Why market structure matters

Greg Mankiw introduces an article critical of the possibility of the current health reform bills reducing health care costs by writing:

Let's review some basic principles of supply and demand: If a government policy increases the demand for a service, the price of that service tends to rise. If the government prevents prices from rising, shortages develop. The quantity provided is then determined by supply and not demand. In the presence of such excess demand, the result could be a two-tier market structure. Consumers who can somehow pay more than the government-mandated price will be able to purchase the service, while those paying the controlled price may be unable to find a willing supplier.

Everything he writes is true - if markets are competitive. If sellers (insurance companies, health care providers) have monopoly power, then it is possible to reduce prices while increasing quantity supplied. I know this because I read it in a book: N. Gregory Mankiw, Principles of Economics (5th edition), Chapter 15.