Why have copyright and patents?

My previous post on the protection of intellectual property does raise an interesting question, Why have things like copyright and patents at all? An answer may be found in terms of incomplete contracts. Jean Tirole writes,

Consider the patent system. It has long been recognized that patents are an inefficient method for providing incentives for innovation since they confer monopoly power on their holders. Information being a public good, it would be ex post socially optimal to award a prize to the innovator and to disseminate the innovation at a low fee. Yet the patent system has proved to be an unexpectedly robust institution. That no one has come up with a superior alternative is presumably due to the fact that, first, it is difficult to describe in advance the parameters that determine the social value of an innovation and therefore the prize to be paid to the inventor, and, second, that we do not trust a system in which a judge or arbitrator would determine ex post the social value of the innovation (perhaps because we are worried that the judge might be incompetent or would have low incentives to become informed, or else would collude with the inventor to overstate the value of the innovation or with the government to understate it). A patent system has the definite advantage of not relying on such ex ante or ex post descriptions (although the definition of the breadth of a patent does). (Jean Tirole, "Incomplete Contracts: Where Do We Stand?" Econometrica, Vol. 67, No. 4 (Jul., 1999), pp. 741-781.)