### Learning Objectives

After you have actually review this area, you need to be able to answer the following concerns.

You are watching: Based on the quantity equation for the velocity of money, if m = 100, v = 3, and y = 200, then p =

What is the quantity concept of money? What is the classic dichotomy? According to the quantity theory, what determines the inflation price in the long run?

We start by presenting a frame to highlight the connect between money growth and inflation over lengthy durations of time.The structure complements our conversation of inflation in the brief run, had in Chapter 10 "Understanding the Fed". The quantity theory of moneyA partnership among money, output, and prices that is supplied to examine inflation. is a partnership among money, output, and also prices that is provided to study inflation. It is based upon an audit identity that deserve to be traced ago to the circular flow of income. Amongst various other points, the circular circulation tells us that

nominal spending = nominal gross residential product (GDP).

The “nominal spending” in this expression is brought out making use of money. While money consists of many kind of different assets, you can—as a metaphor—think of money as consisting completely of dollar bills. Nominal spfinishing in the economic situation would then take the form of these dollar bills going from perchild to perboy. If tbelow are not extremely many kind of dollar bills loved one to full nominal spending, then each bill need to be connected in a large number of transactions.

The velocity of moneyNominal GDP divided by the money supply. is a measure of just how quickly (on average) these dollar bills readjust hands in the economic climate. It is calculated by dividing nominal spfinishing by the money supply, which is the complete stock of money in the economy:

velocity of money=nominal spendingmoney supply=nominal GDPmoney supply.

If the velocity is high, then for each dollar, the economic climate produces a big amount of nominal GDP.

Using the reality that nominal GDP amounts to real GDP × the price level, we check out that

velocity of money=price level × real GDPmoney supply.

And if we multiply both sides of this equation by the money supply, we get the amount equationAn equation stating that the supply of money times the velocity of money equals nominal GDP., which is one of the most famed expressions in economics:

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

Let us view how these equations work by looking at 2005. In that year, nominal GDP was about \$13 trillion in the USA. The amount of money circulating in the economy was around \$6.5 trillion.In Chapter 9 "Money: A User’s Guide", we questioned the reality that there is no simple single definition of money. This number describes a number dubbed “M2,” which has money and also additionally deposits in financial institutions that are easily accessible for spending. If this money took the create of 6.5 trillion dollar bills altering hands for each transaction that we count in GDP, then, on average, each bill need to have actually changed hands twice throughout the year (13/6.5 = 2). So the velocity of money was 2 in 2005.

Toolkit: Section 16.16 "The Circular Flow of Income"

You have the right to review the circular flow of income in the toolkit.

## The Classical Dichotomy

So far, we have actually just written an interpretation. Tright here are two measures that take us from this definition to a theory of inflation. First we use the quantity equation to give us a theory of the price level. Then we research the growth rate of the price level, which is the inflation price.

In macrobusiness economics we are always cautious to distinguish between nominal and real variables:

Prior to the Great Depression, the leading see in business economics was an financial theory called the classical dichotomyThe dichotomy that real variables are identified independently of nominal variables.. Although this term sounds imposing, the concept is not. According to the classical dichotomy, genuine variables are determined independently of nominal variables. In other words, if you take the long list of variables used by macroeconomic experts and also create them in 2 columns—actual variables on the left and nominal variables on the right—then you deserve to number out all the real variables without needing to know any kind of of the nominal variables.

Following the Great Depression, financial experts turned rather to the aggregate expenditure modelThe connection between planned spfinishing and also output. to much better understand also the fluctuations of the accumulation economic situation. In that frame, the classic dichotomy does not hold. Economists still believe the classical dichotomy is crucial, but this day financial experts think that the timeless dichotomy just uses in the long run.

The classical dichotomy have the right to be checked out from the following thought experiment. Start via a instance in which the economic situation is in equilibrium, meaning that supply and also demand are in balance in all the various markets in the economic climate. The classical dichotomy tells us that this equilibrium determines loved one prices (the price of one great in regards to another), not absolute prices. We deserve to understand also this outcome by thinking around the industries for labor, products, and credit.

Figure 11.2 "Labor Market Equilibrium" presents the labor industry equilibrium. On the vertical axis is the real wage because households and firms make their labor supply and also demand decisions based upon actual, not nominal, weras. Households desire to know just how a lot added usage they deserve to obtain by working more, whereas firms want to know the expense of hiring more labor in terms of output. In both instances, it is the genuine wage that determines financial selections.

Figure 11.2 Labor Market Equilibrium Now think around the industries for goods and also services. The demand for any excellent or service depends on the genuine income of family members and the actual price of the good or service. We deserve to calculate real prices by correcting for inflation: that is, by separating each nominal price by the aggregate price level. Household demand also decisions depend on real variables, such as genuine earnings and family member prices.If you have actually studied the ethics of microeconomics, remember that the budacquire constraint of a family members relies on income divided by the price of one good and also on the price of one great in terms of an additional. If there are multiple items, the budacquire constraint can be figured out by separating revenue by the price level and by dividing all prices by the exact same price level. The exact same is true for the supply decisions of firms. We have currently said that labor demand also depends on only the genuine wage. Hence the supply of output additionally counts on the actual, not the nominal, wage. More mainly, if the firm provides various other inputs in the manufacturing process, what matters to the firm’s decision is the price of these inputs loved one to the price of its output, or—more generally—family member to the as a whole price level.If you have stupassed away the principles of microeconomics, the problem that price amounts to marginal cost is used to characterize the output decision of a firm. What matters then is the price of the input, family member to the price of output.

What around credit markets? The supply and also demand for credit depends on the real interemainder rate. This means that those providing credit think about the rerevolve they get on making loans in actual terms: although the loan may be proclaimed in regards to money, the supply of credit actually relies on the real return. The very same is true for borrowers: a loan contract might stipulate a nominal interest rate, however the actual interest price determines the price of borrowing in terms of goods. The supply of and demand also for crmodify is depicted in Figure 11.3 "Crmodify Market Equilibrium".

Figure 11.3 Credit Market Equilibrium The credit industry equilibrium occurs at a quantity of crmodify extended (loans) and a actual interemainder rate where the quantity provided is equal to the quantity demanded.

Toolkit: Section 16.1 "The Labor Market", Section 16.4 "The Credit (Loan) Market (Macro)", and also Section 16.5 "Correcting for Inflation"

You deserve to testimonial the labor industry and the credit industry, along with the underlying demand and supply curves, in the toolkit. You can likewise evaluation how to correct for inflation.

The classical dichotomy has actually a vital implication that we can examine via a comparative statics exercise. Recontact that in a comparative statics exercise we examine just how the equilibrium prices and output change as soon as something else, external of the market, alters. Here we ask: what happens to actual GDP and also the long-run price level as soon as the money supply changes? To find the answer, we start via the amount equation:

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

Previously we debated this equation as an identity—something that must be true by the interpretation of the variables. Now we rotate it right into a theory. To perform so, we make the assumption that the velocity of money is addressed. This implies that any type of increase in the money supply should rise the left-hand also side of the amount equation. When the left-hand side of the quantity equation rises, then, for any kind of given level of output, the price level is higher (equivalently, for any type of offered value of the price level, the level of real GDP is higher).

What then transforms once we change the money supply: output, prices, or both? Based on the timeless dichotomy, we know the answer. Real variables, such as real GDP and the velocity of money, stay continuous. A readjust in a nominal variable—the money supply—leads to changes in other nominal variables, but genuine variables execute not readjust. The fact that transforms in the money supply have no long-run impact on actual variables is dubbed the long-run neutrality of moneyThe reality that transforms in the money supply have actually no long-run result on genuine variables..

Toolkit: Section 16.8 "Comparative Statics"

You have the right to uncover more details on how to conduct comparative static exercises in the toolkit.

How does this check out of the impacts of monetary plan fit with the financial transmission mechanismA device explaining just how the actions of a central bank affect aggregate financial variables, in specific genuine GDP.?See Chapter 10 "Understanding the Fed". The financial transmission device describes that the monetary authority affects aggregate spfinishing by changing its targain interemainder rate.

The financial authority alters interemainder rates. Changes in interemainder rates affect spending on durables by firms and also family members. Changes in spending influence accumulation spfinishing through a multiplier result.

Remember that the monetary authority transforms interest prices through open-industry operations. If it desires to rise accumulation spfinishing, it does so by cutting interemainder rates, and also it cuts interest rates by purchasing government bonds via money. An interest price cut is equivalent to an increase in the supply of money, so the monetary transmission mechanism likewise teaches us that a boost in the supply of money leads to a boost in accumulation spfinishing.Tright here is one distinction, uncrucial here, which is that the financial transmission mechanism does not necessarily suppose that the velocity of money is constant. The monetary transmission device is useful when we want to understand the short-run results of monetary policy. When researching the lengthy run, it is less complicated to work via the quantity equation and to think about monetary policy in terms of the supply of money rather than interest rates.

Finally, a reminder: in the short run, the neutrality of money does not hold. This is bereason in the brief run we assume stickiness of nominal wages and/or prices. In this instance, transforms in the nominal money supply will certainly bring about alters in the genuine money supply. With sticky weras and/or prices, the classic dichotomy is broken.

## Long-Run Inflation

We now usage the amount equation to administer us with a concept of long-run inflation. To do so, we use the rules of development rates. One of these rules is as follows: if you have two variables, x and y, then the growth rate of the product (x × y) is the sum of the development rate of x and the growth rate of y. We deserve to use this to the quantity equation:

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

The left side of this equation is the product of two variables, the money supply and the velocity of money. The ideal side is also the product of two variables. So we obtain

development price of the money supply + development price of the velocity of money = inflation rate + development rate of output.

We have used the reality that the growth price of the price level is, by definition, the inflation rate.

We proceed to assume that the velocity of money is a consistent.In reality, the velocity of money could additionally grow over time as a result of developments in the financial sector. Saying that the velocity of money is consistent is the exact same as saying that its development price is zero. Using this truth and also rearvarying the equation, we uncover that the long-run inflation rate relies on the distinction between exactly how swiftly the money supply grows and how swiftly output grows:

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

The long-run expansion rate of output does not depfinish on the expansion price of the money supply or the inflation rate. We understand this because long-run output growth counts on the buildup of funding, labor, and technology. From our discussion of labor and credit markets, equilibrium in these industries is defined by real variables. Equilibrium in the labor market depends on the real wage and not on any type of nominal variables. Likewise, equilibrium in the crmodify market tells us that the level of investment does not depend on nominal variables. Due to the fact that the capital stock in any period is simply the build-up of previous investment, we know that the stock of resources is also independent of nominal variables.

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Because of this tright here is a direct connect in between the money supply growth rate and the inflation rate. The classical dichotomy teaches us that transforms in the money supply do not affect the velocity of money or the level of output. It follows that any kind of transforms in the growth price of the money supply will certainly present up one-for-one as alters in the inflation price. We say even more about financial policy later, but notification that there are prompt ramifications for the conduct of monetary policy:

In a flourishing economy, there are even more transactions occurring, so there is generally a require for even more money to facilitate those transactions. Therefore some development of the money supply is more than likely desirable to complement the increased earnings. If the monetary authorities want a stable price level—zero inflation—in the lengthy run, then they have to attempt to set the expansion price of the money supply equal to the (long-run) growth price of output. If the financial authorities desire a low level of inflation in the lengthy run, then they need to aim to have actually the money supply grow just a little little bit faster than the growth rate of output.

Keep in mind that this is simply a concept. The amount equation holds as an identification. But the presumption of constant velocity and the statement that long-run output growth is independent of money development are assertions based on a body of theory. We now look at exactly how well this theory fits the facts.

### Key Takeaways

The quantity theory of money states that the supply of money times the velocity of money equates to nominal GDP. According to the classical dichotomy, real variables, such as genuine GDP, usage, investment, the real wage, and the actual interest rate, are established independently of nominal variables, such as the money supply. Using the quantity equation together with the timeless dichotomy, in the lengthy run the inflation rate equates to the rate of money growth minus the expansion price of output.