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