₦airaland Forum

Okay, let's break this down. If the value of currency B is now one-third of its exchange rate versus the dollar a year ago, it means:

Last year, 1 unit of currency B bought $X dollars.
This year, 1 unit of currency B buys X/3 dollars.
Or, looking at it from the dollar perspective:

Last year, $1 bought Y units of currency B.
This year, $1 buys $3Y units of currency B (because you need three times more B to get the same dollar).
Now, let's consider the country's GDP. GDP is typically measured first in the local currency (currency B). Let's say the country's GDP in currency B was GDP
B
​
both last year and this year, based on your "all else equal" assumption which implies the volume of goods and services produced and their prices in local currency haven't changed.  

To get the GDP in dollars, you convert the local currency GDP using the exchange rate:

GDP
dollar
​
=GDP
currencyB
​
×(Exchange Rate in dollars per unit of currency B)

Let's apply this:

Last Year: GDP
dollar_old
​
=GDP
B
​
×X
This Year: GDP
dollar_new
​
=GDP
B
​
×(X/3)
Now, compare the new dollar GDP to the old dollar GDP:

GDP
dollar_new
​
=GDP
B
​
×(X/3)=(GDP
B
​
×X)/3=GDP
dollar_old
​
/3

So, mathematically, if the nominal GDP measured in local currency remains exactly the same (GDP
B
​
is constant), and the only change is that the exchange rate of currency B to the dollar falls to one-third of its previous value, then the country's GDP measured in dollars would indeed also be one-third of what it used to be.

However, the "all else equal" assumption is highly unlikely to hold in reality when a currency loses two-thirds of its value. A drastic currency depreciation like this would have significant impacts on the local economy:

Inflation: Import costs would skyrocket, leading to higher prices for many goods and services within the country. This would likely increase the nominal GDP measured in currency B, even if the real output (volume of goods and services) doesn't change much.
Changes in Output: Exports might become cheaper and potentially increase, while imports become more expensive and likely decrease. Domestic consumption and investment could also be affected by the resulting economic uncertainty and inflation.
Debt Burden: If the country or its businesses have dollar-denominated debt, the cost of servicing and repaying it in local currency terms triples, potentially leading to defaults and financial instability, which would negatively impact local GDP.
Confidence and Capital Flows: A sharp currency drop can trigger capital flight and reduce investor confidence, impacting economic activity.  
Because of these real-world effects, the GDP
B
​
figure itself would almost certainly not remain the same. It would likely increase due to inflation but could decrease due to reduced real economic activity caused by the crisis.

Therefore, while the mechanical conversion using the new exchange rate would result in the dollar GDP being one-third (assuming local GDP is unchanged), in reality, the actual dollar-measured GDP would be the result of both the exchange rate fall and the complex changes in the local currency GDP caused by the economic shock. The actual outcome could be a fall to roughly one-third, more than one-third, or less than one-third, depending on the magnitude of inflation and the change in real economic activity in local currency terms.

But based purely on the isolated effect described in your question and the "all else equal" assumption (meaning GDP
B
​
is constant), the dollar-measured GDP would fall to one-third.