The Exchange Rate Closes the Loop

In micro, the exchange rate was one price among many. In macro, it is the very price that adjusts to match the saving-investment gap.

When our 💰 money gets pricier, our goods get pricier too. Foreign buyers buy less, and net exports fall. The equilibrium rate is where net exports equal the saving-investment gap. The formula below finds that spot. When government borrowing widens a deficit, the currency rises and net exports worsen by exactly that much.

For example, imagine the corner 🏪 shop suddenly charges more for 🍬 candy. Shoppers drift to the shop next door, and the pricey shop sells less. A pricier currency works the same way. Foreign buyers drift away until exports fall enough to restore the balance.

NX(ε)=N0−nεNX(\varepsilon) = N_0 - n \varepsilon
ε∗=N0−(S−I)n\varepsilon^* = \frac{N_0 - (S - I)}{n}

Part of these learning paths

Examples & Exercises

Government borrowing drags the country's net saving down to S−I=−30S - I = -30: a deficit country.

With the net-export schedule NX(ε)=90−5εNX(\varepsilon) = 90 - 5\varepsilon, what are the equilibrium exchange rate ε∗\varepsilon^* and net exports?

S−I=−30S - I = -30, n=5n = 5 — the currency appreciates to ε∗=24\varepsilon^* = 24.
Show proof

  1. The equilibrium rate is where net exports hit the identity's target: solving 90−5ε∗=−3090 - 5\varepsilon^* = -30 gives ε∗=(90+30)/5=24\varepsilon^* = (90 + 30) / 5 = 24.

  2. With net saving at 00 the rate would have been (90−0)/5=18(90 - 0) / 5 = 18, so the deficit appreciated the currency by 66, and net exports landed at exactly the deficit, −30-30. The exchange rate moved to make the identity true.

Now take the same deficit, S−I=−30S - I = -30, but with net exports twice as sensitive to the exchange rate (n=10n = 10).

What is the equilibrium rate, and how does the appreciation compare with the previous problem?

S−I=−30S - I = -30, n=10n = 10 — ε∗=12\varepsilon^* = 12, and the appreciation is halved.
Show proof

  1. ε∗=(90+30)/10=12\varepsilon^* = (90 + 30) / 10 = 12. Net exports are the same −30-30 as before — the identity fixes net exports, not the exchange rate.

  2. The exchange rate moves less instead.

    At balance (S−I=0S - I = 0) the rate would be 90/10=990 / 10 = 9, so the appreciation is 12−9=312 - 9 = 3 — half of the previous problem's 66.

    When each point of the exchange rate shakes net exports twice as hard, the rate only needs to travel half as far to deliver the same adjustment.

7. The Open Economy and Trade