You sure don't seem to have a grasp on the topic of inflation. Do you understand that the year YOU used (1977) had a real dollar minimum wage of $9.82 an hour?
I understand inflation just fine.
You don't grasp the concept of value. "real dollar" is a bullshit term you made up. The fact that dollars must be adjusted to inflation to provide an accurate representation of purchasing power
should clue you in to the nature of fiat currency and the relation it has to value, but it doesn't because you lack the foundational knowledge of economics.
An apple is an apple. If an apple costs $1, it is an apple. If an apple costs $5 it is still an apple. Altering the number of dollars paid for an apple does not alter the value of the apple. $5 simply diminishes in purchasing power to what $1 was.
An hour of unskilled labor does not increase in value to an economy because leftists and bureaucrats dictate that more dollars be spent to purchase it. It adds no more value, no more goods and services are produced. Nothing save devaluing the purchasing power of the dollars used will happen. Nothing else can happen, because dollars are not value, they are simply MARKERS of value. Economies seek equilibrium, and will eventually return to the point that the number of dollars paid are a true representation of the value produced. Moronic acts such as arbitrary increases in minimum wage create disequilibrium for a time, but the market seeks to smooth the flow of currency to the value pegged to it.
You of the left believe that you can bully reality, but you can't. You can force $15 to be paid for $7.25 of value, which you are doing. But the market will simply adjust so that $15 has the same purchasing power as $7.25.
Markets will seek equilibrium.