Appendix 6.1: Determination of Equilibrium Income in Open Economy

Appendix 6.1: Determination of Equilibrium Income in an Open Economy

Once consumers and firms can buy goods produced both at home and abroad, we must draw a careful distinction between two ideas that coincide in a closed economy but part ways in an open one: the domestic demand for goods (everything residents want to spend, wherever the goods are made) and the demand for domestic goods (the demand that actually falls on goods produced within the country). The gap between them is created by exports and imports.

National Income Identity for an Open Economy

In a closed economy there are three sources of demand for domestically produced goods — consumption $C$, government spending $G$ and domestic investment $I$ — so

In an open economy, exports $X$ are an extra source of demand for domestic goods that comes from abroad, and so must be added; imports $M$ are that part of domestic demand which is met by foreign goods, and so must be subtracted. Adding imports to both sides of the demand-for-domestic-goods identity gives the national income identity for an open economy:

Rearranging,

or, writing net exports as $NX = X - M$,

A positive $NX$ (exports greater than imports) means a trade surplus; a negative $NX$ (imports greater than exports) means a trade deficit.

Exports, Imports and the Marginal Propensity to Import

To find equilibrium income we treat investment and government spending as autonomous, exactly as in the closed-economy case, and we now also specify how imports and exports behave.

The demand for imports depends on domestic income $Y$ and on the real exchange rate $R$ (the relative price of foreign goods in terms of domestic goods). Higher income raises imports; a higher $R$ makes foreign goods dearer and so lowers imports. Exports are, by definition, another country's imports, and so depend on foreign income $Y_f$ and on $R$. Here we hold the price levels and the nominal exchange rate constant, so $R$ is fixed, and we treat foreign income — and therefore exports — as exogenous, $X = \bar{X}$.

Imports are then written with an autonomous part and an income-induced part:

Here $m$ is the marginal propensity to import — the fraction of an extra rupee of income spent on imports — a concept exactly analogous to the marginal propensity to consume.

Equilibrium Income

At equilibrium, output equals planned expenditure. Substituting the consumption function $C = \bar{C} + c(Y - T)$, the autonomous items and the import function into $Y = C + I + G + X - M$:

Collecting all the autonomous terms into $\bar{A} = \bar{C} - cT + \bar{I} + \bar{G} + \bar{X} - \bar{M}$,

The Open Economy Multiplier

Equilibrium income is the product of two things: the level of autonomous expenditure $\bar{A}$ and the autonomous expenditure multiplier. Because the marginal propensity to import $m$ is positive, the multiplier in an open economy is smaller than in a closed economy:

Example 6.2. Suppose $c = 0.8$ and $m = 0.3$. The closed-economy and open-economy multipliers are then

So if domestic autonomous demand rises by $100$, output rises by $500$ in the closed economy but by only $200$ in the open economy. …