# Why does optimal allocation call for unlimited distribution of information?

In his seminal paper Arrow (1962) states that information should be distributed without limit if an optimal allocation is to be achieved. Quote (p. 614-615):

The cost of transmitting a given body of information is frequently very low. If it were zero, then optimal allocation would obviously call for unlimited distribution of the information without cost. (...) The owner of the information should not extract the economic value which is there, if optimal allocation is to be achieved; but he is a monopolist, to some small extent and will seek to take advantage of this fact.

Quote (p. 616-617):

In the first place, any information obtained, say a new method of production, should, from the welfare point of view, be available free of charge (apart from the cost of transmitting information). This insures optimal utilization of the information but of course provides no incentive for investment in research. In an ideal socialist economy, the reward for invention would be completely separated from any charge to the users of the information. In a free enterprise economy, inventive activity is supported by using the invention to create property rights; precisely to the extent that it is successful, there is an underutilization of the information.

Arrow makes the point that creating a market for information is difficult given the peculiar nature of the commodity information. But if information did not have those special attributes: Couldn't information be "produced" by an organization and sold without welfare loss? Why do property rights lead to suboptimal allocation in the case of information?

Reference:

Kenneth Arrow, 1962. "Economic Welfare and the Allocation of Resources for Invention," NBER Chapters, in: The Rate and Direction of Inventive Activity: Economic and Social Factors, pages 609-626 National Bureau of Economic Research, Inc. url: https://ideas.repec.org/h/nbr/nberch/2144.html

Suppose you have a product that you can distribute for constant marginal cost $c$. For every $v\geq0$ assume there are some consumers who value the good at $v$. The net welfare created when someone consumes the good is their value minus the cost of production.

Thus, if we want to maximise the total social surplus (net of costs), we should give the good to every consumer for whom $v-c\geq0$. Since a consumer will choose to buy the good if the price, $p$, is below their willingness to pay (i.e., if $v-p\geq0$), setting $p=c$ ensures the efficient outcome where exactly the consumers with value greater than marginal cost consume the good.

Now suppose we have an information good that can be distributed digitally for zero marginal cost ($c=0$). The above reasoning implies that the socially efficient price is $p=0$! Intuitively, giving you a copy of the good does not cost society anything (because information can be infinitely digitally duplicated), so even if you only get a tiny benefit from consuming it, that benefit will produce a (small but positive) net increase the total social surplus. But the only way to make sure that people who get very small (but positive) value from the good choose to consume it is to give them the good for free.

Arrow's broader point is that this produces a problem: if the price of an information good (e.g. a movie) is zero then firms have no profit incentive to produce movies at all, and then nobody gets any surplus. Eeek! The way society solves this problem is to say "if you make a movie, you get copyright, which means you have the monopoly right to sell that movie". The profits that come from being a monopolist over the movie are the rewards to the firm for having made it in the first place. But, of course, the monopolist movie studio will set $p\gg0$, so some consumers will not buy it even though they could be served as zero cost and this will increase welfare.

If you know your Econ 101 then this can be understood through the lens of some textbook models. Remember that in a basic textbook model of a market, the social surplus is the area below the demand curve but above the marginal cost curve. Social surplus is maximised when $p=MC$, which, for information goods, means $p=0$.

now think of a texbook monopoly model (where the monopoly comes because you own the copyright or patent): the monopolist will set $p>MC$ and this produces a deadweight loss, which is the inefficiency Arrow refers to.

• Clear and good answer, thank you. In summary: The welfare loss results from the monopolist not charging marginal costs. If he would charge a competitive price $p=mc$ there would be no welfare loss. A monopolist using perfect price discrimination would not lead to welfare loss too, right? – Fusscreme Apr 7 '17 at 17:35
• @Fusscreme that's right. In fact, the zero MC property of information goods allows a lot of monopolists to achieve a kind of price discrimination through selling millions of information goods together in one bundle (e.g. songs in a spotify subscription). If there are a million songs in the bundle then predicting the consumer's average value per song is much easier (thanks to the law of large numbers) so the monopolist can set the price much closer to consumers' willingness to pay. See people.stern.nyu.edu/bakos/big.pdf – Ubiquitous Apr 7 '17 at 19:47
• I have a question about your comment on the solution. Monopoly does not exist de facto because information is copied whether monopolists (copyright holders) permit it or not. Maybe society solves this problem in another way? – beroal Apr 8 '17 at 6:41
• @beroal Yes, it's true that some (indeed, many) people copy the good for free. They are the so-called pirates. But as long as there are some people who are quite unwilling to use an illegal copy, the copyright holder will have significant power to set $p>MC$ and the same kind of inefficiencies arise as if it were a de facto monopoly. We know that such people exist because the revenues from digital music last year were \$6.2bn. For patented inventions, the patent holder is much closer to being a de facto monopolist because courts regularly enforce patent-holder rights. – Ubiquitous Apr 8 '17 at 7:37
• @Ubiquitous: What about production costs? We've only talked about distribution costs so far. Shouldn't the quote read: "The cost of transmitting a given body of information is frequently very low. If it were zero, then optimal allocation would obviously call for unlimited distribution of the information without cost besides a contribution to production costs." I know this sounds insignificant but there might be some importance to it. Please also note my follow-up question: economics.stackexchange.com/questions/16222/… – Fusscreme Apr 11 '17 at 14:41