Question

This exercise deals with approximating growth rates of "combined quantities", e. g.,nominal GDP Y NOM, ₜ =Y ₜ * P ₜ , with real GDP Yₜ and the GDP deflator Pₜ, or realGDP per capita Y_{t}/S_{t} with population S_{t}

(a) Show that the growth rate of Y NOM, t is approximately equal to the sum of thegrowth rate of Y_{t} and the inflation ratepi t = P ₜ -P ₜ - 1 P ₜ-1
g Y NOM,ₜ ₋₁, ₜ approx g Y,ₜ₋₁,ₜ + pi ₜ

Answer 1

The growth rate of nominal GDP can be approximated by adding the growth rate of real GDP to the inflation rate, which is an indicator of price changes over time.

Step-by-step explanation:

The student's exercise involves calculating the growth rate of nominal GDP, which can be approximated by adding the growth rate of real GDP to the inflation rate. Nominal GDP (YNOM,t) is the product of real GDP (Yt) and the GDP deflator (Pt). The inflation rate, represented by πt, is calculated using the formula πt = (Pt - Pt-1) / Pt-1. The approximation can be explained using the formula:

growth rate of nominal GDP ≈ growth rate of real GDP + inflation rate

This approximation works because it assumes that the changes in prices and quantities are relatively small. It allows us to understand the growth rate of a combined quantity, like nominal GDP, by breaking it down into its components of real growth and changes in price level, which is inflation.