### Learning Objectives

After you have read this section, girlfriend should have the ability to answer the adhering to questions.

You are watching: Suppose that velocity rises while the money supply stays the same. it follows that

What is the quantity theory of money? What is the classical dichotomy? according to the quantity theory, what determines the inflation rate in the lengthy run?

We start by presenting a framework to to mark the link in between money growth and also inflation over lengthy periods the time.The framework complements our discussion of inflation in the quick run, consisted of in thing 10 "Understanding the Fed". The amount theory that moneyA relationship amongst money, output, and prices the is provided to examine inflation. Is a relationship amongst money, output, and also prices the is provided to research inflation. That is based on an audit identity that deserve to be traced earlier to the circular circulation of income. Among other things, the circular circulation tells united state that

nominal spending = nominal gross domestic product (GDP).

The “nominal spending” in this expression is lugged out using money. If money consists of numerous different assets, friend can—as a metaphor—think that money as consisting completely of dollar bills. In the name spending in the economic climate would then take the type of this dollar receipt going from human being to person. If there are not really many disagreement bills family member to complete nominal spending, then each bill have to be affiliated in a big number the transactions.

The velocity the moneyNominal GDP divided by the money supply. Is a measure up of just how rapidly (on average) this dollar bills change hands in the economy. The is calculated by separating nominal spending by the money supply, i m sorry is the total stock that money in the economy:

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

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

Using the fact that nominal GDP equates to real GDP × the price level, we see that

velocity of money=price level × real GDPmoney supply.

And if us multiply both political parties of this equation by the money supply, we gain the amount equationAn equation stating that the supply of money time the velocity of money amounts to nominal GDP., which is one of the most famed expressions in economics:

money it is provided × velocity the money = price level × genuine GDP.

Let us see just how these equations occupational by looking at 2005. In the year, nominal GDP was about \$13 trillion in the unified States. The amount of money circulating in the economic climate was around \$6.5 trillion.In chapter 9 "Money: A User’s Guide", we disputed the truth that there is no an easy single an interpretation of money. This number refers come a number dubbed “M2,” which consists of currency and likewise deposits in financial institutions that room readily obtainable for spending. If this money take it the form of 6.5 sunshine dollar bills an altering hands because that each transaction that us count in GDP, then, ~ above average, each bill need to have readjusted hands twice throughout the year (13/6.5 = 2). Therefore the velocity of money was 2 in 2005.

Toolkit: ar 16.16 "The Circular circulation of Income"

You deserve to review the circular circulation of income in the toolkit.

## The timeless Dichotomy

So far, we have just written a definition. There are two measures that take united state from this an interpretation to a concept of inflation. First we usage the amount equation to provide us a theory of the price level. Climate we examine the growth rate the the price level, i beg your pardon is the inflation rate.

In macroeconomics we are always careful come distinguish between nominal and also real variables:

Prior to the great Depression, the leading view in economics was an economic theory referred to as the classical dichotomyThe dichotomy that genuine variables are figured out independently of nominal variables.. Although this term sounds imposing, the idea is not. According to the timeless dichotomy, actual variables are determined independently of in the name of variables. In other words, if you take the lengthy list of variables offered by macroeconomists and also write castle in two columns—real variables ~ above the left and also nominal variables ~ above the right—then you can number out all the actual variables there is no needing to know any of the in the name variables.

Following the good Depression, financial experts turned rather to the accumulation expenditure modelThe relationship in between planned spending and also output. To far better understand the fluctuations of the aggregate economy. In that framework, the timeless dichotomy does not hold. Economic experts still think the classic dichotomy is important, yet today economic experts think that the classical dichotomy only uses in the long run.

The classic dichotomy can be checked out from the complying with thought experiment. Begin with a instance in i beg your pardon the economic climate is in equilibrium, an interpretation that supply and demand are in balance in all the different markets in the economy. The classic dichotomy tells us that this equilibrium identify relative prices (the price the one good in regards to another), not absolute prices. We deserve to understand this result by thinking about the sectors for labor, goods, and also credit.

Figure 11.2 "Labor industry Equilibrium" presents the labor sector equilibrium. ~ above the upright axis is the real wage due to the fact that households and also firms do their labor supply and demand decisions based on real, no nominal, wages. Family members want come know just how much added consumption they can obtain by functioning more, vice versa, firms want to recognize the expense of hiring much more labor in terms of output. In both cases, it is the genuine wage that determines financial choices.

Figure 11.2 Labor market Equilibrium

Now think about the sectors for goods and also services. The need for any an excellent or business depends ~ above the real earnings of households and also the real price of the good or service. We can calculate genuine prices through correcting for inflation: the is, by splitting each in the name price by the aggregate price level. Household demand decisions depend on actual variables, together as real income and relative prices.If you have actually studied the values of microeconomics, remember the the budget constraint the a family members depends on income separated by the price that one an excellent and on the price the one good in terms of another. If there are multiple goods, the budget plan constraint deserve to be determined by separating income by the price level and by separating all prices by the same price level. The exact same is true because that the supply decisions the firms. Us have currently argued the labor demand depends on just the genuine wage. Therefore the it is provided of output likewise depends on the real, not the nominal, wage. Much more generally, if the firm provides other input in the production process, what matters to the this firm decision is the price of these inputs family member to the price of its output, or—more generally—relative to the overall price level.If you have studied the ethics of microeconomics, the condition that price amounts to marginal cost is supplied to characterize the output decision the a firm. What matters then is the price of the input, relative to the price of output.

What about credit markets? The supply and also demand for credit relies on the genuine interest rate. This means that those supplying credit think around the return they receive on making loans in genuine terms: return the loan might be proclaimed in terms of money, the it is provided of credit actually relies on the actual return. The same is true because that borrowers: a loan contract may stipulate a nominal attention rate, but the actual interest price determines the cost of borrowing in terms of goods. The it is provided of and demand for credit is portrayed in number 11.3 "Credit sector Equilibrium".

Figure 11.3 Credit market Equilibrium

The credit market equilibrium wake up at a quantity of credit prolonged (loans) and also a genuine interest price where the quantity supplied is equal to the quantity demanded.

Toolkit: section 16.1 "The labor Market", ar 16.4 "The credit (Loan) sector (Macro)", and Section 16.5 "Correcting because that Inflation"

You deserve to review the job market and the credit transaction market, together with the basic demand and also supply curves, in the toolkit. You can likewise review exactly how to correct for inflation.

The timeless dichotomy has a an essential implication that we can study with a comparative statics exercise. Recall that in a compare statics practice we examine exactly how the equilibrium prices and also output change when miscellaneous else, exterior of the market, changes. Right here we ask: what happens to real GDP and the long-run price level as soon as the money it is provided changes? To find the answer, we begin with the amount equation:

money it is provided × velocity that money = price level × genuine GDP.

Previously we discussed this equation together an identity—something that need to be true by the definition of the variables. Currently we turn it into a theory. To carry out so, we make the assumption that the velocity of money is fixed. This method that any type of increase in the money it is provided must boost the left-hand next of the amount equation. When the left-hand side of the quantity equation increases, then, for any kind of given level the output, the price level is higher (equivalently, for any given value of the price level, the level of genuine GDP is higher).

What then transforms when we change the money supply: output, prices, or both? based on the timeless dichotomy, we recognize the answer. Real variables, together as genuine GDP and also the velocity that money, continue to be constant. A adjust in a nominal variable—the money supply—leads to alters in various other nominal variables, but real variables execute not change. The fact that transforms in the money supply have no long-run result on real variables is referred to as the long-run neutrality that moneyThe truth that changes in the money supply have actually no long-run result on actual variables..

Toolkit: ar 16.8 "Comparative Statics"

You have the right to find an ext details on exactly how to conduct comparative revolution exercises in the toolkit.

How go this watch of the impacts of monetary policy fit through the monetary transmission mechanismA system explaining how the action of a main bank influence aggregate economic variables, in specific real GDP.?See chapter 10 "Understanding the Fed". The financial transmission mechanism defines that the monetary authority affects aggregate spending by transforming its target interest rate.

The monetary authority transforms interest rates. Changes in attention rates affect spending ~ above durables by firms and also households. Alters in spending influence aggregate spending v a multiplier effect.

Remember that the financial authority changes interest prices through open-market operations. If it desires to boost accumulation spending, it does therefore by cutting interest rates, and it cut interest rates by purchasing federal government bonds through money. An interest rate reduced is indistinguishable to boost in the it is provided of money, so the financial transmission mechanism also teaches united state that boost in the supply of money leader to boost in accumulation spending.There is one difference, not important here, which is that the financial transmission system does no necessarily suppose that the velocity that money is constant. The monetary transmission mechanism is helpful when we want to recognize the short-run results of monetary policy. As soon as studying the lengthy run, the is simpler to work-related with the quantity equation and also to think about monetary policy in regards to the it is provided of money quite than interest rates.

Finally, a reminder: in the brief run, the neutrality the money does no hold. This is since in the short run us assume stickiness of nominal wages and/or prices. In this case, alters in the in the name of money supply will certainly lead to alters in the real money supply. V sticky earnings and/or prices, the classic dichotomy is broken.

## Long-Run Inflation

We now use the quantity equation to carry out us v a theory of long-run inflation. To perform so, we use the rule of growth rates. One of these rules is together follows: if you have two variables, x and also y, climate the growth rate that the product (x × y) is the sum of the development rate that x and also the expansion rate that y. Us can apply this come the quantity equation:

money it is provided × velocity the money = price level × real GDP.

The left next of this equation is the product of 2 variables, the money supply and also the velocity the money. The best side is an in similar way the product of two variables. So we obtain

expansion rate that the money it is provided + growth rate the the velocity that money = inflation price + expansion rate of output.

We have actually used the reality that the development rate the the price level is, through definition, the inflation rate.

We proceed to assume the the velocity the money is a constant.In fact, the velocity of money might also grow over time as a result of developments in the financial sector. Saying the the velocity of money is consistent is the same as saying the its development rate is zero. Utilizing this fact and rearranging the equation, we find that the long-run inflation price depends top top the difference in between how promptly the money supply grows and also how swiftly output grows:

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

The long-run development rate of calculation does not depend on the growth rate of the money it is provided or the inflation rate. We recognize this because long-run output expansion depends on the build-up of capital, labor, and technology. From our conversation of labor and credit markets, equilibrium in these industries is described by actual variables. Equilibrium in the labor market depends top top the real wage and not on any nominal variables. Likewise, equilibrium in the credit industry tells us that the level of invest does not rely on in the name of variables. Since the resources stock in any period is just the accumulation of previous investment, we know that the stock of funding is likewise independent of in the name of variables.

See more: Should Mike Are You The One Real World Seattle: Bad Blood (Episode 8)

Therefore there is a straight link in between the money supply expansion rate and also the inflation rate. The timeless dichotomy teaches us that transforms in the money supply perform not influence the velocity that money or the level the output. It adheres to that any type of changes in the expansion rate that the money supply will display up one-for-one as alters in the inflation rate. Us say more about financial policy later, but notification that over there are prompt implications because that the command of financial policy:

In a cultivation economy, there are an ext transactions taking place, so over there is generally a need for much more money come facilitate those transactions. Hence some development of the money supply is probably desirable to enhance the increased income. If the financial authorities want a stable price level—zero inflation—in the lengthy run, climate they should shot to collection the expansion rate the the money supply same to the (long-run) growth rate of output. If the financial authorities desire a low level of inflation in the lengthy run, then they must aim to have actually the money supply prosper just a small bit faster than the development rate the output.

Keep in mind the this is simply a theory. The amount equation holds together an identity. But the presumption of consistent velocity and the statement that long-run output growth is elevation of money development are assertions based upon a human body of theory. We currently look at how well this concept fits the facts.

### Key Takeaways

The quantity theory of money says that the it is provided of money time the velocity the money equates to nominal GDP. According to the classical dichotomy, real variables, such as genuine GDP, consumption, investment, the actual wage, and also the genuine interest rate, are figured out independently of nominal variables, such as the money supply. Utilizing the quantity equation along with the classic dichotomy, in the lengthy run the inflation rate equals the rate of money expansion minus the development rate of output.

### Checking her Understanding

Is the actual wage a in the name variable? What around the money supply? If velocity that money reduce by 2 percent and also the money supply does not grow, deserve to you say what will happen to in the name GDP growth? have the right to you to speak what will take place to inflation?