Price level

Theoretical foundation

The classical dichotomy is the assumption that there is a relatively clean distinction between overall increases or decreases in prices and underlying, “nominal” economic variables. Thus, if prices overall increase or decrease, it is assumed that this change can be decomposed as follows:

Given a set ${\displaystyle C}$ of goods and services, the total value of transactions in ${\displaystyle C}$ at time ${\displaystyle t}$ is

${\displaystyle \sum _{c\in C}(p_{c,t}\cdot q_{c,t})=\sum _{c\in C}[(P_t\cdot p_{c,t}^{\prime })\cdot q_{c,t}]=P_t\cdot \sum _{c\in C}(p_{c,t}^{\prime }\cdot q_{c,t})}$

where

${\displaystyle q_{c,t}}$ represents the quantity of ${\displaystyle c}$ at time ${\displaystyle t}$

${\displaystyle p_{c,t}}$ represents the prevailing price of ${\displaystyle c}$ at time ${\displaystyle t}$

${\displaystyle p_{c,t}^{\prime }}$ represents the “real” price of ${\displaystyle c}$ at time ${\displaystyle t}$

${\displaystyle P_t}$ is the price level at time ${\displaystyle t}$

The general price level is distinguished from a price index in that the existence of the former depends upon the classical dichotomy, while the latter is simply a computation, and many such will be possible regardless of whether they are meaningful.