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Sem 5 Prep
← Open Economy MacroIncome determination in a small open economy

Formulas for this chapter

Open economy equilibrium

I + X = S + M Equivalently X - M = S - I In changes dI + dX = dS + dM

Any question with four functions. The middle form answers every question about what a surplus or deficit implies; the third form is what policy questions need.

I, X
Injections: autonomous investment and autonomous exports. Class case 150 and 300
S, M
Leakages: saving and imports, both functions of income. Class case -100 + 0.25Y and 150 + 0.15Y
X - M
The trade balance, also net foreign investment

The three import measures

MPM = dM / dY APM = M / Y income elasticity of imports = MPM / APM

MPM whenever you need the multiplier. APM and the elasticity whenever the question is about whether imports are outrunning growth.

MPM
Marginal propensity to import, the slope of M(Y). Class case 150/1,000 = 0.15
APM
Average propensity to import. Class case 300/1,000 = 0.30, falling as income rises
elasticity
Percentage change in imports per percentage change in income. Class case 0.5 at income 1,000

Foreign trade multiplier

k' = 1 / (MPS + MPM) dY = k' x d(autonomous injections) dM = MPM x dY

Sizing the income and trade-balance effect of any autonomous change. The third line is the one that turns an income answer into a trade balance answer.

k'
The foreign trade multiplier. Class case 1/0.40 = 2.5, against the closed-economy 4
MPS + MPM
The total leakage per unit of income, which is the slope of the S + M line

Equilibrium income shortcut

Y = (autonomous injections - combined intercept) / (MPS + MPM) Class case: Y = (450 - 50) / 0.40 = 1,000

Under exam time pressure. Then verify by evaluating S, I, M and X separately at the answer.

autonomous injections
I + X
combined intercept
The constant term of S + M. Class case -100 + 150 = 50
Step 3 of 24
The real wordsTheory

The equilibrium condition, three ways

Injections must equal leakages. There are now two of each.

I + X = S + M (injections = leakages) X - M = S - I (rearranged) dI + dX = dS + dM (in changes)

The middle form is the one examiners love, so read it aloud: a surplus in the trade balance must be matched by an equal excess of saving over domestic investment, at the equilibrium level of income.

The third form is the one you actually compute with, because policy questions are always about changes.

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