# 9.8: AA-DD and the Current Account Balance

- Page ID
- 25382

Learning objective

- Derive a graphical mechanism in the AA-DD model to represent the effects of changes in the superequilibrium on the current account balance.

In later chapters we will use the AA-DD model to describe the effects of policy changes on macroeconomic variables in an open economy. The two most important macro variables are the exchange rate and the current account (trade) balance. The effects of changes on the exchange rate are vividly portrayed in the AA-DD diagram since this variable is plotted along the vertical axis and its value is determined as an element of the equilibrium. The current account (CA) variable is not displayed in the AA-DD diagram, but with some further thought we can devise a method to identify the current account balance at different positions in the AA-DD diagram.

First, note that there is no “equilibrium” current account
balance in a floating exchange rate system. Any balance on the
current account is possible because any balance can correspond to
balance on the balance of payments. The balance of payments is made
up of two broad subaccounts: the current account and the financial
account, the sum of whose balances must equal zero. When the
balances sum to zero, the foreign demand for domestic goods,
services, income, *and* assets is equal to
domestic supply of goods, services, income, and assets. Thus there
must always be “balance” on the balance of payments regardless of
the balances on the individual subaccounts.

## Iso-CAB Line

An **iso-CAB line** is a line drawn on an
AA-DD diagram, Figure 9.8.1 , representing a set of
points along which the current account balance (CAB) is the same.
Note that “iso” is a prefix that means *the same*. In
the adjoining diagram, we have superimposed three-dotted iso-CAB
lines labeled *\(CC\)*, *\(C'C'\)*,
and *\(C^{"}C^{"}\)*. Each line represents a set of GNP
and exchange rate combinations that generate the same balance on
the current account. The higher the CAB line, the larger is the
balance on the current account. Thus the CAB balance
on *\(C^{"}C^{"}\)* is greater than the balance
along *\(CC\)*. Also note that each CAB line is
positively sloped with a slope less than the slope of the DD curve.
Next, we’ll continue with a justification for this description.

Figure \(\PageIndex{1}\): Iso-CAB Lines in an AA-DD Diagram

## Justifying the Shape of the Iso-CAB Line

Consider the superequilibrium point at the intersection of AA
and DD. The positions of these two curves are determined by the
values of the exogenous variables in the model, including the
domestic price level (*\(P_{$}\)*), the foreign price level
(*\(P_{£}\)*), tax revenues (*\(T\)*), and transfer
payments (*\(TR\)*), among others. The intersection of the
two curves determines the equilibrium GNP level
(*\(Y_{$}\)*) and the exchange rate (*\(E_{$/£}\)*)
(not labeled in diagram). Recall from __Chapter 9 "The AA-DD
Model"__, __Section 9.2 "Derivation of the DD
Curve"__ that the DD curve is derived from the aggregate
demand function, one component of which is the current account
function. The current account function, as shown below, is a
function of all the variables listed immediately above:

Thus at the intersection of AA and DD there are presumed known
values for the exogenous variables and determined values for the
endogenous
variables, *\(E_{$/£}\)* and *\(Y_{$}\)*.

All these values could, in principle, be plugged into the
current account demand function (*\(CA^{D}\)*) to determine
the CA balance at the equilibrium. Let’s assume that value is given
by *K*, as shown in the above expression.

Now let’s consider movements in the superequilibrium to other
points on the diagram. Let’s suppose that the equilibrium moved to
point *x* directly to the right. That could arise
from a rightward shift of DD and an upward shift of AA. We will
also assume that this shift did not arise due to changes
in *\(P_{$}\)*, *\(P_{£}\)*, *\(T\)*,
or *\(TR\)*, the other exogenous variables that affect
the current account. (More on this issue below.) One possibility is
an increase in the money supply and an increase in investment
demand. Note that these shifts are not depicted.

At point *x*, GNP is higher while the exchange rate
and the other exogenous variables are the same as before. Since an
increase in *\(Y_{$}\)* raises disposable income,
which reduces current account demand, the current account balance
must be at a lower level at point *x* compared to
the initial equilibrium.

If the equilibrium had shifted to
point *z* instead, then GNP is lower while the
exchange rate and the other exogenous variables are the same as
before. Since a decrease in *\(Y_{$}\)* lowers
disposable income, which raises current account demand, the current
account balance must be at a higher level at
point *z* compared to the initial equilibrium.

Next, suppose the equilibrium had shifted to
point *y* instead. In this case, the exchange rate
(*\(E_{$/£}\)*) is lower while GNP and the other exogenous
variables are the same as before. Since a decrease
in *\(E_{$/£}\)* reduces the real exchange rate,
which reduces current account demand, the current account balance
must be at a lower level at point *y* compared to
the initial equilibrium.

Finally, suppose the equilibrium had shifted to
point *w*. In this case, the exchange
rate, *\(E_{$/£}\)*, is higher while GNP and the other
exogenous variables are the same as before. Since an increase
in *\(E_{$/£}\)* raises the real exchange rate,
which increases current account demand, the current account balance
must be at a higher level at point *y* compared to
the initial equilibrium.

Since a movement
to *w* and *z* results in an
increase in the current account balance, while a shift
to *x* or *y* causes a reduction
in the balance, the line representing a constant CAB must be
positively sloped.

Another way to see this is to use
the *\(CA^{D}\)* function above. Suppose the CAB
is originally at the value *K*. If the exchange rate
(*\(E_{$/£}\)*) rises, ceteris paribus, then CA will rise.
We can now ask how GNP would have to change to get back to a CA
balance of *K*. Clearly, if *Y* rises,
disposable income rises and the current account balance falls.
Raise GNP by precisely the right amount, and we can get the CAB
back to *K*. Thus an increase
in *\(E_{$/£}\)* must accompany an increase in GNP
to maintain a fixed current account balance and therefore an
iso-CAB line must be positively sloped.

The last thing we need to show is that the iso-CAB line is less
steeply sloped than the DD line. Suppose the economy moved to a
point such as *v*, which is on the same DD curve as the
original superequilibrium. Recall from __Chapter 9 "The AA-DD
Model"__, __Section 9.2 "Derivation of the DD Curve"__,
the DD curve is derived from a change in the exchange rate and its
effect on equilibrium GNP in the G&S market alone. The increase
in the exchange rate causes an increase in current account demand
through its effect on the real exchange rate. This causes an
increase in aggregate demand, which inspires the increase in GNP.
When equilibrium is reached in the G&S market, at
point *v*, aggregate supply, *Y*, will
equal aggregate demand and the following expression must hold:

The left side is aggregate supply given by the equilibrium value
at point *v* and the right side is aggregate
demand. Since GNP is higher at v, consumption demand
(*\(C^{D}\)*) must also be higher. However, because the
marginal propensity to consume is less than one, not all the extra
GNP will be spent on consumption goods; some will be saved.
Nevertheless, aggregate demand (on the right side) must rise up to
match the increase in supply on the left side. Since all the
increase in demand cannot come from consumption, the remainder must
come from the current account. This implies that a movement along
the DD curve to *v* results in an increase in the
current account balance. It also implies that the iso-CAB line must
be less steeply sloped than the DD curve.

## Using the Iso-CAB Line

The iso-CAB line can be used to assess the change in the
country’s current account balance from any exogenous variable
change except changes
in *\(P_{$}\)*, *\(P_{£}\)*, *\(T\)*,
and *\(TR\)*. The reason we must exclude these
variables is because the current account demand function is also
dependent on these exogenous variables. If tax revenues increased,
for example, all the iso-CAB lines would shift, making it much more
difficult to pinpoint the final effect on the current account
balance.

However, for monetary policy changes and government spending
fiscal policy changes, the iso-CAB line will work. Anytime the
superequilibrium shifts above the original iso-CAB line, the
economy will move onto another iso-CAB line with a higher balance.
(This is like the shift to point *v* in
Figure 9.8.1 .) Recall that the *\(CA = EX -
IM\)*, which can be positive or negative. If CAB were in
surplus originally, an increase in the CAB (as with a movement
to *v*) would imply an increase in the CA surplus.
However, if the CAB were in deficit originally, then an increase in
CAB implies a reduction in the deficit. If the increase in the CAB
were sufficiently large, the CAB could move from deficit to
surplus.

In a similar way, anytime the superequilibrium shifts below an initial iso-CAB line, the CAB surplus will fall, or the CAB deficit will rise.

Remember that the iso-CAB line is only used a reference to track the current account balance. The iso-CAB line is not used to determine the superequilibrium. For this reason, the iso-CAB line is plotted as a dashed line rather than a solid line.

key takeaways

- An iso-CAB line is a line drawn on an AA-DD diagram, representing a set of points along which the current account balance (CAB) is the same.
- An iso-CAB line is positively sloped and with a slope that is less than the slope of the DD curve.
- The iso-CAB line can be used to assess the change in the
country’s current account balance from any exogenous variable
change except changes
in
*\(P_{$}\)*,*\(P_{£}\)*,*\(T\)*, and*\(TR\)*.

exercise

**Jeopardy Questions**. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”- Of
*greater than*,*less than*, or*equal*, the current account balance for an exchange rate and GNP combination that lies above an iso-CAB line relative to a combination that lies on the line. - Of
*greater than*,*less than*, or*equal*, the current account surplus for an exchange rate and GNP combination that lies below an iso-CAB line relative to the surplus for a combination that lies on the line. - Of
*greater than*,*less than*, or*equal*, the current account deficit for an exchange rate and GNP combination that lies below an iso-CAB line relative to the deficit for a combination that lies on the line. - Of
*higher*,*lower*, or*equal*, the position of an iso-CAB line for a country with a current account deficit relative to an iso-CAB line when the country runs a surplus. - Of
*positive*,*negative*, or*zero*, this describes the slope of an iso-CAB line. - Of
*steeper*,*flatter*, or*the same*, this describes an iso-CAB line relative to a DD curve.

- Of