Don Boudreaux has a very good posting at Cafe Hayek, pointing out that just because a firm can (and does) raise its prices, and just because a firm gains market share, those data are not necessarily indications that the firm has market power. His argument is that generally it is the firms that offer better quality, better service, and more of what consumers want that are able to grow and still charge more for their products.
The upshot is that observing that a firm has the ability to profitably raise the prices of its outputs is not necessarily an observation of that firm’s “power” in the output market. Likewise, observing that an employer has the ability to lower the monetary pay of its workers without having all of those workers quit is not necessarily an observation of that firm’s “power” in the labor market. Such observations are perhaps – and in a market economy are almost certainly – only evidence of complex and mutually advantageous bargains struck between firms, consumers, and workers.
If firms are able to elevate prices and still retain their customers, other firms will copy them, and even try to out-compete them. Hence, a better indication of market power is how high the barriers to entry into the market are. Industry concentration, firm size, and price-cost margins (no matter how they are measured) are much less reliable as measures of market power.
If there are high barriers to entry, a firm might well have market power and be able to raise prices and keep them high, earning a "monopoly" return. But if firms are in industries with low barriers to entry (e.g. fast food!!), it is next to impossible for them to earn persistently high profits that are not attributable to their offering something better to their customers, something the customers want and are willing to pay for.
And what is the greatest source of high barriers to entry? Gubmnt regulations. I wrote about this over 40 years ago here:
“Barriers to Entry as a Measure of a Firm's Monopoly Power,” The American Economist 18 (Spring 1974): 33-35.