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Macro Unit 3

A city like Ankh-Morpork was only two meals away from chaos at the best of times.

Every day maybe a hundred cows died for Ankh-Morpork. So did a flock of sheep

and a herd of pigs, and the gods alone knew how many ducks, chickens, and geese.

Flour? He’d heard it was eighty tons, and about the same amount of potatoes, and

maybe twenty tons of herring. He didn’t particularly want to know this kind of thing,

but once you started having to sort out the everlasting traffic problem, these were the

kind of facts that got handed to you.

Every day, forty thousand eggs were laid for the city. Every day, hundreds, thou-

sands of carts and boats and barges converged on the city with fish and honey and

oysters and olives and eels and lobsters. And then think of the horses dragging this

stuff, and the windmills... and the wool coming in, too, every day, the cloth, the

tobacco, the spices, the ore, the timber, the cheese, the coal, the fat, the tallow, the

hay EVERY DAMN DAY.[...]

Against the dark screen of night, Vimes had a vision of Ankh-Morpork. It wasn’t

a city, it was a process, a weight on the world that distorted the land for hundreds of

miles around. People who’d never see it in their whole life nevertheless spent that life

working for it. Thousands and thousands of green acres were part of it, forests were

part of it. It drew in and consumed...

...and gave back the dung from its pens, and the soot from its chimneys, and steel,

and saucepans, and all the tools by which its food was made. And also clothes, and

fashions, and ideas, and interesting vices, songs, and knowledge, and something which,

if looked at in the right light, was called civilization. That was what civilization meant.

It meant the city.

Was anyone else out there thinking about this?

— Terry Pratchett, Night Watch

Once one starts to think about [economic growth], it is hard to think about any-

thing else.

— Robert Lucas

Measuring Q over Multiple Years

We’ve already seen how total production in an economy is measured within a single

year: we measure Q (output) by measuring Y (spending), calculated as GDP by

government statisticians. But now we need to consider how to compare output across

multiple years.

It’s time to think in more detail about the difference between nominal and real

measures of spending.

Introducing “Real” Spending

We’ve already seen nominal spending as our measure of production.

Total Spending = Y n

The problem with this, of course, is that we’re attempting to measure something

tangible — the real output of a country — with a nominal figure. We can change the

currency that we use to measure the economy, from dollars to cents to yen to euros

to yuan, but this change in our units will, of course, not change the actual tangible

output of the economy.

So how do we get a measure of real production, out of a nominal figure? We do

this by using a index year.

Total Real Spending = Y r (2017) = 19 trillion USD

This is to say that we choose as our ruler (our unit of measure) a certain year’s

production itself. Then every other year of production gets measured against this index

year. Technically, we can choose any year we want for the index, but it’s generally a

good idea to choose a relatively recent index year. As we go further back in time, we

have a less intuitive notion of what prices used to mean. In addition, error creeps in

from technological and quality changes.

By choosing a particular index year, we’re saying the economy is “19 trillion dollars”

in new real production. Then we use that ruler of “this index year” to measure other

years, based on how they compare to “this index year”. An economy of 20 trillion

dollars is bigger in real production, compared to the base year. An economy of 18

trillion dollars is smaller in real production, compared to the base year.

Let’s look at a small example to illustrate this.

Suppose that an economy produces are 10 gallons of milk at 5 dollars a gallon, and

also 10 loaves of bread at 3 dollars a loaf. Then we would measure this economy at a

total production of 80 dollars.

GDP Year 1

Item Q P Total

Milk 10 5 50

Bread 10 3 30

Y n 80

But what if in the very next year, we measure the economy by the long list of real

production, and it is smaller. There are only 9 gallons of milk and 9 loaves of bread

produced, but the price of milk is now 10 dollars a gallon and the price of bread is

now 5 dollars a loaf. Then if we count all of the nominal spending in the economy, we

get, Y n = 135 dollars.

GDP Year 2

Item Q P Total

Milk 9 10 90

Bread 9 5 45

Y n 135

If we look at the nominal spending on new production, the number by itself, it

might seem like the economy is bigger than it was, since spending is now 135 dollars

instead of 80 dollars as it was the year before. But when we look at the real thing

Q — the actual list of real production — we can see that the economy is smaller:

there was less milk, and less bread. We need a way to distinguish between total real

production and nominal spending.

We need a way to distinguish between Y n and Y r, or between nGDP and rGDP.

As mentioned, we can use the index year in order to do this. Let’s say we chose

the first year as our index year. Then “real production” in Year 1 would be measured

normally, which is to say nominally. We say that Y n = Y r = 80. nGDP and rGDP are

exactly the same in the index year. To measure real production in Year 2, we take the

list of Year 2 production (in our example, 9 gallons of milk and 9 loaves of bread) and

assign Year 1 prices to Year 2 production. By using Year 1 prices, we get Year 2 real

production in 72 dollars, which is appropriately smaller because less was produced.

We create our own yardstick for real production by assigning one year as our real

index year. Then that is the year by which every other year’s production is measured.

GDP Year 2 (with Year 1 prices)

Item Q P (Year 1) Total

Milk 9 5 45

Bread 9 3 27

Y r = rGDP 72

That is clearly smaller than Year 1 production of 80. The adjustment shows the

decrease in real production.

This is how we use spending — a nominal figure! — in order to measure real

production in an economy over multiple years. We use spending for a specific year as

our yardstick, our unit of measure, and then use that yardstick (index) year in order

to measure how large production is in other years.

The General Price Level

Now we have two measures for Year 2: we have the original amount of nominal spending

Y n2 which we found by just counting up all the spending. And we also have Y r 2 , an

attempt to measure real production for Year 2, which we tabulated by using our index

year’s prices multiplied by production during Year 2.

In our example for Year 2, nominal spending was 135 and real production was 72.

We can divide nominal by real to get a measure of the general price level P : the

GDP deflator.

GDP Deflator = Nominal Spending Real Production

In our example, the GDP Deflator gives us a new general price level P of 1.875.

Price levels start with their first year normalized at 1.1 In the price figures above,

milk is twice as expensive in Year 2, and bread not quite twice as expensive. The

1It is much more common to normalize these price level numbers by multiplying them by 100. In that case, the price level in the index year is 100, and in Year 2 the price level is 187.5. This is like thinking in percentages. But for the purpose of this class, we can do without this normalization. This means that the general price level P in our index year is always 1.

inflation rate is the percentage change in our general price level P , and so using the

usual formula for percentage changes on the general price level, Pnew−Pold Pold

× 100, we get

an 87.5% inflation rate.

Keep in mind that the GDP Deflator does not give the inflation rate directly! It

gives the new general price level P , with the index year having a normalized general

price level of 1.

An Oddity in the Measurements

The irony here is that nominal spending is easier to measure, but what we care about is

real production. Nominal spending is the actual variable that government statisticians

first try to find out every year: how many dollars changed hands to buy new goods and

services. They try to survey the economy in order to compile a statistical summary of

the list of all items produced within the country every year, multiply the list by the

prices, and then add it up. That is nominal spending, Y n, and it is the first variable

that is measured.

It is a more complicated, and necessarily fuzzier process, to turn nominal figures

into “real” figures. We care about real production, not arbitrary sticker prices, but

real production is harder to achieve and understand and measure. It is actually very

difficult to measure inflation. For example: there was less bread made in Year 2 in the

example above, but how do we know that the bread was the “same”? Maybe the Year

2 bread was of a much higher quality, and that higher quality did not show up in the

data! How exactly can we measure this quality objectively? Inflation is very tricky.

Mathematical Identities

Mathematical identities are very different from functions.

Identities are dangerous.

A great amount of economic misunderstanding comes from people who have seen

an identity, and assumed a cause-and-effect relationship without justification. This

happens all the time. I don’t know what to say here except to warn you, and keep

warning you, about the dangers of identities.

The thing you need to keep in mind is that identities are mere definitions. Defini-

tions are helpful to the extent that they give us a deep, precise language we can use

to talk about reality with insight. But identities are not reality, and by themselves

without the help of theory, they do not give us any direct insight into reality.

An Example

The most important identity in accounting is that what we own minus what we

owe equals our net worth. Or another way to express this:

Assets − Liabilities = Owner’s Equity

This is the accounting equation. It seems pretty obvious. Yet I have seen an

identity this simple misunderstood. Another way to write this equation (the way the

accountants normally write it) is this way:

Assets = Liabilities + Owner’s Equity

I’ve seen people approach this identity and say, “This equation says an increase in

debt implies an increase in assets!” No. No no no no no.

NOOOOOOOOOOOOOO!!!

The number one mistake in economics is reasoning from a price change. The

number two mistake is reasoning from an identity.

The problem here is they were treating it like a function, rather than an identity.

Never reason from an identity. They were looking at an increase in the right-hand

side (RHS) and assuming that that increase would correspond to (cause) an increase in

the left-hand side (LHS). But an increase in debt can correspond to a decrease in net

worth, without touching assets on the other side of the equation. For example, if you

have outstanding credit card debt with a high rate of interest, then when the interest

is applied, your debt will increase. You’ll have more debt in the form of interest owed,

but that additional debt will not increase your assets! Your assets are stationary. That

additional debt will decrease your personal net worth instead.

The equation is still true. Identities are always true, by definition. But the LHS

of an equation can stay exactly the same, while the different terms of the RHS can

rearrange themselves, going up and down to make sure the identity balances.

Changing our definitions does not change the world. In order to understand the

world, we need a theory of cause and effect to tell us how the world works, and even

after we have that theory, we need to test it against reality to see if our theory genuinely

corresponds to the way the world actually works. Identities can give a nice language

to talk about the world — identities can be the backbone on which functions can be

built — but the language does not tell us directly how the world works. We have to

figure out how the world works by looking at the world.

The Components of GDP: Remember the Seed Economy

GDP as measured divides, by definition (by identity) into two main components. We

have already discussed these two main ideas: we can eat our seeds, or plant our

seeds. With respect to spending, these two components are called consumption and

investment.

Y = C + I

This is macroeconomics, not finance class. This is the Story of Stuff, and so in-

vestment means building new capital goods. Stocks and bonds and savings accounts

are just pushing paper, and do not count for this story. The only thing that counts for

investment, as defined in macro, is the creation of new capital goods, which are stuff

that will help us create more stuff in the future. This is, again, the choice between

the present and the future. Consumption is done for today, and then the stuff is gone.

Investment is the creation of stuff today (capital goods), for the purpose of having

more stuff in the future. This is a fundamental tradeoff that we as individuals face,

and also the tradeoff that our civilization faces.

It would be a mistake to grind literally all of our available wheat seeds into flour,

with none left over to plant in the ground. We need to preserve some seed corn to

plant, so that we have more wheat in the future.

The problem with this identity is that people look at it and assume they know

how to increase production. Consumption spending is around 70% of total spending.

People look at that figure and come to the wrong conclusions. “We live in a con-

sumption economy! Just put the money in people’s hands, and they will spend it for

consumption, and that will increase GDP.”

NOOOOOOOOOOOOOO!!!

Not necessarily the case! Never reason from an identity. In fact, consumption

spending is relatively more stable during recessions than investment spending. During

a recession, it is investment that falls off the cliff. Altho consumption drops, it drops

by much less.

More broadly, we need to remember our story of cause-and-effect, as expressed in

our production function.

Total Production = F (labor, capital, natural resources, ...)

Spending more on C will not necessarily increase Y . We will still have the same

amount of productive resources, which means we will just be eating our seeds, instead

of planting them. Y could stay the same, in this story. Instead, a bigger amount of

C would correspond to a smaller amount of I, with a potentially fixed Y on the LHS.

We will have less investment spending, and therefore less capital in the future, and

therefore less real production in the future.

Identities can confuse people. It is not necessarily the case that increasing con-

sumption will increase output! Instead, we might just be sacrificing the future in favor

of present consumption.

The Difference Between Rich and Poor

The difference between rich countries and poor countries is relatively “simple” in the

statistics: rich countries have a lot of capital goods per person.

They have factories, roads, energy infrastructure, educated workers, and all other

kinds of machines. Poor countries have very few machines and equipment per person.

That’s pretty much it, in the main economic numbers. That’s the “difference”. The

lesson is clear in the data. If a poor country wants to become a rich country, they need

to invest. They need to use less of their production on consumption in the present,

and more of their production to save (to invest) for the future. And, of course, they

need that saving to be on smart and productive capital goods, rather than on wasteful,

corrupt spending to pad the country’s numbers.

This is a tricky thing, isn’t it?

Poor countries have the smallest amount of production. This means that the

majority of their production, by sheer physical necessity, needs to be oriented toward

mere subsistence. The people need to have enough to eat, need a roof over their head,

need the most basic of medical care if someone breaks a leg. They need to consume

in order to meet basic needs.

If the average person in a poor country has kidney failure, then their life is over.

There is simply not enough surplus production to create capital goods: not enough dial-

ysis machines to keep them alive, not enough hospitals to provide transplant surgery,

not enough pharmaceutical production to prevent organ rejection medications after a

transplant. The difference between rich and poor can be very stark.2 And the poor

don’t have the production to invest easily, in order to become rich. They have very

little surplus.

“It takes money to make money” is a weird saying, but there’s some truth to it.

It takes resources in order to invest those resources, in order to create more resources.

It’s a conundrum for the peoples of the world who start with so little to invest.

How do poor countries become rich?

The short, unhelpful answer to this question has already been offered: they need to

save. They need to invest rather than consume. The longer answer confronts the

deeper question: how do they do that, if they start with so little?

Unfortunately, this might be more of a political science question than an economics

question. They need a society that rewards investment, that encourages and protects

the accumulation of capital. This requires controls on corruption, a fair court sys-

tem that holds people to their contractual promises, and a certain amount of public

toleration for a certain amount of inequality in savings outcomes.

It’s a simple fact that human beings are different. One consequence of that fact is

that human beings have different capacities for production, and different propensities

to save and invest. People who save more over time will, on average, become much

wealthier than their peers who save less, whether that lack of savings is through random

misfortune or personal profligacy. A country that provides strong incentives to save

will have people with vastly different savings rates, and thus over time, people with

different wealth levels.

It is iniquitous to look away from the ravages of poverty. At the same time, the

more ideal anti-poverty programs are those that encourage rather than discourage the

determinants of real production: successful countries support the accumulation of cap-

2One of my past students, still a teenager, suffered sudden kidney failure. She was hours from death before the doctors recognized what had happened and put her on the dialysis machine.

In a poor country, she would have simply died. Economic development is important.

ital. The US government has many programs which, though perhaps well-intentioned,

very likely interfere with the country’s ability to save.

What is saving?

From a personal standpoint, the idea of saving is simple. All of us have a certain

amount of income, and a certain amount of outgo (expenditure). In order to save, we

must have more income than we do outgo. This is saving from our personal perspective.

But this is macro. What’s the problem when we go from the individual perspective

to the macro perspective?

The Circle of Spending

Every dollar that I spend goes somewhere. The money I spend does not (we hope)

disappear into the void between the stars to ride out existence on a lonely path of

nothingness until the heat death of the universe.

My dollars, when spent, end up in other people’s hands. My outgo is somebody

else’s income.

Likewise, my income derives from some source out there in the world. I earn

income because some institution (in my case, the University of Miami) gave me that

income. My income is somebody else’s outgo (expenditure). And so, it is possible for

me personally to have an income greater than my outgo. But it is not possible, for the

economy as a whole (on the macro-est of macro levels), to have our incomes in total

exceed our outgo.

Income = Outgo

This is an unavoidable macro equation. As soon as you think about it, you realize

that it is quite obviously and quite unavoidably the case. (It is unfortunately not so

obvious, before you have thought about it the first time.) So the question, again: what

is saving? How do we as a society save, when we cannot possibly spend less than our

income, because when all of us are counted together, our saving is our income?

Saving is production less consumption.

An individual can define their saving as their income less their outgo. What we earn,

and don’t spend, is our saving. But that doesn’t work for macro, as we’ve seen.

In macro, saving is production less consumption. What we save, as a civilization,

is the production that we created that we didn’t consume. Our saving is the seeds we

grew, but did not eat.

Saving in the Seed Economy

We’ve just defined saving as our production Y less our consumption C.

S = Y − C

We can look back on our production identity:

Y = C + I

I = Y − C

S = I

This is an identity in a closed economy. (It is true by definition in a closed economy.)

Another way to express this idea is to say that saving, on a macroeconomic level,

is the creation of investment goods. To save is to create new capital goods: to plant

our seeds, instead of consuming them.

To save is to invest. To save is to create capital goods.

The problem is that it’s difficult to plant seeds, rather than eat them, when an

economy has barely enough seeds to survive. Our species, for most of our history,

lived on the edge of subsistence. We did not have a large surplus which could be

invested in capital goods. There were few seeds to plant, because so many needed to

be eaten. Here is a graph I stole showing real output of our species, per person, for

most of our history.

It is only in very recent times, in the wake of the Industrial Revolution, that human

civilization has persistently created a surplus large enough to create real wealth on

large scales. Most of our ancestors lived in grinding poverty. It took our ancestors a

very, very long time to figure out how to create a coordinated social system that would

encourage saving, and therefore investment in capital goods, on a large enough scale

to create a genuine middle-class.

In the context of world history, the Industrial Revolution looks like a miracle.

In modern days, the countries that break out of their poverty trap are, all of them,

connected to world trade markets. They are able to use their comparative advantage

for labor-intensive goods to trade with the developed world, which greatly expands

their possibilities for production.

We’ve already seen how this works!

Comparative advantage: the availability of trade allows a surplus far in excess of

what they could’ve accomplished without trade. The surplus can be saved (read: they

can create investment goods such as new factories, new roads, new equipment), and the

new investment goods fuel further growth. This creates a positive cycle of economic

development. This is, for example, the recent story of China, India, and many other

developing countries.

What this process requires is global cooperation, meaning participation in world

markets, and a political system that allows accumulation of capital. How to accomplish

those things is, however, a trickier problem. This process is easy to describe in its

roughest outlines, but that does not mean it is easy to do. It’s a political issue of great

difficulty.

Expanding the Components of GDP: Government

In this unit, we can add one more component of GDP: government spending.

Y = C + I + G

The problem with this component is that it is not necessarily enlightening on its

own. How can the government spend? It can spend on stuff that is used immediately

and disappears (like eating seeds) or it can spend on infrastructure that lasts for a

long time and helps us make more stuff in the future (like planting seeds). In other

words, the government itself can consume or invest.

Y = C + I + GC + GI

Again, we need to keep in mind that this is an identity. It is not necessarily the

case that more government spending will automatically increase total production! It’s

possible that more government spending might decrease investment, in which case it

would not help with total production.

If we want to expand total production, we need to think about the production

function.

Total Production = F (labor, capital, natural resources, ...)

Only if government spending can somehow affect these items should we see an

increase in production. Which leads us to...

Unemployment and Capacity Utilization: a Brief Introduction

It is possible to have people in the country who want to work but who do not have jobs.

It is also possible to have factories which are operating at less than total productive

capacity. This leads to a couple related questions:

1) Why would we as a society have valuable resources available, which we were not

using for production? That does not make any obvious sense. If there are hundred-

dollar bills lying around on the sidewalk, someone should be picking them up.

2) If it is actually the case that the economy is operating at less than potential,

then even so, that does not necessarily mean that the government can do anything

about it. There are some problems in this world that nobody can fix. Maybe this is

one of them?

But supposing that this problem exists, and supposing that the government can

help, how would it help? We can look at the factors of production for our answer: the

government would help either reducing unemployment in some fashion (more labor),

or by increasing utilization of current industrial capacity (more capital). Please no-

tice! This is not just a case of “increasing G must increase Y ”. That’s not how this

would work. Whatever action the government takes — regardless of whether it spends

more money! — must put more people to work, or use our industrial capacity more

efficiently. It is people and machines, working together, that create more production

in the economy.

It is not “spending” that makes things. People make things, and we use tools to

make things. We need more people working, using better tools, if we want to make

more things. In order to recognize whether it is possible for unemployment to be

pushed down, or capacity utilization to be pushed up, we need to understand what

might go wrong in an economy that keeps us from our potential.

And in order to understand that, we need to talk about money.

The Equation of Exchange

The following Equation of Exchange is an identity. It is true by definition.

M V = P Y

The right-hand side we have recently seen: P is the general price level, which

can be measured by the GDP deflator, and Y in this case is Y r, or real production

(measured by rGDP). You might recall from our discussion of the GDP deflator:

GDP Deflator (P ) = Nominal Spending Real Production (Y )

Or to algebraically rearrange that equation:

P Y = Nominal Spending

When we multiply real production by the price level, what we’re left with is nominal

spending.

This means that P Y is also something we’ve seen before! P Y is nominal spending,

or nGDP. So what we’re looking at in the Equation of Exchange, expressed a different

way, is:

nGDP = nGDP

That is not very enlightening. But this is exactly what the Equation of Exchange

says, in most primitive form. After all, the LHS must equal the RHS, and we can

already see that the RHS is nGDP (nominal spending). So that leaves two more

variables to deal with, M and V on the LHS. When we multiply those two variables

together, we get nominal spending. What are they?

M is easily remembered: it is the money supply (variously defined). We find out

the value of M by looking out in the world and seeing how much money there is, by

whatever definition of money we’re using. We find P and Y , likewise, by going out in

the world and measuring.

The only variable left is V , the velocity of money. This V is defined specifically to

make the equation work.

V ≡ nGDP M

The triple-equal sign, if you have not seen it, is equivalence, which is a fancy way

of saying we are making a definition. The velocity of money is being defined here by

nominal spending in the economy divided by the money supply.

The idea behind the “velocity of money” is that the average dollar bill might change

hands many times over a year, or it might move more slowly.

Stocks vs Flows

This is very simple idea with a slightly fancy name.

The human body has about 5 liters of blood. But the blood isn’t stationary. It

is pumped through the human body continually by the heart, so that the heart can

pump nearly 8000 liters of blood in a single day. It’s the same blood, being circulated

and recirculated.

5 liters is the stock of blood that human beings have. A “stock” is the amount,

the level, at any given time. When you get into a bathtub, that tub has a stock of

a certain amount of water. The M2 money stock of the United States (the amount

of money which includes not just circulating currency but also savings and checking

accounts) is around 14 trillion dollars.

For the accountants in the audience: the “balance sheet” is a list of different stocks.

These stocks include assets (a stock of what you own), liabilities (a stock of what you

owe), and the difference between them (equity, or the stock of your net worth).

Keep in mind that stocks are like photographs. A cross-section of reality. Time is

frozen. If I look at my own stock of assets today, the amount of money in my bank

account, it will be slightly different from my stock of assets tomorrow. If I look away,

and then look back, the amount of water in the bathtub can change. A stock is a

photograph at a certain point of time.

The flow of blood through your aorta is around 7500 liters per day. A requires a

time dimension. When I turn on the faucet to the bathtub, water flows into it. I might

barely open the spigot, and the flow will be very small: a gallon will flow into the tub

every hour. Or I can open the spigot all the way, and create a faster flow of several

gallons every minute..3 The idea behind the velocity of money is a flow, specifically,

how fast the average dollar is changing hands.

The national debt is a stock, just like the water in the bathtub is a stock. It’s a

certain level of debt, a certain amount that the United States government owes. The

national deficit is a flow: it’s the change of stock over a certain time period. In the

case of the deficit, we measure the flow over an annual basis.

Our sum total of capital equipment is a stock. It’s the number of machines we

have at any given moment. Investment is a flow: it’s the increase in our amount of

capital goods. But just as there is a spigot which introduces water into a bathtub,

there is also a drain that lets water out. Depreciation is a reduction of our total

capital goods, as they get worn out and break. If we imagine our total amount of

capital goods as water in a bathtub (a stock), we must also consider the two flows

that influence that stock: investment is new water from the spigot going into the tub

of capital, and depreciation is water going out the drain.

For the accountants: both the income statement and the statement of cash flows

are used to measure business flows. And to say it again, the balance sheet is used to

measure business stocks.

In economics: what is GDP? Is it a stock or a flow? (Hint: Is there a time

dimension? Is GDP measured at a certain frozen instant of time, like a photograph,

or is it a measured flow over a long period of time?)

Answer: GDP is a flow! It’s the production of new goods and services over an

entire year. GDP is a flow of new production that was created over that time period.

The consumption part of that production is consumed immediately. The investment

part of that production goes into capital goods, which will increase our stock of capital

goods. But capital goods depreciate! If we include this negative flow — the destruction

of previously created capital goods — in our GDP calculates, we get a new idea: Net

Domestic Product. NDP = GDP − Depreciation.

The 5 liters of blood in your body (stock) flows through your aorta at a rate of

around 7500 liters per day (flow: notice the time dimension). Important fact: with a

3Mathematical note: the derivative is the measure of a flow, but at a single instant as the time period gets compressed smaller and smaller, “at the limit” as we would describe it today. Newton discovered the calculus as he worked to calculate instantaneous flows in physics like acceleration.

fast enough pump, like your heart, even a small stock can support a very large flow.

If there are 20 dollars in an economy (M = 20), and the average dollar moves

six times to buy new goods and services (V = 6), then nominal spending (nGDP) in

that economy is 120 dollars. Of course, it is not necessary that every dollar moves

six times. Maybe one dollar doesn’t move at all (it stays in my wallet), while another

dollar moves 12 times to buy new production. The average will still be 6.

And this is what the Equation of Exchange says: the money supply times the av-

erage spend-rate of a dollar (M V ) is one way to break down nGDP. Another way to

break down nGDP is to look at the general price level P and multiply by real produc-

tion Y . These two views of nominal spending must equal each other, by definition:

M V = P Y .

That is the identity. It is the definition, the language we’re creating to think about

the flow of money in the economy.

Now let’s apply it.

The Quantity Theory of Money

We move now from identity (always true) to theory (must be tested against reality).

I’m going to assume here that the velocity of money is constant: V = V̄ , where V̄ is

some constant. This says that people spend the money that they possess at roughly

the same rate. I’m going to state, also, that real production Y is also a constant, and

does not depend on money. Production is a function of real resources, not money, so

Y = Ȳ , where Ȳ is a function of real production.

Using the language of the Equation of Exchange (always true), the quantity theory

of money says this:

M V̄ = P Ȳ .

Now, supposing that the government issues more money M, what should we expect

to happen? If money doubles, and both the velocity of money and also real production

are fixed, then what does the theory say will be the necessary result?

Prices must double. Double the money supply, and you double prices, because

money is not a factor of production. The quantity theory of money says that the price

level depends on the amount of money.

Is it true?

Broadly speaking, in the long run, yes. The relationship between the money supply

and the price level has been extremely strong in the past. For a quick look at the data

from Barro, it looks like this.

A pretty good fit, on the very long time frames that Barro was using in his dataset.

Notice that the fit is better for high-inflation countries. At a low rate of inflation, there

is more opportunity for random noise to interfere with the basic relationship.

But now let’s look at the US monetary base since the Great Recession. What

happened to base money?

The thick grey bar shows the Great Recession. We can see that the monetary base

exploded from around 0.8 trillion in 2008 to a little less than 4 trillion today. What

happened to prices in this time?

The US exploded its monetary base, but inflation has remained muted. There was

a small bit of deflation in late 2008/early 2009, but there was no spike of prices when

the central bank exploded the monetary base.

Hmmm...

The Short Run

Let’s review our previous picture of total real production, which I called “aggregate

supply”.

One change I want to make to this graph: from now on, it will show real production

as Y/t rather than Q/t. This is to emphasize that we’re in a different space here than

for the market of an individual good.

Aggregate supply is a vertical line, showing no relationship between real production

Y and the general price level P . Notice, too, that I’ve relabeled that line as Long-

Run Aggregate Supply, or LRAS. Obviously, we will soon be thinking soon about

aggregate supply in the short run, SRAS. But first, some background.

A Small Economy with Sticky Prices

The following model is the single most important idea behind the business cycle.

If you want to understand recessions, then this is where we begin.

Suppose we have a small economy of workers who trade with each other the output

of their professions. There are 10 workers who each earn 10 dollars every day, working

for each other. Nominal spending is 100 dollars per day. Let’s use today as Day 1,

will be our index, our yardstick, to say that real production is also 100 dollars: on Day

1, this economy created 100 dollars worth of real stuff.

Now suppose for whatever strange reason that nominal spending in the economy

drops to 90 dollars on Day 2.

But let us suppose also that, in the short run, prices are sticky: the price does

not change. There is 90 dollars of spending on Day 2, but each worker must still be

paid the full 10 dollars in order to work.

The Single Most Important Fact of the Business Cycle

If each worker earns a sticky wage of 10 dollars, and there is 90 dollars of nominal

spending in the economy, then there is not enough spending to employ every worker

on Day 2. One of the workers will be out of a job. 90 dollars of spending cannot be

divided among ten people, when each person must be paid the same wage that they

were paid the day before: 10 dollars. This is just a basic mathematical fact. It is an

identity, and necessarily true. When 9 people are paid 10 dollars, only 9 people are

working, and real production in the economy has dropped from an output of 100 to

an output of 90.

Using the equation of exchange: suppose that nominal spending M V has dropped.

Suppose further that P is “sticky”, or fixed, in the short run.

(M V )↓ = P̄ Y↓

If the LHS decreases for some reason, and P is fixed, then this necessarily means

that Y has also dropped. The drop of M V and the drop of Y must go with each

other.

In the long run, prices can eventually adjust. This is actually how we can define

the long run! The short run is a short enough period of time that some prices are

still sticky. The long run is sufficient time for markets to clear, mean all relevant

prices have had time to adjust.4

If wages are very sticky, it can take a long time to reach the long run, a long time

for the wages of everyone to drop down to 9 dollars each. But when wages drop, 90

dollars of spending is sufficient to pay 10 people 9 dollars each. At that point, real

production returns to its original level. Only after wages have adjusted can the last

person return to work.

Remember, however, that identities are not informative by themselves. In order

for this relationship to have meaning in the real world, we need to know whether

wages actually are sticky. We need not just this simple identity, but also an empirical

observation. Are wages sticky?

Empirical Fact: Wages are sticky.

It is an extremely well-documented fact in economics that wages are sticky.

4Note the correspondence here with the micro definition: In the short run, firms are stuck with sticky prices like contractual leases which means they are unable to easily alter the amount of capital available. But in the long run, those contracts end, which means that the prices and quantities of capital can be renegotiated.

If wages weren’t sticky in the downward direction, we would expect to see wage

changes form a distribution resembling the normal (Gaussian/bell) curve. The nice

symmetry of our distribution is destroyed at 0% wage change. This indicates that there

is resistance to negative wage changes — that is, there is resistance to any wage cut.

Workers will accept a wage increase: this price is not sticky in the upward direction!

But workers will not readily accept a wage cut.

This was perhaps first noticed by the economist Irving Fisher in the early 20th

century. Fisher was independently wealthy from his own invention of an early proto-

Rolodex. Fisher had employees in his company, and he decided to index his employee’s

wages to local prices. When local prices were higher, he paid them more to compensate.

When prices were lower, he paid them less. His employees were happy to receive higher

wages, when prices were higher.

His employees would become outraged whenever he paid them less, even when

prices were lower.

This lead Fisher to coin the term Money Illusion. He tried to explain to them

the principle that two nominals make a real: it was not the absolute amount of money

they were paid that mattered, but rather how much they could buy with the money

they were paid. His employees were not, however, good economics students, and they

resisted this compelling analysis.5 Unless given an enormously compelling reason,

5A joke! There are rational reasons to resist a cut in wages, as we will see.

employees resist any and all wage cuts. This is true even during times of deflation,

when the general price level is dropping.

The single best work on this issue that I’ve read is Truman Bewley’s Why Wages

Don’t Fall During a Recession. It summarizes hundreds of interviews with employers,

HR managers, etc., about why they might not cut wages even during bad times. Some

of my own work also investigates microeconomic reasons why workers might resist any

and all wage cuts.

Short-run Aggregate Supply

We now have a story about money that influences the production function. This gives

us a picture of short-run aggregate supply.

It slopes up! It looks a bit like the normal supply curve.

But it is, of course, completely different.

It’s graphed on a different space: P is the general price level here, not the price of

one good, and Y is real production. And of course, it must necessarily slope up for an

entirely different reason, because it exists in a different space.

Our story regarding the slope of aggregate supply depends on the specific point

where we are standing today. What matters is not the general price level, which is

arbitrary, but rather movement from the sticky price level where we are today. The

idea here is that many prices — most especially wages — need time to adjust. If total

spending in the economy drops (as it did in our example above) while prices remain

sticky, then it is a necessary mathematical fact that a smaller amount of spending

cannot be spread over the same number of people. If nominal spending drops,

then real production must also necessarily drop whenever prices are sticky.

Looking at our production function:

Total Production = F (labor, capital, natural resources, ...)

Why does Y decrease, with a decrease in P ? Not for any direct reason!

It is an indirect cause-and-effect relationship. The problem is that certain prices are

sticky, especially wages. Therefore when total spending drops, we see a corresponding

drop in L. This is part of our story of cause-and-effect. It is the decrease in L that

leads to a decrease in Y .6

This explains why SRAS (short-run aggregate supply) slopes upward to the point

where the economy is today. But what happens if aggregate spending exceeds the

amount of spending today. What if spending tomorrow explodes?

Inflation is a drug.

Irresponsible governments often rely on large amounts of new money in order to finance

their spending. This money (as we have seen) will be inflationary.

As people receive the money, they will at first believe themselves to be wealthier

— despite the fact that there is a limit to the amount of capital and labor in their

economy! They have larger balances of cash, but they will be considering that money

compared to the old price level. Having a higher perceived income will lead them to

spend their money, and the people who receive that money will also spend, and so

forth.

At least, people might even temporarily work harder in the perception that times

are especially good. L will be a bit higher, leading to higher Y . This bit of extra hard

work will push up production ever-so-slightly past the level that they would choose if

given full knowledge of the situation. But eventually, reality will come crashing down:

there is a hard limit on resources.

6In future, we will also discuss why a decrease in prices, or more specifically a decrease in nominal spending, can also lead to a decrease in K along with L. In this unit, however, we will focus on L.

This is another example of Money Illusion. But people will soon realize that the

inflation is just a trick. The hard work will not be suitably rewarded. More and more

money will be chasing the same amount of goods, and that means prices must rise.

This is why SRAS will continue to slope upward even past the LRAS, but not

very far past. More nominal spending will temporarily lure out more production, but

the after that, the result will be inflation.

Aggregate Demand

We now have the concept of short-run aggregate supply, and therefore we can see a

way that total nominal spending in the economy might influence real production: it

is through the stickiness of prices, most especially the price of labor, which is the

wage. So now we need to ask ourselves how changes in the general price level, and real

output, might be determined.

The entire point of having two curves — supply and demand — is that the inter-

section of those two curves is meaningful. We need some notion of aggregate demand.

I’m going to define aggregate demand in the easiest fashion possible.

Aggregate demand is nominal spending.

Remember from the Equation of Exchange breakdown that nGDP = P Y . Now look

again at the space where we are graphing our aggregate supply curves:

The space is P compared to Y . This means that any given amount of nominal

spending P Y will show up, on this space, as a downward-sloping rectangular hy-

perbola. Why is it called that? Choose a certain amount of nominal spending, such

as 100 dollars. This amount of total spending could be a price level of 1 with real

output of 100; or a price level of 4 with real output of 25; or a price level of 10 with

output of 10; etc, in combinations that plot out a hyperbola in the space.

P × Y = 100

P = 100

Plotting 100 dollars of nominal spending onto the same space:

This aggregate demand curve represents 100 dollars of nominal spending (of nGDP).

Each point on the curve represents P × Y . The curve is a hyperbola, and each one of

those points on the AD curve forms a rectangle, starting from the origin and going up

to the curve: P × Y = nGDP. Every rectangle formed in this manner has exactly the

same area, because each and every rectangle is a combination of P × Y that adds up

to the same amount of total nominal spending (100 in this case).

This is why the definition is so elegant. And also, so easy to draw.

A shift in aggregate demand represents a change in the total amount of nominal

spending in the economy. We don’t even have to call these curves aggregate supply

and aggregate demand. We can refer instead to “total production” and “nominal

spending” — as I have been doing this entire course! AS naturally refers to total

production, whereas AD refers to nominal spending.

I’m going to continue to use AS and AD, but only because everyone else does so.

But keep in mind that this is different from the reasoning behind normal supply and

demand. They’re named similar things because they look like similar curves, but they

are different concepts, and the curves are shaped the way they are for different reason.

They must naturally be different, because they exist in different spaces.

The Big Question

We know where real production comes from. The course started with that idea, that

real production comes from real productive resources: labor, capital, natural resources,

etc. We know also why real production (AS) is shaped the way it is. In the long run,

real production has no relationship with the price level. In the short run, changes in

the price level can change real production because prices are sticky.

Aggregate demand has also been defined. We know that a certain level of nominal

spending must slope down, because it will form a rectangular hyperbola on the space

we’re using for our graph.

The big question here is: What causes the AD curve to shift?

This is the number one biggest question in business cycle research. What might

cause people to change the amount of dollars that they spend?

Questions regarding Aggregate Demand

Influences on aggregate demand (nominal spending) potentially include fiscal policy,

monetary policy, and various shocks to spending, such as financial shocks or savings

shocks.

Fiscal policy is the control of government taxation and spending. Congress is in

direct control of annual discretionary fiscal policy in the US: they choose discretionary

appropriations every year, and can also change the tax rate by passing a law (subject

to being signed by the president). Some kinds of fiscal policy are “baked-in”, which

is spending that was determined by laws passed by previous Congresses. These are

referred to as “automatic stabilizers”. Congress does not have to pass a new law,

because they already passed older laws that mandate spending in certain environments,

such as unemployment benefits

The other kind of policy most often mentioned with respect to aggregate demand is

monetary policy. Monetary policy is determined by the monetary authority of the

country, which is to say, the central bank. In the US, the central bank is the Federal

Reserve. The Federal Reserve is a government agency, however it is “independent” of

the normal operations of Congress. When people refer to the “government” making

policy, they are almost always referring to Congress or the executive making fiscal

policy, and not to the Fed. (Congress created the Fed, and could pass a law that

eliminated the Fed, but that is politically very unlikely.)

The other commonly discussed potential shock to nominal spending in a financial

shock, e.g. the Lehman bankruptcy crisis of 2008. It is widely believed that the

financial crisis was the shock that led to the Great Recession (altho I will discuss other

possible interpretations).

Differences of Opinion

Broadly speaking, there are three main macroeconomic “schools of thought” with re-

spect to the business cycle, and the determinants of aggregate demand. Keynesians

believe that monetary policy can be limited in certain situations (e.g. when the nom-

inal interest rate reaches 0%), and in those situations, fiscal policy can still be potent.

The most famous of this group was John Maynard Keynes, after whom this school of

thought was named.

Monetarists believe in the broad potency of monetary policy to influence nominal

spending. They generally believe that money works more quickly, and more power-

fully, to influence nominal spending in the economy than fiscal policy. The most

famous monetarist, and founder of the school, was Milton Friedman. I am personally

a monetarist, too, of a more modern variety.

There are also New Classicals (I didn’t make up these names...) who generally be-

lieve that the government cannot help at all with the business cycle, and that anything

the government does will be ultimately counterproductive. I will spend only a little

time discussing this school of thought because it is, quite frankly, stupid.

In addition to these macroeconomic schools, there are also various heterodox ap-

proaches to the subject. I will spend relatively little time on them, but will provide at

least some outside recommendations for more reading.

The most common macroeconomic belief (I believe) is a hybrid form of monetarism,

when nominal interest rates are positive, and Keynesianism, when nominal interest

rates are at 0%. This is to say that (I believe) most macroeconomists believe the

Fed strongly influences nominal spending when interest rates are positive, but that

problems arise with monetary policy when interest rates are at or near 0%.

Determinants of Aggregate Demand

What determines total nominal spending in an economy? What is the cause of spend-

ing? What is it a function of?

Nominal Spending = f(?, ?, ?)

The Short Answer

One monetarist answer is that the central bank chooses the level of nominal spending

in the economy.

Nominal Spending = f(Central Bank Choice)

Can I level with you?

I think this is pretty clearly the best answer to this question. Put down your pens,

close your laptops. This class is over!