Question

if the aggregate price level at time t is denoted by pt, the inflation rate from time t - 1 to t is defined as

$\pi_t = (p_t - p_{t - 1})/p_t$

$\pi_t = (p_{t + 1} - p_{t - 1})/p_{t - 1}$

$\pi_t = (p_t - p_{t - 1})/p_{t - 1}$

$\pi_t = (p_{t + 1} - p_t)/p_t$

Explanation:

Inflation rate is the percentage change in the price level from one period to the next. The formula for the inflation rate from time \( t - 1 \) to \( t \) should be the change in price level (\( P_t - P_{t - 1} \)) divided by the initial price level (\( P_{t - 1} \)). Let's analyze each option:

• First option: Divides by \( P_t \), not the initial price, so incorrect.
• Second option: Uses \( P_{t + 1} \) and \( P_{t - 1} \), which is not the change from \( t - 1 \) to \( t \), incorrect.
• Third option: \( \pi_t=\frac{P_t - P_{t - 1}}{P_{t - 1}} \), this is the correct formula as it's the change in price (\( P_t - P_{t - 1} \)) over the initial price (\( P_{t - 1} \)).
• Fourth option: Uses \( P_{t + 1} \) and divides by \( P_t \), incorrect for inflation from \( t - 1 \) to \( t \).

Answer:

\( \boldsymbol{\pi_t = (P_t - P_{t - 1})/P_{t - 1}} \) (the third option, written as the formula here)