International Finance Theory and Policy
by Steven M. Suranovic

Finance 60-1

Derivation of the DD-Curve

The DD-curve is derived by transferring information described in the G&S market model onto a new diagram to show the relationship between the exchange rate and equilibrium GNP. The original G&S market, depicted in the top part of the adjoining diagram, plots the aggregate demand function (AD) with respect to changes in US GNP (Y$). Aggregate demand (AD) is measured along the vertical axis and aggregate supply (GNP) is measured on the horizontal axis. As discussed in Section 50-6, the AD function is dependent upon several different exogenous variables, most notably the exchange rate between domestic and foreign currency (E$/£). However, AD is also affected by investment demand (I), government demand (G), government tax revenues (T), government transfer payments (TR), and the price level in the domestic (P$) and foreign (P£) countries. The endogenous variable in the model is US GNP, Y$. (See the table below for easy reference.) In this exercise, since our focus is on the exchange rate, we label the AD function in the adjoining diagram as AD(E$/£, ...), where the ... is meant to indicate there are other unspecified variables that also influence AD.

G&S Market

Exogenous Variables

E$/£I††† GTTR P$††† P£

Endogenous Variable

Y$

Initially, letís assume the exchange rate is at a value in the market given by E1$/*. We need to remember that all of the other variables that affect AD are also at some initial level. Written explicitly we could write AD as AD(E$/£1, I1, G1, T1, TR1, P$1, P£1). The AD function with exchange rate E1$/£ intersects the 45į-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$/£2, ceteris paribus. This corresponds to a depreciation of the US dollar with respect to the British pound. The ceteris paribus assumption means that investment, government, taxes, etc. , stay fixed at levels I1, G1, T1, etc. Since a dollar depreciation makes foreign G&S relatively more expensive and domestic goods relatively cheaper, AD shifts up to AD(E$/£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 is as the set of aggregate DDemand equilibria.

A note about equilibria

An equilibrium in an economic model typically corresponds to a point towards 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 off of the DD-curve, like at I in the lower diagram above, the exchange rate is E$/£2 and the GNP level is at Y$1. This corresponds to point I in the upper diagram above 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 and hence 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 adjoining 3-D diagram). The hills rise up to the right and left.along the upward sloping DD curve. Just as gravity will move a drop of water down the hill to the river valley, so in much the same way, firm behavior will move GNP, right or left to the lowest point along the DD-curve.

International Finance Theory and Policy - Chapter 60-1: Last Updated on 3/20/05

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