<p>From your comments it seems that it is immaterial for your question that it is the <em>government</em> whose willingness to pay (WTP) you want to elicit. It might as well be any agent with a well defined WTP function. If this is correct, then you can of course use the classic <a href="https://en.wikipedia.org/wiki/Becker%E2%80%93DeGroot%E2%80%93Marschak_method" rel="nofollow noreferrer">Becker–DeGroot–Marschak mechanism</a>. However, you should be prepared for the possibility that you have to sell your house.</p>

CC BY-SA 4.0
2022-09-19T13:41:33.953Z
I thought it was clear that I wanted to elicit the government's willingness to pay (at least the highest WTP besides the owner's I am ok with the government finding that different agent and getting them to buy for the number they declared.) **I want my government to declare the highest price it would buy at if I so decided.** what edit do you suggest to make that clear?
George Ntoulos
CC BY-SA 4.0
2022-09-19T13:49:57.270Z
**In another common method, the subject is presented with a series of sequentially increasing or random-order monetary amounts. They must decide if they would prefer to have that amount of money or the item at hand. Then, one of these numbers is chosen either specifically by the experimenter or is randomly generated. If the chosen number is less than the amount of money at which the subject stated they would prefer the item, the subject must purchase the item.** It seems that the mechanism remains the same if the granularity is infinite and the "experimenter" is the tax payer. I.e my proposal.
George Ntoulos
CC BY-SA 4.0
2022-09-20T08:52:07.810Z
@GeorgeNtoulos, under a BDM mechanism the government declares the "highest price it would buy at", i.e. its WTP. That's what you asked for, right? That's what you get.
VARulle
CC BY-SA 4.0
2022-09-20T11:45:59.390Z
Wouldn't it be also incentive compatible if the government declared some number (supposed to be the WTP) and then the tax payer texided to keep their property or sell at the supposed WTP the government declared? Wouldn't it be equivalent to choosing an amount and the experimenter choosing?
George Ntoulos
CC BY-SA 4.0
2022-09-20T13:25:03.560Z
@GeorgeNtoulos, no, this mechanism is not incentive compatible. If the government truthfully declares its WTP and then either doesn't buy or buys at this price, then it is guaranteed a fixed surplus of 0. This is not optimal under the mechanism.
VARulle
CC BY-SA 4.0
2022-09-20T13:46:30.687Z
But what I said is that it is not the government that decides (whether the government has to buy) but the taxpayer. If the government declares anything greater than the WTP it risks paying what it declared (it will collect more taxes but will pay more than it was ready to pay for the asset). If it declares less it will collect less taxes (but has the chance to get the asset for less that its WTP). The governments WTP needs to be declared exactly for tax purposes.
George Ntoulos
CC BY-SA 4.0
2022-09-20T14:24:23.040Z
@GeorgeNtoulos, yes, it's the owner who decides, but it's still the government who buys (or not), as I wrote. The tax issue is another thing. Additionally, the owner wouldn't want to sell if the randomly determined price of the BDM mechanism is too small. In this case, the BDM wouldn't work. But in the end I think the questions needs to be rewritten to make it clear what assumptions on the objective functions of owner and government you are making.
VARulle
CC BY-SA 4.0
2022-09-24T15:54:39.110Z
I don't know if I made any progress. I don't know how to account for uncertainty on Z (intuitivelly the Government would select a value just below Z of Z if it was higher than all other valuations for the asset).
George Ntoulos
CC BY-SA 4.0
2022-09-19T12:11:22.943Z
2022-09-19T12:11:22.943Z
VARulle
<p>I think I understood your question. You want a mechanism through which the government and the owner of the non-monetary asset interact in such a way that the tax charged is &quot;fair&quot;, right? If this is correct I think the issue here is to define what would be a &quot;fair&quot; tax, and in your question you are assuming that fairness will be for the tax to the depend on the government valuation. However, I believe the government's value for someone's house, for example, has no reason to be different from the house's market value, so I think what you want is simply that the basis value for the tax to be the house's market value, but this should be public information.</p>
<p>The problem is that there are illiquid assets, like a house, such that the market value is not as precise as the price of a stock, and in this case the government might have an incentive to claim that the asset's value is more than it actually is to earn more taxes as it happened to you. I believe that the most obvious solution to this problem is to have more precise estimates of the asset's value, and in this sense there is no incentive problem so it is unnecessary to design an incentive compatible mechanism since there is no reason for the government's value for your house be different than its market value.</p>
<p>The book Radical Markets by Eric Posner and Glen Weyl look at this problem from another perspective, and by that I mean that the tax does not depend on the government's valuation, as you proposed, but on the owner's valuation. They proposed substituting the current rules of property taxation to Harberger taxation. In a system with Harberger taxation the taxes an individual pays depends on the owner's assessment of the asset's value, and if there is another person willing to pay the price the owner reported, then the owner has to sell it. A formalization of this idea can be found in <a href="https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=2471&amp;context=law_and_economics" rel="nofollow noreferrer">Ownership of the Means of Production (2016)</a> by Weyl and Zhang.</p>

CC BY-SA 4.0
2021-12-21T19:36:04.510Z
I did not ask for a fair price or a fair tax. I did not ask of an interaction. I asked about a simple game (a mechanism) that would make the government spit out its indiferrence price (I might think that that it is fair but that is another issue we are comparing apples and oranges here). I prefer the choice to be the owner's to sell the property and not another person's to buy it.
George Ntoulos
CC BY-SA 4.0
2021-12-21T22:42:26.597Z
Now I think I don't understand your question, I thought you wanted to find a way to avoid the government overestimating the value of non-monetary assets to increase tax revenue. When you say that the government sets an arbitrary price to tax a non-monetary property I think about the government choosing a value for your house to tax it, and since I think it is unlikely that the government will have any use for a random house I would say that its value is just the price the government can get by selling it, that is, its market value.
Pedro Ozenda
CC BY-SA 4.0
2021-12-22T06:48:12.763Z
If its value (the government's indifference price) is just the price the government can get by selling it (that is fine by me I) I want the government to declare it (the property's value, the government's indiferrence price, in the end the price the government can get by selling it). The government may use the property (not just a random house but the specific asset it is evaluating) in a lot of different ways including renting it or the government itself using it. My motivation for wanting the government to declare the indifference price shouldn't have any weight in itself on the answer.
George Ntoulos
CC BY-SA 4.0
2021-12-22T06:53:55.893Z
Which means I don't want alternatives that lead to a "fair" tax but I want the government to declare its indiferrence price (even if it is the price it can get by selling it). Nothing else no alternatives. And what the government will do and what it will do with each specific property in the end is of no concern. In this question I am only asking how to make the government declare its indifference prince. Secondarily (not a part of the question) I want the government to make the best use possible out its property (but I am not asking how can that happen it is just a matter of good governance).
George Ntoulos
CC BY-SA 4.0
2021-12-21T19:20:35.167Z
2021-12-21T19:20:35.167Z
Pedro Ozenda
<p>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.</p>
<p>Government: X is worth Y</p>
<p>Me: Sold (or not if I so wish)</p>
<p>How can we force (make an incentive compatible mechanism for) the government to reveil its indifference price towards all goods/property to be Taxed?</p>
<p>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).</p>
<p>How I went about trying to solve the problem.</p>
<p>The government has a WTP Y (because either it values the asset at Y or because it can sell at Y if no agent has a higher WTP than the owner then obviously Y=Z)
The owner has a WTS Z</p>
<p>The government want to maximize their wealth.</p>
<p>So everytime anything lower than Y (X&lt;Y) will not be declared because
The government would lose on taxes (it can increase the tax revenues until Y without worrying about having to purchase)</p>
<p>On the other hand when it declares something higher than Z the owner will sell making the government earn the tax rate but lose MR of 1.</p>
<p>Let's say the tax rate in not constant but proportional to some tax rate for the highest valued asset</p>
<p><span class="math-container">$\dfrac{x^2}{2w} + Y - X$</span> is the function of the of the government</p>
<p>We can see that when x &lt; w (always true since w is the highest valued asset)
The government actually loses more than it earns for declaring anything higher</p>
<p>I don't know how to account for uncertainty on Z</p>

CC BY-SA 4.0
2021-11-03T23:07:00.660Z
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?
axelniemeyer
CC BY-SA 4.0
2021-11-04T06:32:13.880Z
@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).
George Ntoulos
CC BY-SA 4.0
2021-11-04T06:33:01.720Z
@axelniemeyer I want the assesments to be personalized and equal to the governments indifference price.
George Ntoulos
CC BY-SA 4.0
2021-11-04T20:46:04.520Z
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?
axelniemeyer
CC BY-SA 4.0
2021-11-04T23:42:26.917Z
@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.
George Ntoulos
CC BY-SA 4.0
2021-11-04T23:48:04.203Z
@axelniemeyer Can you please explain what is the russian roulete mechanism and what you mean with resale price? The taxpayer should not be able to commit not to rebuy the house (I don't understand the importance of the commitment). The taxrate is also decided by the government but it should be previously known for both (at present it only decided one the valuation of the good) so it should be considered constant and exogenous (still it should be a variable and not a numerical value).
George Ntoulos
<microeconomics><mathematical-economics><game-theory><auctions><mechanism-design>
Mechanism design making the Government reveil its indiferrence price towards goods
George Ntoulos
# Mechanism design making the Government reveil its indiferrence price towards goods

(Asked by: username_0 on 2021-10-30)

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).

How I went about trying to solve the problem.

The government has a WTP Y (because either it values the asset at Y or because it can sell at Y if no agent has a higher WTP than the owner then obviously Y=Z)
The owner has a WTS Z

The government want to maximize their wealth.

So everytime anything lower than Y (X

On the other hand when it declares something higher than Z the owner will sell making the government earn the tax rate but lose MR of 1.

Let's say the tax rate in not constant but proportional to some tax rate for the highest valued asset

$\dfrac{x^2}{2w} + Y - X$ is the function of the of the government

We can see that when x < w (always true since w is the highest valued asset)
The government actually loses more than it earns for declaring anything higher

I don't know how to account for uncertainty on Z

**Tags:** microeconomics, mathematical-economics, game-theory, auctions, mechanism-design
> **Comments:**
> **username_1**: 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?  
> **username_0**: @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).  
> **username_0**: @axelniemeyer I want the assesments to be personalized and equal to the governments indifference price.  
> **username_1**: 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?  
> **username_0**: @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.  
> **username_0**: @axelniemeyer Can you please explain what is the russian roulete mechanism and what you mean with resale price? The taxpayer should not be able to commit not to rebuy the house (I don't understand the importance of the commitment). The taxrate is also decided by the government but it should be previously known for both (at present it only decided one the valuation of the good) so it should be considered constant and exogenous (still it should be a variable and not a numerical value).  

---

## 2 answers

### Answer by username_2 on 2022-09-19. Score: 0

From your comments it seems that it is immaterial for your question that it is the *government* whose willingness to pay (WTP) you want to elicit. It might as well be any agent with a well defined WTP function. If this is correct, then you can of course use the classic [Becker–DeGroot–Marschak mechanism](https://en.wikipedia.org/wiki/Becker%E2%80%93DeGroot%E2%80%93Marschak_method). However, you should be prepared for the possibility that you have to sell your house.

> **Comments:**
> **username_0**: I thought it was clear that I wanted to elicit the government's willingness to pay (at least the highest WTP besides the owner's I am ok with the government finding that different agent and getting them to buy for the number they declared.) **I want my government to declare the highest price it would buy at if I so decided.** what edit do you suggest to make that clear?  
> **username_0**: **In another common method, the subject is presented with a series of sequentially increasing or random-order monetary amounts. They must decide if they would prefer to have that amount of money or the item at hand. Then, one of these numbers is chosen either specifically by the experimenter or is randomly generated. If the chosen number is less than the amount of money at which the subject stated they would prefer the item, the subject must purchase the item.** It seems that the mechanism remains the same if the granularity is infinite and the "experimenter" is the tax payer. I.e my proposal.  
> **username_2**: @GeorgeNtoulos, under a BDM mechanism the government declares the "highest price it would buy at", i.e. its WTP. That's what you asked for, right? That's what you get.  
> **username_0**: Wouldn't it be also incentive compatible if the government declared some number (supposed to be the WTP) and then the tax payer texided to keep their property or sell at the supposed WTP the government declared? Wouldn't it be equivalent to choosing an amount and the experimenter choosing?  
> **username_2**: @GeorgeNtoulos, no, this mechanism is not incentive compatible. If the government truthfully declares its WTP and then either doesn't buy or buys at this price, then it is guaranteed a fixed surplus of 0. This is not optimal under the mechanism.  
> **username_0**: But what I said is that it is not the government that decides (whether the government has to buy) but the taxpayer. If the government declares anything greater than the WTP it risks paying what it declared (it will collect more taxes but will pay more than it was ready to pay for the asset). If it declares less it will collect less taxes (but has the chance to get the asset for less that its WTP). The governments WTP needs to be declared exactly for tax purposes.  
> **username_2**: @GeorgeNtoulos, yes, it's the owner who decides, but it's still the government who buys (or not), as I wrote. The tax issue is another thing. Additionally, the owner wouldn't want to sell if the randomly determined price of the BDM mechanism is too small. In this case, the BDM wouldn't work. But in the end I think the questions needs to be rewritten to make it clear what assumptions on the objective functions of owner and government you are making.  
> **username_0**: I don't know if I made any progress. I don't know how to account for uncertainty on Z (intuitivelly the Government would select a value just below Z of Z if it was higher than all other valuations for the asset).  

---

### Answer by username_3 on 2021-12-21. Score: 0

I think I understood your question. You want a mechanism through which the government and the owner of the non-monetary asset interact in such a way that the tax charged is "fair", right? If this is correct I think the issue here is to define what would be a "fair" tax, and in your question you are assuming that fairness will be for the tax to the depend on the government valuation. However, I believe the government's value for someone's house, for example, has no reason to be different from the house's market value, so I think what you want is simply that the basis value for the tax to be the house's market value, but this should be public information.

The problem is that there are illiquid assets, like a house, such that the market value is not as precise as the price of a stock, and in this case the government might have an incentive to claim that the asset's value is more than it actually is to earn more taxes as it happened to you. I believe that the most obvious solution to this problem is to have more precise estimates of the asset's value, and in this sense there is no incentive problem so it is unnecessary to design an incentive compatible mechanism since there is no reason for the government's value for your house be different than its market value.

The book Radical Markets by Eric Posner and Glen Weyl look at this problem from another perspective, and by that I mean that the tax does not depend on the government's valuation, as you proposed, but on the owner's valuation. They proposed substituting the current rules of property taxation to Harberger taxation. In a system with Harberger taxation the taxes an individual pays depends on the owner's assessment of the asset's value, and if there is another person willing to pay the price the owner reported, then the owner has to sell it. A formalization of this idea can be found in [Ownership of the Means of Production (2016)](https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=2471&context=law_and_economics) by Weyl and Zhang.

> **Comments:**
> **username_0**: I did not ask for a fair price or a fair tax. I did not ask of an interaction. I asked about a simple game (a mechanism) that would make the government spit out its indiferrence price (I might think that that it is fair but that is another issue we are comparing apples and oranges here). I prefer the choice to be the owner's to sell the property and not another person's to buy it.  
> **username_3**: Now I think I don't understand your question, I thought you wanted to find a way to avoid the government overestimating the value of non-monetary assets to increase tax revenue. When you say that the government sets an arbitrary price to tax a non-monetary property I think about the government choosing a value for your house to tax it, and since I think it is unlikely that the government will have any use for a random house I would say that its value is just the price the government can get by selling it, that is, its market value.  
> **username_0**: If its value (the government's indifference price) is just the price the government can get by selling it (that is fine by me I) I want the government to declare it (the property's value, the government's indiferrence price, in the end the price the government can get by selling it). The government may use the property (not just a random house but the specific asset it is evaluating) in a lot of different ways including renting it or the government itself using it. My motivation for wanting the government to declare the indifference price shouldn't have any weight in itself on the answer.  
> **username_0**: Which means I don't want alternatives that lead to a "fair" tax but I want the government to declare its indiferrence price (even if it is the price it can get by selling it). Nothing else no alternatives. And what the government will do and what it will do with each specific property in the end is of no concern. In this question I am only asking how to make the government declare its indifference prince. Secondarily (not a part of the question) I want the government to make the best use possible out its property (but I am not asking how can that happen it is just a matter of good governance).  

---

