What are the current economic theories of product advertising? Are there any well known economic theory references about advertising? It seems you could think of advertising as imposing a negative externality on other producers or on consumers in that it takes up bandwidth, or a positive one instead in that its a way of subsidizing programming or generating public information... 

Should we put Pigouvian taxes on advertising or instead subsidize the necessary infrastructure?

This post is about advertising , but does not have any references:
There is a vast literature in both economics and marketing on advertising. Some highlights relevant to your specific question:


A classic paper (Grossman and Shapiro 1984) looks at competitive advertising and indeed finds that advertisers tend to send too many ads. Intuitively, some customers attracted by an ad aren't new demand, but rather simply stolen from a rival firm. Sending the ads these consumers saw wasted resources without creating any genuinely new trade, and are therefore sub-optimal.
More recent work (such as Anderson and de Palma, 2012, and van Zandt, 2004) considers information overload: the problem that ads crowd out other ads when consumers have limited attention. Again, this leads to sellers sending too many ads.


More generally, Bagwell (2007) has a nice survey of the economic literature on advertising.



Incidentally, it is also conceivable that there might be too few ads in equilibrium for some kinds of product. For example, if you and I both sell products that are very similar and the main function of ads is to inform consumers about the characteristics of those products then advertising is a public good. I would prefer to free-ride and let you bear the expense of advertising to inform consumers. I can take the money I save on advertising and use it to offer lower prices or better quality and thereby capture the demand of the consumers you so generously informed. The fact that arrangements such as vertical integration or franchising help to mitigate this free-riding problem is one reason why such arrangements are sometimes viewed more favourably by competition authorities.