Income in an open economy

In an open economy, demand for domestic goods is:

Y = C + I + G + X − M = C + I + G + NX

where NX (net exports) = X − M. A positive NX is a trade surplus.

Exports depend on foreign incomes, so here they are fixed (exogenous). Imports rise with our own income: M = M̄ + mY, where m is the marginal propensity to import, the share of extra income spent on imports.

Then equilibrium income is:

Y = A ÷ (1 − c + m), where A is all autonomous spending (including X − M̄).

The open economy multiplier, 1 ÷ (1 − c + m), is smaller than the closed one, 1 ÷ (1 − c), because part of every round of spending leaks abroad as imports. For example, with c = 0.75 and m = 0.25, the open multiplier is 1 ÷ 0.5 = 2, while the closed one would be 4.

So: a rise in exports raises income (an injection), and an autonomous rise in imports lowers it (a leakage).