Why Does A Higher Minimum Wage Lead To Higher Prices?

The main reason why prices tend to rise with wages is that public corporation stock prices are tied to their quarterly/annual earnings. Corporations that desire their stock prices to rise are always looking for ways to increase their profits and show earnings growth.
Increased wages raise expenses for a corporation by a factor of its total workforce affected by the wage increase. This lowers earnings/profits, and causes a chain reaction (via analyst downgrades) that results in their stock price declining. An obvious candidate for making up for the lost profits is to raise prices and/or find cheaper labor (Asia/Mexico) and cheaper materials/ingredients.

One complicating factor is that a general workforce with higher wages has higher purchasing power. Yet, as the workforce exercises this power in the market place, it signals higher demand which tends to trigger both higher prices from current suppliers and the entry into the market of alternative suppliers who try to compete on price and volume.

Not saying any of this is good or bad. Just pointing out the general mechanism. Perhaps someday we can return our society back to a 1950s/1960s business mentality when "maximizing shareholder value" wasn't the A#1 priority of corporate CEOs.