# Price level

The general price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set. Typically, a price level is approximated with a price index.

## 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 $C$ of goods and services, the total value of transactions in $C$ at time $t$ is

$\sum_{c\,\in\, C} (p_{c,t}\cdot q_{c,t})=\sum_{c\,\in\, C} [(P_t\cdot p'_{c,t})\cdot q_{c,t}]=P_t\cdot \sum_{c\,\in\, C} (p'_{c,t}\cdot q_{c,t})$

where

$q_{c,t}\,$ represents the quantity of $c$ at time $t$
$p_{c,t}\,$ represents the prevailing price of $c$ at time $t$
$p'_{c,t}$ represents the “real” price of $c$ at time $t$
$P_t$ is the price level at time $t$

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.

## Significance

If, indeed, a general price level component could be distinguished, then it would be possible to measure the difference in overall prices between two regions or intervals. For example, the inflation rate could be measured as

$\frac{P_{t_1}-P_{t_0}}{t_1 -t_0}$

and “real” economic growth or contraction could be distinguished from mere price changes by deflating GDP or some other measure.

$\frac{(GDP)_{t_1}}{P_{t_1}}-\frac{(GDP)_{t_0}}{P_{t_0}}$