### 6.3 The IS curve in the open economy: real depreciation and trade balance

If trade relations with the rest of the world are ignored, there is no need to distinguish between the domestic demand for goods and the demand for domestic goods. However, if one wants to analyze an open economy, this distinction has to be made.
For domestic demand, i.e. those goods and services that are in demand by residents (or in the domestic market) $Y=C+I+G.$ still applies. The curve of domestic demand is called the DD curve.
However, domestic production, economic growth, recession and boom refer to the demand for domestic goods, which includes trade relations with abroad. This means that domestic demand must be corrected for exports and imports because a part of domestic demand is covered by foreign goods and a part of the demand for domestic goods comes from foreigners. We refer to the curve of demand for domestic goods as the ZZ curve. The equation is $Y=C+I+G+X-\mathit{Im}∕\mu .$ The difference between exports and imports is called the trade balance (surplus or deficit).
Here, imports are indicated with their value so as not to compare apples (or Mercedes) (domestic) with pears (or Hundai) (foreign). For this purpose the imports are converted with the real exchange rate $\mu$. The ZZ curve is flatter than the DD curve, since a part of domestic demand is covered by foreign goods - the imports.
The following macroeconomic variables influence the system and are used as controllers in the graph: government expenditure G, foreign income Y* and the real exchange rate $\mu$. Altogether, the IS curve of the open economy looks like this:

 $Y=C\left(Y-T\right)+I\left(Y,r\right)+G+X\left({Y}^{\ast },\mu \right)-\mathit{Im}\left(\mu \right)∕\mu .$

Income, taxes, interest rates affect domestic demand as described in the previous chapters. In addition, an increase in income causes an increase in imports. A change (decrease = real depreciation) in the real exchange rate has three effects: (1) increase in exports, (2) decrease in imports and (3) increase in the relative price of foreign goods in units of domestic goods 1/$\mu$. For the trade balance to improve in response to a depreciation, the effects 1 and 2 (increase in exports and decrease in imports) must have a stronger impact than the third (relative decline of the value of domestic goods). This is the case when the Marshall-Lerner condition applies. We assume this, since it is the rule. The trade balance reacts positively to a real depreciation.
If one compares the ZZ-curve and the DD-curve in a $Y$ -demand-diagram, two points stand out. There is an intersection of the two curves and for low $Y$ the ZZ-curve runs above the DD-curve, for high $Y$ it runs below. The difference between the ZZ-curve and the DD-curve represents net exports (NX) or the trade balance surplus, i.e. exports-imports/$\mu$ At the intersection, the value of domestic demand corresponds to the demand for domestic goods. This means that as much is imported as is exported. The trade balance is in equilibrium. If domestic GDP rises, the demand for domestic goods rises proportionately less, since part of the demand is generated abroad, and the trade balance becomes negative. If domestic GDP decreases, the trade balance becomes positive, c.p.
The economy is in equilibrium when production $Y$ equals demand, i.e. the above equation

 $Y=C\left(Y-T\right)+I\left(Y,r\right)+G+X\left({Y}^{\ast },\mu \right)-\mathit{Im}\left(\mu \right)∕\mu$

is fulfilled.

In the graph above, production is shown as the angle bisector $Y$=$Y$ demand as the ZZ-curve and the economic equilibrium as the intersection $\mathit{Eq}0$. In the initial position, the trade balance is balanced. Using the slider, a change in the real exchange rate can be simulated. You can see the increase in foreign demand (blue) in the case of a real depreciation. As described above, the increase in foreign demand is always higher than the increase in net exports (black) in the new equilibrium. In the case of an appreciation, of course, the reverse is true.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de