*May I know how the following formula is derived:*

*% Δ* *Real GDP = % Δ*

*Nominal GDP*–

*Inflation Rate*

First, we know that Real GDP is derived from Nominal GDP, by multiplying it against the GDP Deflator:

*Real GDP = Nominal GDP * ( CPI _{Base} / CPI _{Current} )*

But before we move on, due to the long-ish math expressions that will follow, some truncation would be needed here:

*Real GDP = R*

*Nominal GDP = N*

*CPI _{Base} = B*

*CPI _{Current} = C*

So then we can re-write our earlier expression as:

*R = N * ( B / C )*

We then differentiate the expression to derive:

*δR = B * ( δN * C – δC * N ) / C ^{2}*

Notice that:

- The quotient rule for differentiation is utilised here; and
*B*is a constant here, and therefore not subject to the differentiation.

Since:

*% Δ* *Real GDP =* *( Δ* *Real GDP* / *Real GDP ) * 100*

We can plug our differentiation result from earlier into the expression:

*% Δ* *R ≈ * *[ B * ( δN * C – δC * N ) / C ^{2}*

*] / R * 100*

Since *R = N * ( B / C )*, we can further transform the expression:

*% Δ R ≈ [ B * ( δN * C – δC * N ) / C ^{2}] / [ N * ( B / C ) ] * 100*

It looks complicated! But with some patience, you should be able to simplify the expression to derive:

*% Δ R ≈ ( δN / N – δC / C ) / * 100*

And therefore:

*% Δ R ≈ % Δ N – % Δ C*

Since the inflation rate is defined mathematically as * % Δ C*, therefore:

*% Δ R ≈ % Δ N – Inflation Rate*

And *voilà*! Proof completed! If you have queries or comments, feel free to comment below.