How to determine the cost of a good Can the cost of any good be determined based on its ratio to a minimum wage?

For instance, if 10 years ago, eggs cost \$2 / dozen and the minimum wage is \$10 / hr (eggs cost 20% of the minimum wage) and at present, due to inflation, eggs cost \$2.50 / dozen and the minimum wage is \$15 / hr (eggs now cost 16% of the minimum wage).

Could it be said that the cost of eggs have decreased despite a rise in prices due to inflation?
While you're on the right track, minimum wage is not the best way to get at it. What you're discussing is called "real wages", and it is usually calculated based on some average wage, as many workers make more than minimum wage. So yes, the price of eggs has gone down (if minimum wage is a useful metric for average income).