The Trade Balance Is Saving minus Investment

In micro, a tariff was a story about one import market. In macro, the whole country's saving and investment set the trade balance.

If saving beats investment, the leftover 💰 money flows abroad. If investment beats saving, the country borrows from abroad. The gap always matches, as in the formula below. A tariff moves neither saving nor investment. So the trade balance ends up right back where it started.

For example, say your classmates collect 100 🍬 candies. If they eat 70 and save 30, those 30 can be lent to the next class. If they want to eat 120, they must borrow 20 from next door. A country's trade works the same way: it is the gap between what is saved and what is spent.

NX=S−INX = S - I
S=S0+sr∗S = S_0 + s r^*
I=I0−br∗I = I_0 - b r^*

Part of these learning paths

Examples & Exercises

A small open economy faces a world interest rate of r∗=5%r^* = 5\%. A thrift campaign lifts saving by 2020 (saving shift +20+20).

What are saving, investment, and net exports, and does this country lend to the rest of the world or borrow from it?

Rate 5%5\%, saving shift +20+20 — the country becomes a lender.
Show proof

  1. Saving is S=60+8⋅5+20=120S = 60 + 8 \cdot 5 + 20 = 120: the rate-driven base of 100100 plus the campaign's 2020.

  2. Investment is I=140−8⋅5=100I = 140 - 8 \cdot 5 = 100.

    Saving beyond what domestic investment absorbs, 120−100=20120 - 100 = 20, is left over — and that leftover is exactly net exports, NX=S−I=+20NX = S - I = +20, lent abroad.

    The country is a lender.

Counterexample

A country with saving and investment both at S=I=100S = I = 100, so a trade balance of 00, slaps a tariff on imports. At the initial exchange rate, imports drop from 150150 to 120120.

Yet after some time, net exports are back at 00. What happened?

Verdict

The claim is false — a tariff cannot change the trade balance, and net exports end up back at 00

Tariff on — imports dip to 120120 at first, but NXNX returns to 00.
Show proof

Counterexample and verification

  1. Step 1 (the micro view): exports stay at 150150 while imports fall to 120120, so net exports seem to improve to 150−120=+30150 - 120 = +30. In the partial-equilibrium picture, the tariff "worked".

  2. Step 2 (the macro view): the tariff moved neither saving nor investment, so the identity still demands NX=S−I=0NX = S - I = 0.

    The currency appreciates by 5%5\%, imports climb back, and net exports slide from +30+30 back to 00.

    The trade balance is the one thing protection cannot change — only saving and investment can.

7. The Open Economy and Trade