Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market.

We know that prohibiting it( equivalent to an ad valorem tax rate of at least 100%) would lead to maximum incentives for a black market.

As the ad valorem tax rate( or as any amount of taxes do) increases the incentives for a black market increases because the elbow room for profit increases.

One might reduce the consumption directly in the regulated transparent market but they do not know what happens in the unregulated hidden black market. You would just notice the consumption and if it is greater than the regulated market provides you could infer there is a positive supply from the black market or if you prohibit sales in the regulated market any consumption would be one that the black market supplied for.

How could one minimize the total consumption of a good( e.g cigarettes or petroleum/fuel) knowing the fiscalization is less than perfect( bribes, lack of control, etc); i.e the probability of being fined is not 100%(probably much less), and that any single fine should not be greater than the social cost; a principle of fairness I only caused Y damage you can at most fine me for Y?

We also know that when one increases the penalty the cost does not always increase. For example raising the fine might make anyone breaking the law a hero and the social cost of "crime"(buying cigarettes) could decrease.

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    $\begingroup$ This seems a bit vague. (I took the liberty of removing all the unnecessary tags.) $\endgroup$
    – Giskard
    Jan 31 '20 at 18:27
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    $\begingroup$ Also, I am not sure "a tax rate of at least 100%" means what you think it means in this context. A 100% VAT does not confiscate all revenue made from sales, it confiscates half by making the gross price 100% larger than the net price. $\endgroup$
    – Giskard
    Jan 31 '20 at 18:28
  • $\begingroup$ @Giskard I actually think that all of the original tags described perfectly the question. It is certainly about consumer theory and decision theory. While it is also very related to Game Theory. One would need to apply Backwards Induction and think how will the agents act given a certain Policy. A king of Subgame Perfect Nash equilibrium. In which the 2 players decide on diferent turns. Probably the Mathematical Economics was quitte vague. But the question is certainly not about the black market in itself. $\endgroup$ Jan 31 '20 at 18:41
  • $\begingroup$ @Giskard It was about minimizing consumption while recognizing the existance and taking into account the black market. A VAT is a value-added-tax. It is not a tax on revenue it is on the value added. The difference between the price and the inputs( a kind of mark-up. When I said tax I mean an ad valorem tax. A tax on the revenue in itself. 100% tax rate in an ad valorem tax would get 100% of the revenue. $\endgroup$ Jan 31 '20 at 18:45

That is a BIG question, take simply the case of illegal substances. I think that simply taking an econ perspective can be very restrictive, there is a lot of intersection with political science, even military, or law enforcement issues, public sentiment, etc.

It is clear that if you cannot perfectly enforce the law so that the black market is always a possibility, you will not be able to get the quantity to zero. Further, in order to minimize it, you need to think carefully about what are the benefits of reducing the consumption of one extra unit and the costs of doing it. When it comes to black markets we have very noisy information about either of these two. Countries like Colombia, Mexico and th US have tried improving their muscle to enforce the law and punish producers and consumers that break the prohibition, but there is growing evidence that it is not a very effective strategy that has many side effects, the most obvious one is violence.

Other approaches, like Amsterdam, rather aim at providing information so that people know the bad consequences of being addicted, perhaps in an attempt to tamper demand, along with providing ways to use recreational drugs in a safer way (what some people call harm reduction approach). The logic, of course, is that instead of decreasing consumption, decreasing the bad consequences that arise from consumption.

  • $\begingroup$ But we are in Economics. I do not want to discuss the pros and the cons of minimizing. I do not want to discuss interdisciplinarity( there obviously is interdisciplinarity so I took it for granted just accept that there is interdisciplinarity and move on). I do not want to discuss the side effects (violence). I want to learn about minimizing the consumption of one(or a few) good(s). When asked to solve a monopoly you do not go around asking why maximize profit and mention that there are side effects. $\endgroup$ Feb 1 '20 at 0:45
  • $\begingroup$ Do you outright prohibit the consumption, purchase and production or do you put an ad valorem tax lower than 100% so as to reduce the incentives for people to create a black market? Is a fine absolutely equal to the social costs best for the minimization of consumption or a lesser fine is better to leave room for the social punishment? $\endgroup$ Feb 1 '20 at 0:49
  • $\begingroup$ You missed my point... "in order to minimize it, you need to think carefully about what are the benefits of reducing the consumption of one extra unit and the costs of doing it." depending on what you assume in your model, your answer will look veery different... If you wanted an algorithm about how to do it, well set up the equations, construct the lagrangean and set the forst order conditions to zero. I thought your question was way more interesting. $\endgroup$
    – Regio
    Feb 2 '20 at 1:37
  • $\begingroup$ Let me rephrase then. The social cost of every unit is greater than the sum of the utility surplus from the market and the cost to reduce said unit of consumption. My question was not about the motives or incentives to reduce. Just take it for granted. And respect it like you respect that the monopolists wants to maximize their profits. The problem is abstract. There are no closed forms for the lagrangean. And I am not sure that every problem in economics can be solved by constructing the lagrangean, diferrentiating and setting the derivative to 0. What about Rational Expectations? $\endgroup$ Feb 2 '20 at 2:02
  • $\begingroup$ Rational Expectations, Dynamic Optimization and Dynamic Games are few examples when I can't seem to construct a Lagrangean. What did you think I was asking? $\endgroup$ Feb 2 '20 at 2:04

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