# Price level

Price level

A 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, “real” 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:$sum_\left\{c,in, C\right\} \left(p_\left\{c,t\right\}cdot q_\left\{c,t\right\}\right)=sum_\left\{c,in, C\right\} \left[\left(P_tcdot p\text{'}_\left\{c,t\right\}\right)cdot q_\left\{c,t\right\}\right] =P_tcdot sum_\left\{c,in, C\right\} \left(p\text{'}_\left\{c,t\right\}cdot q_\left\{c,t\right\}\right)$where:$q_\left\{c,t\right\},$ represents the quantity of $c$ at time $t$:$p_\left\{c,t\right\},$ represents the prevailing price of $c$ at time $t$:$p\text{'}_\left\{c,t\right\}$ represents the “real” price of $c$ at time $t$:$P_t$ is the price level at time $t$

A 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 price-level component could be distinguished, then it would be possible to "measure" the difference in overall prices between to regions or intervals. For example, the inflation rate could be measured as:$frac\left\{P_\left\{t_1\right\}-P_\left\{t_0\left\{t_1 -t_0\right\}$and “real” economic growth or contraction could be distinguished from mere price changes by deflating GDP or some other measure.:$frac\left\{\left(GDP\right)_\left\{t_1\left\{P_\left\{t_1-frac\left\{\left(GDP\right)_\left\{t_0\left\{P_\left\{t_0$

*Price index
*Equation of exchange
*Quantity theory of money
*Wage level

References

* McCulloch, James Huston; "Money and Inflation: A Monetarist Approach" 2e, Harcourt Brace Jovanovich / Academic Press, 1982.
* Mises, Ludwig Heinrich Edler von; "Human Action: A Treatise on Economics" (1949), Ch. XVII “Indirect Exchange”, §4. “The Determination of the Purchasing Power of Money”.

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