Symmetry in Deception: Similarities between "Unit Labor Cost" and "Money Relative to Output"

Consider the mathematical deception entangled in the "Unit Labor Cost" (ULC) calculation, and in the comparison of "money relative to output" (MRTO) to inflation. Both follow the same pattern:

1. Divide GDP by a price index to get a fraction called "real" GDP.
2. Use this fraction as the denominator of another fraction.
3. Compare the result to inflation, and find similarity.

The MRTO uses this formula: (M2) / (GDP/Prices)
The ULC uses this formula: (Total Labor Cost) / (GDP/Prices)

In both cases we divide by the fraction (GDP/Prices). The schoolboy's rule "To divide by a fraction, invert and multiply" tells us that:

The MRTO calculation in fact is (M2 / GDP) * Prices
The ULC calculation in fact is (Total Labor Cost / GDP) * Prices

In both cases a ratio is multiplied by prices, and the resulting numbers climb upward on a path comparable to the path of prices. (For "Prices", both use the GDP Deflator.) Without multiplying by Prices, neither ratio is similar to the trend of prices.

Milton Friedman's "Money relative to output" graphs compare the quantity of money to the "real GDP" ratio, show similarity to inflation, and are used as evidence that printing money causes inflation.

The "Unit Labor Cost" calculation compares Total Labor Cost to the "real GDP" ratio, shows similarity to inflation, and is used as evidence that rising labor costs are the cause of inflation.

These are fraudulent uses of arithmetic, and are not acceptable.