This is a genuinely contested economic and policy question, and reasonable people disagree based on different values and readings of the evidence. Here's the landscape:
Arguments for tying minimum wage to cost of living:
•If wages stay flat while prices rise, low-wage workers' real purchasing power falls—they can afford less over time even though their paycheck looks the same
•Full-time minimum wage work in many places doesn't cover basic expenses like housing, especially in high-cost areas
•Automatic adjustments (indexing to inflation) remove the political fight of periodic wage increases and provide predictability for businesses
Arguments for caution or against automatic increases:
•Some economists worry that mandated wage floors—especially if raised quickly—could reduce entry-level job availability or hours, particularly for younger/less experienced workers, though the empirical evidence here is genuinely mixed and debated among economists
•Cost of living varies enormously by region, so a national minimum wage tied to a national cost-of-living metric may overshoot in low-cost areas and undershoot in high-cost ones
•Some argue targeted anti-poverty tools (EITC, housing subsidies) address income adequacy more efficiently than wage floors, which affect employer costs directly
Where the actual debate sits:
Economists disagree on magnitude of job effects from wage increases—some studies (like Card-Krueger and follow-ups) found minimal employment effects from moderate increases, while others find more significant effects, particularly with larger increases or in different labor market conditions. The disagreement isn't really about whether purchasing power matters, but about the tradeoffs of the policy tool used to address it.
What's driving your interest in this—are you thinking about it from a policy design angle, or something more personal like wage negotiations?