Whenever minimum wage is discussed, inevitably there is some conversation about “if the minimum wage was pegged to inflation, it would be X by now!” ( see, for example ) . Politicians and policy experts often then make recommendations to peg minimum wage to some measure of inflation.
Source: Pegging Minimum Wage to Inflation Will Not Help Minimum-Wage Workers
However, the Law of Demand tells us why this is a poor idea, even moreso than a simple (ie, not-pegged) minimum wage.
The Law of Demand has two parts to it:
1) All else held equal, as the relative price of a good rises, quantity demanded of the good will eventually fall.
2) The longer the relative price of a good remains high, the more elastic demand becomes.
The first part, or the First Law of Demand, tells us that the initial setting of the minimum wage (assuming it is above the equilibrium price), will cause fewer workers to be employed (or some other cut be made depending on the choices firms face).
The second part, or the Second Law of Demand, tells us that if minimum wage were pegged to inflation, employers would look for more and more ways to reduce their labor costs; in technical terms, they will find more and more substitutes for labor (eg, automation). What this indicates is the negative effects of a minimum wage hike will likely be enhanced if the minimum wage were pegged to inflation. Indeed, one of the main reasons minimum wage has so little documented negative effects presently is partly because the real minimum wage is below the prevailing market wage. Pegging minimum wage to inflation would reduce that happy effect.
The Law of Demand is pretty immutable. Minimum wage is no exception to it. You make workers more expensive to hire, people will look for alternatives.