International Finance Theory and Policy
by Steven M. Suranovic
Finance 601

Derivation of the DDCurveThe DDcurve 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_{$}). Aggregate demand (AD) is measured along the vertical axis and aggregate supply (GNP) is measured on the horizontal axis. As discussed in Section 506, the AD function is dependent upon several different exogenous variables, most notably the exchange rate between domestic and foreign currency (E_{$/£}). 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_{$/£}, ...), where the ... is meant to indicate there are other unspecified variables that also influence AD.
Initially, let’s assume the exchange rate is at a value in the market given by E^{1}_{$/*}. 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_{$/£}^{1}, I^{1}, G^{1}, T^{1}, TR^{1}, P_{$}^{1}, P_{£}^{1}). The AD function with exchange rate E^{1}_{$/£} intersects the 45°line at point G which determines the equilibrium level of GNP given by Y_{$}^{1}. These two values are transferred to the lower diagram at point G determining one point on the DDcurve (Y_{$}^{1}, E_{$/£}^{1}). Next, suppose E_{$/£} rises from E_{$/£}^{1} to E_{$/£}^{2}, ceteris paribus. This corresponds to a depreciation of the US dollar with respect to the British pound. The ceteris paribus assumption means that investment, government, taxes, etc. , stay fixed at levels I^{1}, G^{1}, T^{1}, etc. Since a dollar depreciation makes foreign G&S relatively more expensive and domestic goods relatively cheaper, AD shifts up to AD(E_{$/£}^{2}, ...). The equilibrium shifts to point H at a GNP level Y_{$}^{2}. These two values are transferred to the lower diagram at point H determining a second point on the DDcurve (Y_{$}^{2}, E_{$/£}^{2}). The line drawn through points G and H on the lower diagram is called the DDcurve. The DDcurve plots an equilibrium GNP level for every possible exchange rate that may prevail, ceteris paribus. Stated differently, the DDcurve is the combination of exchange rates and GNP levels that maintain equilibrium in the G&S market, ceteris paribus. We can think of is as the set of aggregate DDemand equilibria. A note about equilibria An equilibrium in an economic model typically corresponds to a point towards which the endogenous variable values will converge based on some behavioral assumption about the participants in the model. In this case, equilibrium is not represented by a single point. Instead every point along the DDcurve is an equilibrium value. If the economy were at a point off of the DDcurve, like at I in the lower diagram above, the exchange rate is E_{$/£}^{2} and the GNP level is at Y_{$}^{1}. This corresponds to point I in the upper diagram above where AD > Y, read off the vertical axis. In the G&S model whenever aggregate demand exceeds aggregate supply, producers respond by increasing supply causing GNP to rise. This continues until AD = Y at point H. For all points to the left of the DDcurve, AD > Y, therefore the behavior of producers would cause a shift to the right from any point like I to a point like H on the DDcurve. Similarly, at a point such as J, to the right of the DDcurve, the exchange rate is E_{$/£}^{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 DDcurve, 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 DDcurve. A useful analogy is to think of the DDcurve as a river flowing through a valley. (See adjoining 3D 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 DDcurve. International Finance Theory and Policy  Chapter 601: Last Updated on 3/20/05 