandizement rate equals the rate of money growth minus the growth charge per unit of output.

Checking Your Agreement

1. Is the real wage a nominal variable? What about the coin supply?
2. If velocity of money decreases past 2 percent and the money supply does not grow, tin yous say what will happen to nominal Gdp growth? Can yous say what will happen to inflation?

Source: https://saylordotorg.github.io/text_macroeconomics-theory-through-applications/s15-01-the-quantity-theory-of-money.html

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