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 $p&gt;MC$ and this produces a deadweight loss, which is the inefficiency Arrow refers to.