Adjustment to the Super-Equilibrium

In order to discuss adjustment to the super-equilibrium, we must first talk about how an economy can end up out of equilibrium. This will occur anytime there is a change in one or more of the exogenous variables that cause the AA or DD-curves to shift. In a real economy, we should expect these variables to be changing frequently. Variables such as interest rates will certainly change every day. A variable such as the average expected future exchange rate held by investors probably changes every minute. Each time an exogenous variable changes, the super equilibrium point will shift setting off behavioral responses by households, businesses and investors that will affect the exchange rate and GNP in the direction of the new super-equilibrium. However, as we will indicate below, the adjustment process will take time, perhaps several months or more, depending on the size of the change. Since we should expect that as adjustment to one variable change is in process, other exogenous variables will also change, we must recognize that the Super-equilibrium is really like a moving target. Each day, maybe each hour, the target moves setting off a continual adjustment process.

Despite the fact that, in the real-world economy, an equilibrium may never be reached, the model remains very useful in understanding how changes in some variables will affect the behavior of agents and influence other variables. The model in essence offers us the opportunity to conduct experiments in simplified settings. Changing one exogenous variable and inferring its effect is a comparative statics experiment because of the ceteris paribus assumption. Ceteris paribus allows us to isolate one change and work through its impact with certainty that nothing else could be influencing the result.

Below we'll consider adjustment to two changes; a reduction in investment demand which shifts the DD curve, and an increase in foreign interest rates, which shifts the AA curve.

Reduction in Investment

Consider adjustment to a decrease in investment demand. Begin with an original super-equilibrium where DD crosses AA at point F with GNP at Y_$¹ and exchange rate at E_$/£¹. When investment decreases, ceteris paribus, the DD-curve shifts to the left, as was shown in section 60-2. This shift is shown in the adjacent diagram as a shift from DD to D’D’.    

The quick result is that the equilibrium shifts to point G, GNP falls to Y_$³ and the exchange rate rises to E_$/£³. The increase in the exchange rate represents a depreciation of the US $ value. However, this result does not explain the adjustment process so let’s take a more careful look at how the economy gets from point F to G.

Step 1) When investment demand falls, aggregate demand falls short of aggregate supply leading to a buildup of inventories. Firms respond by cutting back supply and GNP slowly begins to fall. Initially there is no change in the exchange rate. On the graph, this is represented by a leftward shift from the initial equilibrium at point F. (Y_$¹ to Y_$²) Adjustment to changes in aggregate demand will be gradual, perhaps taking several months or more to be fully implemented.

Step 2) As GDP falls so does real money demand, causing a decrease in US interest rates. With lower interest rates, the rate of return on US assets falls below that in the UK and international investors shift funds abroad leading to a $ depreciation (£ appreciation), that is, an increase in the exchange rate E_$/£. This moves the economy upward back to the AA curve. The adjustment in the asset market will occur quickly after the change in interest rates. Thus the leftward shift from point F in the diagram results in adjustment upwards to regain equilibrium in the asset market on the AA curve, as shown.

Step 3) Continuing reductions in GNP caused by excess aggregate demand, results in continuing decreases in interest rates and rates of return, repeating the stepwise process above until the new equilibrium is reached at point G in the diagram.

During the adjustment process, there are several other noteworthy changes taking place. At the initial equilibrium, when investment demand first falls, aggregate supply exceeds demand by the difference Y_$² - Y_$^A. Adjustment in the goods market will be trying to re-achieve equilibrium by getting back to the DD-curve. However, the economy will never get to Y_$^A. That’s because the asset market will adjust in the meantime. As GNP falls, the exchange rate is pushed up to get back onto the AA-curve. Remember, that asset market adjustment takes place quickly after an interest rate change, perhaps in several hours or days, while goods market adjustment can take months. When the exchange rate rises, the $ depreciation makes foreign goods more expensive, reduces imports, and makes US goods cheaper to foreigners, stimulating exports, both causing an increase in current account demand. This change in demand is represented as a movement along the new D’D’ curve. Thus when the exchange rate rises up to E_$/£² during the adjustment process, aggregate demand will have risen from Y_$^A to Y_$^B along the new D’D’ curve. In other words, the “target” for GNP adjustment moves closer as the exchange rate rises. In the end, the target for GNP reaches Y_$³ just as the exchange rate rises to E_$/£³.

Increase in Foreign Interest Rates

Consider adjustment to an increase in the foreign interest rate, i_£. Begin with an original super-equilibrium where DD crosses AA at point F with GNP at Y¹ and exchange rate at E_$/£¹. When the foreign interest rate increases, ceteris paribus, the AA-curve shifts upward, as was shown in section 60-4. This shift is shown in the adjacent diagram as a shift from AA to A’A’.

The quick result is that the equilibrium shifts to point H, GNP rises to Y³ and the exchange rate rises to E³. The increase in the exchange rate represents a depreciation of the US $ value.

The convenience of the graphical approach is that is allows us to quickly identify the final outcome using only knowledge about the mechanics of the AA-DD diagram. However, this quick result does not explain the adjustment process, so let’s take a more careful look at how the economy gets from point F to H.

Step 1)When the foreign interest rate, i_£, rises, the rate of return on foreign British assets rises above the rate of return on domestic US assets in the foreign exchange market. This causes an immediate increase in the demand for foreign British currency causing an appreciation of the £ and a depreciation of the US $. Thus, the exchange rate, E_$/£, rises. This change is represented by the movement from point F to G on the AA-DD diagram. The AA curve shifts up to reflect the new set of asset market equilbria corresponding to the now higher foreign interest rate. Since the foreign exchange market adjusts very swiftly to changes in interest rates, the economy will not remain off the new A'A' curve for very long.

Step 2) Now that the exchange rate has risen to E_$/£², the real exchange has also increased. This implies foreign goods and services are relatively more expensive while US G&S are relatively cheaper. This will raise demand for US exports, curtail demand for US imports and result in an increase in current account and, thereby, aggregate demand. (Note, the new equilibrium demand at exchange rate is temporarily at GNP level Y⁴, which is on the DD curve given the exchange rate E_$/£²). Because aggregate demand exceeds aggregate supply, inventories will begin to fall stimulating an increase in production and thus, GNP. This is represented by a rightward shift from point G. (small arrow)

Step 3) As GNP rises, so does real money demand, causing an increase in US interest rates. With higher interest rates, the rate of return on US assets rises above that in the UK and international investors shift funds back to the US leading to a $ appreciation (£ depreciation), or the decrease in the exchange rate E_$/£. This moves the economy downward, back to the A’A’ curve. The adjustment in the asset market will occur quickly after the change in interest rates. Thus the rightward shift from point G in the diagram results in quick downwards adjustment to regain equilibrium in the asset market on the A’A’ curve, as shown.

Step 4) Continuing increases in GNP caused by excess aggregate demand, results in continuing increases in US interest rates and rates of return, repeating the stepwise process above until the new equilibrium is reached at point H in the diagram.

During the adjustment process, there are several other noteworthy changes taking place. At point G, aggregate demand exceeds supply by the difference Y⁴ – Y¹. Adjustment in the goods market will be trying to re-achieve equilibrium by getting back to the DD-curve. However, the economy will never get to Y⁴. That’s because the asset market will adjust during the transition. As GNP rises, the exchange rate is pushed down, step-by-step, to get back onto the A’A’ curve. When the exchange rate falls, the $ appreciation makes foreign goods cheaper, raising imports, and makes US goods more expensive to foreigners, reducing exports; both of which cause a decrease in current account demand. This change in demand is represented as a movement along the DD curve. Thus when the exchange rate falls during the adjustment process, aggregate demand falls from Y⁴ along the DD curve. In other words, the “target” for GNP adjustment moves closer as the exchange rate falls. In the end, the target for GNP reaches Y³ just as the exchange rate falls to E_$/£³.

International Finance Theory and Policy - Chapter 60-6: Last Updated on 12/2/05