# 9.2: Derivation of the DD Curve

- Page ID
- 20264

learning objective

- Learn how to derive the DD curve from the G&S model.

The DD curve is derived by transferring information described in
the goods and services (G&S) market model onto a new diagram to
show the relationship between the exchange rate and equilibrium
gross national product (GNP). The original G&S market, depicted
in the top part of Figure 9.2.1 , plots the aggregate
demand (*\(AD\)*) function with respect to changes in
U.S. GNP (*\(Y_{$}\)*). Aggregate demand is measured along
the vertical axis and aggregate supply (or the GNP) is measured on
the horizontal axis. As discussed in Figure
9.2.1 as *\(AD(E_{$/£}, …)\)*, where the
ellipsis (…) is meant to indicate there are other unspecified
variables that also influence *\(AD\)*.

Exogenous Variables |
\(E_{$/£}\), \(I\), \(G\),\(T\), \(TR\), \(P_{$}\),\(P_{£}\) |

Endogenous Variable | \(Y_{$}\) |

Table \(\PageIndex{1}\): G&S Market

Figure \(\PageIndex{1}\): Derivation of the DD Curve

Initially, let’s assume the exchange rate is at a value in the
market given by *\(E_{$/*}^{1}\)*. We need to remember
that all the other variables that affect AD are also at some
initial level. Written explicitly, we could write AD
as *\(AD(E_{$/£}^{1}, I^{1}, G^{1}, T^{1}, TR^{1},
P_{$}^{1}, P_{£}^{1})\)*. The AD function with exchange
rate *\(E_{$/£}^{1}\)* intersects the
forty-five-degree line at point *G* which
determines the equilibrium level of GNP given
by *\(Y_{$}^{1}\)*. These two values are transferred to
the lower diagram at point *G* determining one
point on the DD curve
(*\(Y_{$}^{1}\)*, *\(E_{$/£}^{1}\)*).

Next, suppose *\(E_{$/£}\)* rises
from *\(E_{$/£}^{1}\)* to *\(E_{$/£}^{2}\)*,
ceteris paribus. This corresponds to a depreciation of the U.S.
dollar with respect to the British pound. The ceteris paribus
assumption means that investment, government, taxes, and so on stay
fixed at
levels *\(I^{1}\)*, *\(G^{1}\)*, *\(T^{1}\)*,
and so on. Since a dollar depreciation makes foreign G&S
relatively more expensive and domestic goods relatively cheaper, AD
shifts up to *\(AD(E_{$/£}^{2}, …)\)*. The equilibrium
shifts to point *\(H\)* at a GNP
level *\(Y_{$}^{2}\)*. These two values are transferred
to the lower diagram at point *\(H\)*, determining a
second point on the DD curve
(*\(Y_{$}^{2}\)*, *\(E_{$/£}^{2}\)*).

The line drawn through
points *\(G\)* and *\(H\)* on the
lower diagram is called the DD curve. The DD curve plots an
equilibrium GNP level for every possible exchange rate that may
prevail, ceteris paribus. Stated differently, the DD curve is the
combination of exchange rates and GNP levels that maintain
equilibrium in the G&S market, ceteris paribus. We can think of
it as the set of aggregate demand equilibriums.

## A Note about Equilibriums

An equilibrium in an economic model typically corresponds to a point toward which the endogenous variable values will converge based on some behavioral assumption about the participants in the model. In this case, equilibrium is not represented by a single point. Instead every point along the DD curve is an equilibrium value.

If the economy were at a point above the DD curve, say,
at *I* in the lower diagram, the exchange rate
would be *\(E_{$/£}^{2}\)* and the GNP level
at *\(Y_{$}^{1}\)*. This corresponds to
point *\(I\)* in the upper diagram where *\(AD
> Y\)*, read off the vertical axis. In the G&S model,
whenever aggregate demand exceeds aggregate supply, producers
respond by increasing supply, causing GNP to rise. This continues
until *\(AD = Y\)* at
point *\(H\)*. For all points to the left of the DD
curve, *\(AD > Y\)*, therefore the behavior of
producers would cause a shift to the right from any point
like *\(I\)* to a point
like *\(H\)* on the DD curve.

Similarly, at a point such as *\(J\)*, to the right
of the DD curve, the exchange rate
is *\(E_{$/£}^{1}\)* and the GNP level is
at *\(Y_{$}^{2}\)*. This corresponds to
point *\(J\)* in the upper diagram above where
aggregate demand is less than supply (*\(AD < Y\)*). In
the G&S model, whenever supply exceeds demand, producers
respond by reducing supply, thus GNP falls. This continues
until *\(AD = Y\) *at
point *\(G\)*. For all points to the right of the DD
curve, *\(AD < Y\)*, therefore the behavior of
producers would cause a shift to the left from any point
like *\(J\)* to a point
like *\(G\)* on the DD curve.

A useful analogy is to think of the DD curve as a river flowing through a valley. (See the 3-D diagram in Figure 9.2.2 .) The hills rise up to the right and left along the upward-sloping DD curve. Just as gravity will move a drop of water downhill onto the river valley, firm behavior will move GNP much in the same way: right or left to the lowest point along the DD curve.

Figure \(\PageIndex{2}\):* A 3-D
DD Curve*

key takeaways

- The DD curve plots an equilibrium GNP level for every possible exchange rate that may prevail, ceteris paribus.
- Every point on a DD curve represents an equilibrium value in the G&S market.
- The DD curve is positively sloped because an increase in the exchange rate (meaning a decrease in the U.S. dollar value) raises equilibrium GNP in the G&S model.

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?”- This is what has happened to its currency value if an economy’s exchange rate and GNP combination moves upward along an upward-sloping DD curve.
- Of
*greater than*,*less than*, or*equal to*, this is how aggregate demand compares to GNP when the economy has an exchange rate and GNP combination that places it to the left of the DD curve. - Of
*greater than*,*less than*, or*equal to*, this is how aggregate demand compares to GNP when the economy has an exchange rate and GNP combination that places it on the DD curve. - The equilibriums along a DD curve satisfy this condition.