This post continues my series on my upcoming Stanford Law Review paper on Privatization and the Law and Economics of Political Advocacy (see here for the technical paper). The last post set out the basic economic model -- read that post, if you haven't already and if you want to understand this post. This post just elaborates a bit on the basic model -- and applies it to prisons -- before we go on to apply the model to the real world and prisons.

* * *

If one accepts the fundamental assumption of this Part—that the probability of success only depends on the total amount of money in the pot—this simple model is flexible enough to accommodate many institutional details of privatization. The total free-riding result happens whenever one sector has a lower threshold than the other, for whatever reason. In this story, you and your competitor are identical except that you have 90% of the industry and he has 10%. But one's threshold could be lower for other reasons as well.

For instance, suppose that, to add insult to injury, the government not only breaks you up but also subjects your revenues to a high (50%) tax rate. The breakup already altered your spending threshold by making all your curves shift down to 90% of their previous level (see the figures in the previous post). Now, with the 50% tax, your revenue and marginal revenue curves shift further down—to 45% of their original levels. (If your 10% competitor is subject to the same tax, his curves are 5% of the original industry curves.)

So the combination of the breakup and the tax makes you act like a 45% firm. These new percentages—call them "real" shares—no longer need to add up to 100% (in fact, with the 50% tax, they add up to 50%), but they convey the economic intuition that your spending threshold is lower when, for whatever reason, your benefits decrease.

After we determine everyone's "real" shares, the same analysis applies as before: The "biggest" firm does all the advocacy, and the "smaller" firm free rides. The only difference is that we learn who is "biggest" not just by looking at proportions of the market but at shares of total industry revenue. Instead of calling this firm "biggest," we'll call it the "dominant" firm. Thus, if the tax rate on your revenues is 90%, you will act as though your share is 9%; and if your 10% competitor is exempt from the tax, then he, with his 10% share, is actually the dominant actor. Now you will free-ride off him.

In short, anything that affects your revenues affects your "real" share. Suppose, for instance, that your competitor is less profitable than you are: Your 90% share is a monopoly share in a 90% geographic area, while the remaining 10% is divided among 100 competitors who act according to the textbook perfect competition model, where everyone makes zero economic profits. Then those competitors—and thus that entire 10% sector—act as though they had a 0% share.

Or, as a final example, suppose that your competitor is better at advocacy. Perhaps, for whatever reason (maybe he is a slicker lobbyist), each dollar of his is twice as persuasive as a dollar of yours. Then, he acts as though his share is 20%, and his threshold goes up accordingly. All these considerations affect your "real" shares for purposes of choosing how much to spend on advocacy. (In this example, he still won't do anything because 20% is still less than your 90% share.)

This model applies straightforwardly to privatization, which splits up an industry between public and private much as the Antitrust Division could split up a monopolistic firm. To be sure, the public sector is not a "profit maximizer" like a private firm. But the concept of profit maximization needn't be interpreted in a narrow financial sense. Government agencies—or, more precisely, people who work at the agencies and who have some control over what the agencies do—pursue goals of some sort. Whether it is the Pentagon or a state Department of Corrections, a government agency does obtain some benefit from its service provision.

Moreover, agencies are not the only actors; the employees of the agencies, through their unions, also enjoy some benefit from public provision of the service, and they can also participate in political advocacy. The challenge is to determine who the relevant actors are and what benefits they might plausibly seek to maximize. This is what I will try to do in later posts for corrections agencies and corrections officers' unions.

The model implies, at a minimum, that some amount of privatization will decrease advocacy, for two reasons. The first reason is that, as long as the level of privatization does not exceed a certain critical threshold, the public sector will dominate (in terms of "real" share) the whole private sector combined, so the model predicts that whole private sector's advocacy would be zero. The second reason is that as privatization increases, the benefits of service provision to the public sector fall; because the public sector is smaller than it would be without privatization, its advocacy falls.