In the case of Microsoft (MSFT), the breakup remedy proposed by the Department of Justice is highly controversial, even among antitrust economists. The controversy arises because the separate companies would be subject to two different economic forces.

At issue is what economists call "the problem of complements." Two goods are complements if their value to the consumer depends on having both of them available. An extreme example is left shoes and right shoes. A more relevant example for Microsoft is an operating system and applications: An operating system with no applications is about as valuable as a left shoe with no right shoe.

The thorny question is whether consumers are better off with both products produced by the same firm (as happens with left shoes and right shoes) or with them produced by different firms (as the Department of Justice has proposed)?

Suppose Microsoft is broken into two independent "Baby Bills": Microsoft Operating Systems (MOS) and Microsoft Application Packages (MAP). What would happen to the price consumers pay for these complementary products?

The "classical" answer, dating back to Augustin Cournot in 1838, involves pricing incentives. Suppose MAP cuts the price of its flagship product, Office. Demand - and profits - will increase for MOS. But these profits never show up on MAP's bottom line, offering little incentive to cut prices. MOS reasons the same way about cutting the price of its operating system, so the total price of the system is higher with separate firms than with an integrated one.

But this is only part of the story. The modern view of complements notes that each of the separate companies has strong incentives to try to reduce the price of the other company's product. If you were selling right shoes, would you rather see a high or a low price for left shoes? It's the same with MOS and MAP: Each would like to see a low price for the other product, since this reduces the price of the total system. In economics jargon, each company wants to "commoditize the complementory product."

There are a variety of ways to do this. MAP could produce versions for other operating systems, such as Linux, making the operating system market more competitive. MOS would have an incentive to provide better support for other applications, making the Office suite market more competitive. Each company could work with industry bodies to standardize file interchange formats, interfaces and protocols, making it easier for competing operating systems and applications to work together.

It's no accident that Microsoft invested in the Windows Hardware Quality Lab, which pushes standards and compatibility in hardware. And it's no accident that Intel (INTC) has invested in Red Hat (RHAT) Linux. Both investments are ways to stimulate more competition in the complementor's market, leading to cheaper prices.

Commoditizing the complementor seems to be a strong force. The fact that different companies made microcomputer hardware and software has had a lot to do with their dramatic drop in price and increase in performance over the last 20 years. The Justice Department is betting that the same beneficial effects will arise by separating applications from the operating system.