Question

Based on the simplified model of a choice between a domestic currency deposit in dollars and a foreign currency deposit in Euros, illustrate and explain the derivation of the AA curve of Krugman-Obstfeld-Melitz. What does the AA curve represent?

Answer 1

The AA curve show the relationship between the exchange rate and equilibrium GNP. The foreign exchange market, depicted in the top part of Figure 9.4 "Derivation of the AA Curve", plots the rates of return on domestic U.S. assets (RoR$) and foreign British assets (RoR£). The domestic U.S. money market, in the lower quadrant, plots the real U.S. money supply (M$S/P$) and real money demand (L(i$, Y$)). The asset market equilibriums have several exogenous variables that determine the positions of the curves and the outcome of the model. These exogenous variables are the foreign British interest rate (i£) and the expected future exchange rate (E$/£e), which influence the foreign British rate of return (RoR£); the U.S. money supply (M$S) and domestic U.S. price level (P$), which influence real money supply; and U.S. GNP (Y$), which influences real money demand. The endogenous variables in the asset model are the domestic interest rates (i$) and the exchange rate (E$/£).

Initially, let’s assume GNP is at a value in the market given by Y$1. All the other exogenous variables that affect the asset market are also at some initial level such as i£1, E$/£e1, M$ S1, and P$1. The real money demand function with GNP level Y$1 intersects with real money supply at point G1 in the money market diagram determining the interest rate i$1. The interest rate, in turn, determines RoR$1, which intersects with RoR£ at point G2, determining the equilibrium exchange rate E$/£1. These two values are transferred to the lowest diagram at point G, establishing one point on the AA curve (Y$1, E$/£1).

Now, GNP rises from Y$1 to Y$, ceteris paribus. The ceteris paribus assumption means that all exogenous variables in the model remain fixed. Since the increase in GNP raises real money demand, L(i$, Y$), it shifts out to L(i$, Y$2). The equilibrium shifts to point H1, raising the equilibrium interest rate to i$2. The RoR$ line shifts right with the interest rate, determining a new equilibrium in the Forex at point H2 with an equilibrium exchange rate E$/£2. These two values are then transferred to the diagram below at point H, establishing a second point on the AA curve (Y$2, E$/£2).

The line drawn through points G and H on the lower diagram in Figure 9.4 "Derivation of the AA Curve" is called the AA curve.

The AA curve plots an equilibrium exchange rate level for every possible GNP value that may prevail, ceteris paribus. Every point on an AA curve represents an equilibrium value in the money- Forex market. The AA curve is negatively sloped because an increase in the real GNP lowers the equilibrium exchange rate in the money-Forex model.