What Is a Worked Example of Fixed Exchange Rates? (With Assumptions)

Direct answer

A worked example of fixed exchange rates is a step-by-step scenario where a country commits to keep its currency at a specific exchange value against another currency. The central idea is: if the market would otherwise push the rate away from the target, the authority takes actions (commonly via foreign-exchange reserves and/or domestic policy) to bring the realized exchange rate back to the target.

Mechanism or definition

A fixed exchange rate (often called a “peg”) is a system where the exchange value of Currency A is defined relative to Currency B at a target rate, for example “1 unit of Currency A equals X units of Currency B.” The authority’s goal is that actual trades clear at (or very close to) that target rate.

Two roles matter in a worked example:

The target rate: the announced or legally set conversion value Currency A must maintain versus Currency B.
The balancing action: when market participants want to buy more of Currency A or more of Currency B than would be consistent with the target, the authority supplies or absorbs the needed currency (using reserves) and/or changes domestic conditions to reduce the pressure.

To verify understanding, you should be able to track how changes in demand and supply would create pressure on the exchange rate, then explain how “the balancing action” prevents the observed rate from moving.

Evidence or example (numbers and assumptions)

Here is a self-contained worked scenario.

Assumptions (state up front)

Currency A is pegged so that 1 A = 2 B (the target).
The authority is willing and able to use foreign-exchange reserves to maintain the target for the period shown.
We ignore transaction fees, bid–ask spread, and taxes to keep the arithmetic clear.
We consider only one trading decision by market participants: whether they exchange A into B (sell A for B) or exchange B into A (sell B for A).
If excess demand for one side appears, the authority stands ready to take the other side so the traded rate remains 2 B per 1 A.

Step-by-step scenario

Time T0: The economy starts at the target. The market clears so that trades happen at 1 A = 2 B.

Time T1: a change in demand

Suppose, for a short interval, investors want to buy A, meaning they want to sell B to obtain A.
Assume the private market attempts to exchange 50 A for the equivalent value in B at the target: since 1 A = 2 B, they would need 100 B.
In a floating setting, stronger demand for A would typically raise the value of A (meaning fewer B per A). But under a fixed rate peg, the authority must prevent that.

What the authority does (balancing action):

Because private buyers are selling B to buy A, the authority receives B in exchange for A (or supplies additional A) so that the realized trade rate stays exactly at 2 B per 1 A.
Under the simplifying assumption #5, the authority can cover the mismatch to maintain the target.

Numerical outcome at T1 (conservation at the peg):

Private buyers obtain 50 A.
Private sellers deliver 100 B.
The peg arithmetic is consistent: 50 A × 2 B/A = 100 B.

Now a second pressure direction (same peg)

Time T2: demand flips

Assume instead that, at T2, investors want to sell A (so they sell A for B).
Suppose private sellers attempt to exchange 30 A into B at the peg.
At 1 A = 2 B, they would receive 60 B.

Balancing action:

The authority must absorb the A that private sellers want to give up (and supply B), so the rate still clears at 2 B per 1 A.

Numerical outcome at T2:

Private sellers give 30 A.
They receive 60 B.

What you should take away from the example

The worked arithmetic shows that, with a fixed peg and idealized assumptions, the exchange rate does not change when private pressure swings. Instead, the authority’s reserves and/or domestic stance adjust to keep the trade rate anchored to the target.