USING CIRCULAR FLOW DIAGRAMS TO GENERATE NUMERICAL EXAMPLES
Hannes Kvaran
An earlier version of this paper was presented at the 15th annual Teaching Economics Conference at
Robert Morris University and published in the conference proceedings.
ABSTRACT
This paper explores a variety of different approaches by which circular flow diagrams can be adapted to
present numerical examples in macroeconomics. The models allow for exposition of the roles of monetary
and fiscal policy and the differences in monetarist and Keynesian theories, among other topics.
I. INTRODUCTION
The circular flow diagram (CFD), in one of its many variations, is ubiquitous in economics pedagogy.
The use of the diagram to generate illustrative numerical examples has been, as far as I know, unexplored,
but offers rich opportunities. This paper is intended to demonstrate the possibilities of such an approach.
This method has been an integral part of my class for many years. As any teaching strategy, it has
strengths and weaknesses. Some students like it and some don’t but I find it an indispensable part of my
teaching tool-kit.
I find these diagrams to be pedagogically useful on a par supply and demand. Whereas supply and
demand shows the workings of a particular market, circular flow diagrams are the tool designed to view
an entire economy at once.
The diagrams that follow exist in two forms:
1. as hand-drawn diagrams for use in a classroom and in notebooks. This is, to my mind their essential
purpose. In this paper I use word processor drawing tools to laboriously produce the diagrams, but it is
important to see that these can be hand-drawn quickly enough to be a useful complement to lecture. I
use these diagrams as often as I use supply and demand graphs as the complementary analytical tool.
2. as computer programs on the Internet and on a stand-alone program. In this incarnation it is possible
to integrate supply and demand graphs into the diagrams. This allows for a significant expansion of
the model’s scope into issues of cost and technology.
After some introductory remarks, I will explore each of the presentations in turn
Models. Circular flow diagrams come in three broad types, each with four possible variations. Students
are always encouraged to use the simplest model for any particular purpose.
• Open Models are used to demonstrate Keynesian theory. The principle purpose of these diagrams is to
illustrate that fluctuations of aggregate spending are determined by the inequality of leakages and
injections. These models represent the viewpoints of Keynesian theory and therefore better describe
economies in the short run and in periods of underemployment.
• Closed Models are used to demonstrate monetarist or classical theory. These are directed toward
demonstrating crowding out, showing how one sector’s spending impacts others and essentially
disavows the possibility of fiscal policy influencing aggregate demand. These are more appropriate
models for examining an economy at full employment and in the longer run.
• Money Models add the Federal Reserve and/or the demand for money as elements of the economy.
Their conclusions stand mid-way between the open and closed models.
Variations
Each of these four types can be presented in four variations depending on which variable one chooses to
include:
• the Basic Model includes the variables Income, Aggregate Spending, Consumption, Savings and
Investment
• the Treasury Model adds to the basic model the elements of fiscal policy -- taxes, government
purchases, transfer payments and the budget balance.
• the Foreign Sector Model adds to the basic model exports, imports, and foreign financial capital flows.
• the Full Model combines the Treasury and Foreign Sector elements.
Notation and Terminology.
PrM
X
LaM
C
wages
profit
H/B
Y
The usual CFD pictures the economic flow as an exchange between a
household sector and a business sector, mediated by the markets for goods
and factors. I have found it more useful to compress the two sectors into
the “Household/Business Sector” (H/B) and see them as interacting with
the Product Market. This corresponds quite closely to the Federal Reserve
flow of funds approach, which includes the “Domestic Nonfinancial
Private Sector” as a component. The simplest CFD is therefore as shown
in Figure 1. When a Credit Market, a Foreign Exchange Market and a
Treasury are added, the result is quite similar to the economic categories
used in the flow of funds accounts.
Making this slight shift does, however, force another, more substantial
change of perspective. Since households and businesses have been
combined, it is no longer possible to define consumption and investment
PrM
in the traditional NIPA fashion as, respectively, “Spending by
X
Households” and “Spending by Businesses.” Looking at Figure 2 it is
I
clear at the symbol C indicates “Spending out of Income (by both
Households and Businesses)” and that the symbol I represents “Spending
C
LaM
CrM
out of Credit (by both Households and Businesses).” There are several
notation/vocabulary solutions available. One could invent totally new
terminology, or one can continue to use the designations C and I, and
S
even the words “consumption” and “investment” and redefine them. No
doubt there are pitfalls to both approaches; I use an intermediate course.
H/B
Y
At some point I carefully define terms, and then, for the most part,
casually
blur the distinctions between the competing definitions,
Figure 2. The Meanings of C and I
revisiting terminology in the few instances where course content
warrants it. Of all the problems inherent in this approach, I have never felt this one to be important. If this
seems unduly heretical, I invite you to look at the classification systems used in the Fed’s flow of funds
accounts. Also ask yourself, aside from historical convention, which definitional distinction is more
relevant to analyzing a macroeconomy, which question is of primary importance in classifying a spender:
Figure 1. The Simplest Circular
Flow Diagram
“Who are you?” (as NIPA does) or “Where did you get the money?” (as Flow of Funds does). I submit
that, in an age of huge consumer debt and reinvested profits as a significant source of investment that the
latter question is the relevant one.
Some idiosyncratic notational conventions deserve immediate mention:
X = Total Expenditures, aka nominal GDP, aka Aggregate Demand
Y = nominal Income
E = exports
F = Imports
Cd = domestic Consumption = C - F (on the simplifying assumption that all imports are consumer goods.)
M = money supply
III. THE HAND-DRAWN MODELS
In this section I will demonstrate some uses of the diagrams
that are suitable to a lecture presentation. I will start by
doing a comparison of the Keynesian and monetarist views
of an increase of spending by a sector.
PrM
X
Injections
I+G+E
Cd
The open model is used to present Keynesian theory. The
diagram, shown in Figure 3, incorporates onto the circular
S+T+F
Leakages
flow the notions of leakages and injections. A numerical
H/B Y
example begins by placing the initial values onto the
Figure 3. The Open Model
diagram, as in Figure 4. I always use the same initial values,
shown in Appendix 3. Note that, for this example, the model has been simplified to include only one
Leakage (S) and one Injection (I). It is stressed that all the numbers must add
1010
up according to Y = C + Leakages and
1000
1000
410
PrM
PrM
X = C + Injections. The problem asks the
400
400
student to increase Investment by $10. The
results are shown in Figure 5. We see that the
600
600
increased spending has resulted in a rise of
aggregate demand (X). This is initially
interpreted as an economic expansion and “a
400
400
H/B
H/B
good thing according to this model.”
1000
1000
Figure 4. An Open Model Example
Figure 5. Increased Injections
To multiply or not. At this point one has a choice. You can trace the effect of the increased spending
around the circuit several times and derive the multiplier effect, as higher spending means more income,
which means more consumption and so on. Or you can merely note that the model’s prediction is that an
increase of spending (investment, in this case) will induce an economic expansion. My method is to
briefly trace out the multiplier effect once -- because a good student almost certainly notices the
possibility -- and then say that we will content ourselves with noting the rise of aggregate demand,
without tracing its magnitude. (The computerized version includes a module for deriving the multiplier. I
rarely use it). The structure of all problems thereafter is to stop the analysis once the change (or lack
thereof) of X has been noted. This introduces into this method two elements uncomfortable to most
economics teachers. First, Income is (until much later) treated as an exogenous variable, rather than the
object of analysis. Second, the problems do not end in equilibrium. I’ve gotten used to both issues.
My justification for the cavalier disregard for equilibrium and multipliers deserves a quick defense. I find
the most compelling point to be made in a presentation of Keynesian theory is that an exogenous increase
in spending induces an economic expansion and is “good for the economy.” The size of the effect strikes
me as an issue of secondary importance (actually capable of distracting from the essential point).
Furthermore, I think the faith in multipliers has subsided somewhat over the years.
Extensions Starting with this simple problem, a variety of examples can be
used to introduce Keynesian views on issues of savings, investment, fiscal
policy, foreign trade and general philosophy. Figure 6 illustrates an increase
of leakages. The basic use of all the diagrams is also established. As is
typical of economics problems, we begin with the system in equilibrium,
introduce a change, compare the initial state with the outcome, and interpret
the result.
PrM
990
1000
400
600
590
H/B
410
400
1000
Figure 6. Increased Leakages
The closed model is used to present
PrM
X
classical/monetarist theory. While the open model
G
generates decidedly “liberal” conclusions,
E
I
particularly as regards the efficacy of
FxM
CrM
Cd
Trsy
K
B
expansionary fiscal policy, the closed model -d
shown in Figure 7 -- presents the other version of
F
S
T
economic theory. In these models, aggregate
demand never changes -- it always remains equal
H/B
Y
to initial level of income (until money is added to
Figure 7. The Closed Model
the model). The model concentrates on the concept
of opportunity cost by showing changes in one sector’s
The Closed Model notations are:
spending as inevitably being offset by the crowding out of
CrM = The Credit Market
some other sector’s spending. This diagram is introduced a bit FxM = The Foreign Exchange Market
at a time, starting with the “Basic” model that includes only
Trsy = The Government Treasury
the product and credit markets, then adding the Treasury to
K = Foreign Financial Capital Flows
examine fiscal policy, and finally adding the foreign sector to
B = Budget Balance
discuss trade and international capital flows. For most foreign
sector problems, I take the Treasury off. In fact, the entire diagram is fairly rarely used.
To illustrate the use, and political flavor, of the diagram, we
can start by putting numbers on the diagram -- as in Figure
8 -- and then analyze the effect of an increase of
government spending -- as in Figure 9. Important to the use
of the closed model is that the numbers into and out of each
“node” -- the Treasury and the markets -- must add up. For
example, dollars into the credit market must equal dollars
out of the credit market.
Quite a different result emerges than came from the open
model. The increase of the deficit is shown here as
crowding out investment by diverting funds from the
credit market. Prior discussions of the role of investment
on growth are used to suggest that this model criticizes
deficit spending for its anti-growth potential.
1000
PrM
600
H/B
200
200
CrM
Trsy
200
200
1000
Figure 8. Values on the Closed Model
PrM
1000
200
190
CrM
600
200
210
0
-10
Trsy
200
200
Comparison of the Open and Closed Models. In a
H/B
1000
variety of contexts the open and closed models disagree as
to the effects of given policies. For example, expansionary
Figure 9. A Change of Gov’t Purchases
fiscal policy will generate increases in aggregate demand
in the open model, in keeping with Keynesian analysis. In the closed model, in keeping with monetarist
conclusions, the same policy will crowd out investment, with a presumably detrimental effect of future
growth, and leave aggregate demand unaffected. A great power of these diagrams is the capability of fast
side-by-side comparisons of competing theories on a wide variety of issues.
The tax rule is used in analyzing the effect of tax
changes. It is arbitrarily decided that, for every $4 change
of taxes, savings will change by $1 and consumption by
$3. This produces the effect that changes of government
spending are, per dollar, more powerful than tax changes
either for harm or good. Most of us were introduced to this
concept via the differing sizes of the tax and spending
multipliers. See Figures 10 and 11 for examples. It is
instructive to work these problems making different
assumptions about the propensity to consume out of a tax
cut, since the results are the stuff of political debates. The
same tax rule can be applied to both the open and closed
models to, again, illustrate a variety of viewpoints.
PrM
1000
1006
200
200
200
202
200
192
600
606
H/B
1000
Figure 10. An $8 Tax Decrease, Open Model
PrM
1000
200
194
600
606
H/B
CrM
200
202
200
0
-8
Trsy
200
192
1000
Figure 11. An $8 Tax Decrease, Closed Model
The twin deficits problem is a fairly
sophisticated use of the full closed model. In
this application, an increase of government
deficit is financed by foreign capital flows. This
leaves foreigners with fewer dollars with which
to purchase our exports and a trade deficit
results. See Figure 12.
PrM
X
100
90
FxM
H/B
10
CrM
-10
200
210
Trsy
Y
Figure 12. The Twin Deficits
MONEY
The next major class of models extends the tool to
include two new elements, as shown in Figure 13:
I
G
A box labeled “Fed” to indicate the Federal
Reserve Board and a box labeled “Cash” to
CrM
BB
Trsy
C
illustrate the demand for liquidity. These models
act like open models in that it is possible for
dMD
dMS
aggregate demand to change as the result of
T
S
Cash
Fed
changes of either the money supply or money
H/B
Y
demand. I refer to these as “money models” to
Figure 13. The Money Model
avoid the “open” versus “closed” vocabulary. The
dual-headed arrows indicate that money supply and demand can both rise or fall. As with the previous
models, one can use less than the full model. The model shown in Figure 13, for example, excludes the
foreign exchange market.
PrM
X
The Cash box is the most problematic part of the diagram. It is an attempt to describe the velocity of
money -- here assumed inversely related to the demand for money. An increase of the velocity of money
is shown as money coming out of the Cash box; a decrease of velocity ids shown as money entering the
Cash box. Classical theory is illustrated merely by omitting the Cash box and therefore disallowing any
velocity change.
As proficiency with the models grows, it becomes unnecessary to put all the numbers on them. Instead, it
is only necessary to include the changes of values. This results in significantly cleaner diagrams. The
following examples illustrate a few of the issues that can be portrayed in this fashion.
PrM
+5
.
PrM
+5
+5
+5
CrM
CrM
+5
+5
H/B
Trsy
+5
Fed
Fed
1. Printing money raises aggregate
demand
H/B
2. The deficit rises and the Fed monetizes the
debt. Expansionary monetary policy looks
like expansionary fiscal policy.
PrM
PrM
+5
+0
+5
CrM
CrM
+5
Trsy
-5
-5
Cash
Cash
H/B
3. The deficit rises and the public buys the bonds
by reducing Cash. The velocity of money is
increased; spending rises. This is the scenario in
which fiscal policy is actually expansionary.
Cash
-5
Fed
H/B
4. The Fed reduces the money supply – hoping to
cause a recession that will end inflation – and the
public sends out of Cash. The recession does not
happen, or is, at least, delayed.
Let me suggest that some of the scenarios and issues described in these examples are fairly sophisticated
and yet are conveyed quite simply by these diagrams. Furthermore I contend that, at least for some
students, the ability to draw diagrams of situations is useful. We certainly operate of that assumption in
teaching supply and demand analysis.
III. THE COMPUTER MODELS
Computerized versions of these models, dubbed CirF, have been developed and are available online at
http://gnet.acad.gc.maricopa.edu/cirf/cirf/CFFrame.htm and as a download at
http://staff.gc.maricopa.edu/~hkvaran/Macro. The two versions operate essentially the same with a few
minor differences. Computerization led to some interesting pedagogical choices and some significant
extensions of the models. CirF operates in two distinct modes: Flag Mode and Market Mode. I discuss
them each in turn.
FLAG MODE allows the user to enter values for any of the macro variables onto a circular flow
diagram. The program responds with “flags” that change color to alert the user that some values do not
add up. Changing Consumption, for instance, will elicit flags indicating that the equations X = C + I + G
and Y = C + S + T do not hold. The user then adjusts other values to eliminate all flags. This produces a
description of the effects of the initial change.
There is something pedagogically interesting here: the user is told that something is not right and then is
left to discover how to fix it. It is easy to create problems that have multiple solutions, but it is always
possible to constrain the statement of the problem to allow only a single correct answer.
The Open Market Flags are:
Y = Cd + S + T + F (Uses of Income)
X = Cd + I + G + E (Sources of Spending)
Tnet = G + B (Government Budget. Tnet = Taxes, net of Transfer Payments)
The Closed Market adds to the above flags:
S + K + B = I (Credit Market Equilibrium)
E + K = F (Foreign Exchange Market Equilibrium)
The Money Models modify the Credit Market equilibrium condition to:
S + K + B +∆MS= I + ∆MD (Credit Market Equilibrium)
The Open Model
This screen print illustrates an increase
of G of 10. Flags are on at the boxes
for X Spending (because X ≠ C + I +
G) and for Government Treasury
(because T ≠ G + B). The problem
would be completed by entering 10 at
X and -10 at B.
The Closed Model
This illustrates a rise of Imports of 10.
Flags are “on” at The Foreign
Exchange Market (Imports ≠ Exports
plus Foreign Capital) and at Y Income
(the uses of income are currently
greater than income.). There are a
variety of ways to complete this
problem. One solution would be:
reduce domestic consumption by 10,
raise Foreign Capital by 10, increase
Investment by 10.
Money Model
This example shows an increase of the money
supply of 10. Possible solutions are:
increase Investment and Spending by 10,
illustrating an expansion, or
increase liquidity by 10 as the public hoards the
extra liquidity, illustrating a Keynesian liquidity
trap.
MARKET MODE incorporates supply and demand graphs into the circular flow diagram. In this mode
the user enters an exogenous change, or changes, and the model displays the results either via graphs or
tables of hypothetical numbers. This mode also adds variables such as energy costs, technological change
and labor force growth rate as user determined values. Results are displayed for short, medium and long
time horizons.
Here we see the result of an increase of
the money supply: an increase of supply
in the credit market, causing a capital
outflow as interest rates fall. Aggregate
demand and the demand for labor rise.
In this example we have increased the
rate of technical growth from 2% to
3%. The results are displayed for the
medium and long runs as tables of
numbers.
APPENDIX. NOTATION AND VALUES FOR THE VARIABLES.
TABLE 1. NOTATION
Abbreviation Stands for…
Abbreviation
B
Gov’t Budget Balance
I
C
Consumption
K
CrM
Credit Market
LaM
∆MD
Change of Money Demand PrM
∆MS
Change of Money Supply
S
E
Exports
T
F
Imports
Tn
Fed
The Federal Reserve
TP
FxM
Foreign Exchange Market
Trsy
G
Government Purchases
X
H/B
Households & Businesses
Y
Stands for…
Investment
Foreign Financial Capital Flows
Labor Market
Product Market
Saving
Taxes
Taxes, net of Transfers
Transfer Payments
The Government Treasury
Total Expenditures (Agg. Demand)
Income Received by Private Sector
Values
I have found it useful to always use the same sets of starting numbers for the examples. Those values,
however, depend on the variables included in the problem. The very presentation of these numbers
presents a variety of challenges and opportunities. One may discuss the trade-off between simplicity and
correctness (A quote attributed to Einstein is, “You can be correct or you can be clear, but not both.”).
One may present more accurate numbers. My strategy has been to use numbers that are easy, and then to
use real data to point out the inaccuracies of the hypothetical values. Incidentally, if the numbers for
saving seem unrealistically large, consider that saving includes business saving, particularly capital
consumption allowances. The values I use are summarized below.
TABLE 2. VALUES USED
Income (Y)
Consumption (C)
Domestic Consumption (Cd)
Saving (S)
Investment (I)
Taxes (T)
Government Purchases (G)
Budget Balance (BB)
Imports (F)
Exports (E)
Foreign Capital Flows (Kf)
Total Expenditures (X)
Basic
1000
600
NA
400
400
NA
NA
NA
NA
NA
NA
1000
VARIATION
Treasury
Foreign
1000
1000
600
600
NA
500
200
400
200
400
200
NA
200
NA
0
NA
NA
100
NA
100
NA
0
1000
1000
Full
1000
600
500
200
200
200
200
0
100
100
0
1000