# Mechanism design making the Government reveil its indiferrence price towards goods

In order to Tax non-monetary property and wealth the government sets an arbitrary price (they are not even personalized assesments) and often people transact below that price. I have bought and sold below that price. I want my government to declare the highest price it would buy at if I so decided.

Government: X is worth Y

Me: Sold (or not if I so wish)

How can we force (make an incentive compatible mechanism for) the government to reveil its indifference price towards all goods/property to be Taxed?

I want to solve an optimization problem to confirm the incentive compatibility. I am hoping for a stable equilibrium where not only an increase/decrease in the price (any deviation from the indifference price) puts the government in a worse position but also if the government were to declare any other price it would always improve its position be moving closer (the utility function should be unimodal with the mode equal to the government's indifference price and it should have no other local maximum) There should be uncertanty (the government doesn't know the Tax payers' reservation price otherwise the best choice would be to declare their reservation price over your own indifference price).

• I don't understand your question. What do you mean by the government setting a price to tax something? What does it mean for people to transact below that price? Nov 3, 2021 at 23:07
• @axelniemeyer The government (for tax purposes) "says" how much X (for example a house) is "worth". It sets some general and abstract criteria (for example surface area Z\$ per square metre, location the price for a square metre depends on the location, floor a house in the third floor will be worth more than the same house in the basement), And it calculates the Tax you must pay as a percentage of that. The problem is that often what the government calculates is exorbitant (it also inflates thence the Tax payed) and you can find no one to transact at that price (it is merely fictitious). Nov 4, 2021 at 6:32
• @axelniemeyer I want the assesments to be personalized and equal to the governments indifference price. Nov 4, 2021 at 6:33
• I understand what you mean now but the question is still very vague. What kind of model do you have in mind? The government interacting with a single taxpayer in isolation and the valuations of both are their private information? This model is not very good in that the government's valuation comes somewhat out of nowhere. In practice, this valuation should be the resale price, which is more or less common knowledge, so your "russian roulette" mechanism would be the solution. Otherwise, can the taxpayer commit not to rebuy the house? Also, is the taxrate given exogenously? Nov 4, 2021 at 20:46
• @axelniemeyer The government interacts with every taxpayer but since we have variables (we don't need a numerical value for any of them) and we can consider the incentives to be similar (profit-seeking not loss-seeking) we can choose to make the interaction 1-1 to make things easier. Or we can complicate stuff by adding many taxpayers and a liquidity problem (if every taxpayer or at least a lot of them decided to sell maybe the government could not meet the supply). The valuations of both (every person) should probably be private information. Nov 4, 2021 at 23:42