The whole point of a pigouvian tax is to force producers to bear an extra cost equal to the total social cost of a good right? But, the problem this presents is, what if the social cost is very high? This means the pigouvian tax must also be high right? And this will be passed onto consumers right? So, if I was a consumer, wouldn't it be much cheaper for me to turn to black market sources as an alternative to the legal source? This result is inefficient, because more than the socially optimal amount is being produced, and this means there are wider negative externalities borne by the rest of us, and the government is starved of revenue from the pigouvian tax that could actually be used to deal with the problem right, further worsening it?
Like for example, let's take some arbitrary good, say timber. The production of timber results in forest destruction right? Well, if we taxed timber and used the money to reforest areas, relocate animals in danger, etc, that can get expensive right? So, for the sake of argument, let's say the cost is sufficiently high that people start looking for black market alternatives. Then more timber is produced, more habitats destroyed, and there is less money to fix it right?
So, what is the efficient solution here? What should be done? If we lower the tax, we won't have enough to deal with the social cost, if we don't lower it, people turn to the black market and we get less revenue. It is a catch 22 right? What is the right policy here?
My first thought was coasian bargaining, but even then there are the problems of transaction costs and market power in the real world.
What can actually be done here? Is there a possibility?
Ideally, only producer profits would be hit because that means costs cannot be passed onto consumers right? And thus no incentive for the black market would exist. But that only works if we could somehow modify the elasticity of a good, and I don't think that's viable right?