<blockquote>
<p>Are there proper terms to differentiate production-chain, final-consumption, and investment-only goods?</p>
</blockquote>
<p>There aren't in terms of objective/subjective value. You can call final consumption goods final consumption goods, and investment-only goods investment goods etc. but value of all these is considered subjective.</p>
<p>According to our best understanding value of any good and service is derived from marginal utility. This is something that virtually all serious modern economists subscribe to, and this is the theory of value used in virtually all modern economics textbooks (outside of perhaps history of economics thought).</p>
<p>Marginal utility is derived from people's preferences (you can see Varian Microeconomic Analysis ch7-9 for examples how you derive demand from marginal utility and marginal utility from preferences). As a result this implies that all values are subjective and there is no such thing as objective value (objective value was old theory that people subscribed to in middle ages and early enlightenment e.g. Thomas Aquinas or Adam Smith, but virtually all modern economists reject such notion).</p>
<p>As a result there is no way how you can distinguish between them because values of both of those are ultimately purely subjective. For example, if people's preferences would drastically shift in such a way that people consider oil and anything derived from it evil (lets say for environmental reasons) value of oil would drop to zero regardless of the fact that it is a resource that can be used to produce large number of useful products. It does not matter whether somethings is useful or not, you might have life saving vaccine but if people are misinformed and convinced the vaccine is bad by some misinformation campaign (example of preference shift) the value of life saving drug will plummet the same way as value of useless NFT once people don't find it fashionable to hold one.</p>
<blockquote>
<p>Ways to address the subjectivity of value, or proof that these values are indeed equal?</p>
</blockquote>
<p>You can prove that these values are equal in stylized example. Start with utility function:</p>
<p><span class="math-container">$$U = x^{0.5}y^{0.5}$$</span></p>
<p>where <span class="math-container">$x$</span> is let's say bread and <span class="math-container">$y$</span> are NFT pictures of apes.</p>
<p>Subject to budget constraint <span class="math-container">$xp+qy=m$</span> where <span class="math-container">$p$</span> is price of bread and <span class="math-container">$q$</span> price of NFT apes. <span class="math-container">$m$</span> is the person's income say for the purposes of this example it 100. Deriving and solving the system of first order conditions which are marginal utilities of <span class="math-container">$x$</span> and <span class="math-container">$y$</span> plus the budget constraint the person's demand for bread and pictures of apes will be:</p>
<p><span class="math-container">$$x= 50/p \quad \text{and} \quad y =50/q$$</span></p>
<p>Now to derive prices lets assume simple supply function for both bread <span class="math-container">$x=2$</span> and pictures of apes <span class="math-container">$y=2$</span> (these do not need to be constant, we could make these functions arbitrarily complex but it would only make the problem more difficult to solve). This will give us the following set of prices:</p>
<p><span class="math-container">$p = 25$</span> and <span class="math-container">$q=25$</span>.</p>
<p>Given these prices agent will consume 2 units of bread and apes and will derive exactly <span class="math-container">$\sqrt 2$</span> utils from bread consumption and exactly <span class="math-container">$\sqrt 2$</span> utils from consumptions of NFT apes. If we would calculate GDP in this example, the GDP would be equal to <span class="math-container">$px+qy= 25\cdot 2 + 25\cdot 2 =100$</span> which would correctly capture that the agent derives the same value from bread and pictures of apes.</p>
<p>You could make the example more complex with adding layered supply chain but ultimately the reason why firms get some intermediate goods or investment goods is because they are trying to satisfy their customer's demand that is derived from marginal utility and subjective valuation of things.</p>
<p>Now note, nothing above should be interpreted as some sort of endorsement of NFTs. Marginal utility and hence demand for bread over long term will be almost definitely more stable than demand for NFT.    The point is that you can't say that the demand for bread is somehow more objective than the demand for NFT. Both demand for bread and NFT is derived purely from subjective utility function. If utility function changes, e.g. some religion convincing people that eating bread is bad, then bread it loose any value it had previously because its value was ultimately subjective as value of everything is regardless of the fact that bread can nourish you.</p>

CC BY-SA 4.0
2023-06-16T15:07:17.610Z
The utility function is not √x*√y though. It's non-linear, with y losing value in time of crisis. If crises are cyclical, it could be √x+y^sin(t), where t is time. Or something like x*y^log(x), reflecting the dependence.
Therac
CC BY-SA 4.0
2023-06-16T16:17:09.567Z
@Therac That’s inconsequential, if the value comes from utility function it’s prima facie subjective not objective. Also economic cycles are non-regular, but suppose the utility is $U=x^{0.5}y^{0.5*D}$ where D is a dummy that is 0 during economic crisis and 1 outside economic crisis (this dummy approach is better alternative to what you suggest)… it still does not make value of x any more objective than value of y they are both equally subjective, you would just discover a pattern in subjective preferences, as mentioned in my answer some preferences are more stable than other but
1muflon1
CC BY-SA 4.0
2023-06-16T16:19:35.533Z
Whether stable or not they are subjective preferences nonetheless. In this case subjective value of NFT would drop during the crisis because the demand dropped, but that does not mean the value of NFT was somehow more subjective, the value for bread also depends on preferences and there could be shock to preferences for bread that would match the shock you hypothesize NFTs experience during economic crisis
1muflon1
CC BY-SA 4.0
2023-06-16T17:25:23.777Z
I guess both are subjective... Hard to ask the right question. Currently, air has a value of 0, but if its supply falls to 0, other goods drop to 0 in value. So which models to look to that address this sort of value relationships?
Therac
CC BY-SA 4.0
2023-06-16T18:51:21.723Z
@Therac you can use the model above. In fact air has zero value because supply simply outpaces demand. In the utility optimization example above if I would set supply of NFT apes to 100000 their price would be essentially zero. If the supply would go to infinity price would be exactly zero. For air supply is virtually infinite but your demand is finite. This can all be modeled with (advanced) versions of model I presented in my answer. If you wanna see some more advanced versions have a look at Varian Microeconomic Analysis or MWG Microeconomic Theory, but in essence you can just extend
1muflon1
CC BY-SA 4.0
2023-06-16T18:54:57.640Z
what I was doing above to any utility function $U(\mathbf{x})$ you find empirically plausible (where $\mathbf{x}$ is a vector of arbitrary number of inputs i.e. goods and services - you can also add leisure etc), budget constraint will always be $\mathbf{px=m}$ where $\mathbf{p}$ is price vector and $m$ income vector, and then supply can be given by whatever supply function you want, perhaps supply of cars is given by $x_{car} = 20k*p_{car}-100k$. You can also directly include firm profit max behavior where you model also firm production function etc
1muflon1
CC BY-SA 4.0
2023-06-16T18:55:48.640Z
Although be aware that the more equations you add to the model the more difficult it is to solve, and the better computer you will need (you won't be able to solve something like this analytically on paper for diverse industries). Also if you wanna do this with realistic/empirical parameters you will have to do quite a lot of statistical analysis to estimate what parameter values are or go and try to find them in literature
1muflon1
CC BY-SA 4.0
2023-06-16T12:18:46.447Z
2023-06-16T12:25:20.800Z
2023-06-16T12:25:20.800Z
1muflon1
<p>Suppose economies A, B and C have equal GDP. However:</p>
<ul>
<li>90% of A is goods of strictly investment value (artwork, NFTs)</li>
<li>90% of B is tools for producing other goods (resources, machinery)</li>
<li>90% of C is items of necessity (oxygen and water on Mars)</li>
</ul>
<p>In a scenario of fixed-rate growth and unrestricted trade, A=B=C. In recession, the value of non-necessities can drop. So in a world with economic cycles, one could argue that <code>$1T in valuation</code> isn't always equal to <code>$1T in hardware</code>.</p>
<p>Are there terms to differentiate production-chain, final-consumption, and investment-only goods? Or proof that these values are indeed equal.</p>
<p>In terms of utility function, it can be expressed as product X acting as supplement to Y, having zero utility if supply of Y is insufficient. E.g., NFTs require computers, which require electricity.</p>
<p>Venture capitalists use a &quot;vitamins or painkillers?&quot; metaphor, with the implication (true or not) that demand for the latter is more stable. This factors into decision-making, so has an economic value.</p>
<p>Is there any theory or economic model that quantifies stable vs volatile value and dependencies, or differences in sources of value?</p>

<macroeconomics><value>
Quantifying stability and source of value
Therac
# Quantifying stability and source of value

(Asked by: username_0 on 2023-06-16)

Suppose economies A, B and C have equal GDP. However:

* 90% of A is goods of strictly investment value (artwork, NFTs)
* 90% of B is tools for producing other goods (resources, machinery)
* 90% of C is items of necessity (oxygen and water on Mars)

In a scenario of fixed-rate growth and unrestricted trade, A=B=C. In recession, the value of non-necessities can drop. So in a world with economic cycles, one could argue that `$1T in valuation` isn't always equal to `$1T in hardware`.

Are there terms to differentiate production-chain, final-consumption, and investment-only goods? Or proof that these values are indeed equal.

In terms of utility function, it can be expressed as product X acting as supplement to Y, having zero utility if supply of Y is insufficient. E.g., NFTs require computers, which require electricity.

Venture capitalists use a "vitamins or painkillers?" metaphor, with the implication (true or not) that demand for the latter is more stable. This factors into decision-making, so has an economic value.

Is there any theory or economic model that quantifies stable vs volatile value and dependencies, or differences in sources of value?

**Tags:** macroeconomics, value


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## 1 answers

### Answer by username_1 on 2023-06-16. Score: 1 | Accepted answer

> Are there proper terms to differentiate production-chain, final-consumption, and investment-only goods?

There aren't in terms of objective/subjective value. You can call final consumption goods final consumption goods, and investment-only goods investment goods etc. but value of all these is considered subjective.

According to our best understanding value of any good and service is derived from marginal utility. This is something that virtually all serious modern economists subscribe to, and this is the theory of value used in virtually all modern economics textbooks (outside of perhaps history of economics thought).

Marginal utility is derived from people's preferences (you can see Varian Microeconomic Analysis ch7-9 for examples how you derive demand from marginal utility and marginal utility from preferences). As a result this implies that all values are subjective and there is no such thing as objective value (objective value was old theory that people subscribed to in middle ages and early enlightenment e.g. Thomas Aquinas or Adam Smith, but virtually all modern economists reject such notion).

As a result there is no way how you can distinguish between them because values of both of those are ultimately purely subjective. For example, if people's preferences would drastically shift in such a way that people consider oil and anything derived from it evil (lets say for environmental reasons) value of oil would drop to zero regardless of the fact that it is a resource that can be used to produce large number of useful products. It does not matter whether somethings is useful or not, you might have life saving vaccine but if people are misinformed and convinced the vaccine is bad by some misinformation campaign (example of preference shift) the value of life saving drug will plummet the same way as value of useless NFT once people don't find it fashionable to hold one.

> Ways to address the subjectivity of value, or proof that these values are indeed equal?

You can prove that these values are equal in stylized example. Start with utility function:

$$U = x^{0.5}y^{0.5}$$

where $x$ is let's say bread and $y$ are NFT pictures of apes.

Subject to budget constraint $xp+qy=m$ where $p$ is price of bread and $q$ price of NFT apes. $m$ is the person's income say for the purposes of this example it 100. Deriving and solving the system of first order conditions which are marginal utilities of $x$ and $y$ plus the budget constraint the person's demand for bread and pictures of apes will be:

$$x= 50/p \quad \text{and} \quad y =50/q$$

Now to derive prices lets assume simple supply function for both bread $x=2$ and pictures of apes $y=2$ (these do not need to be constant, we could make these functions arbitrarily complex but it would only make the problem more difficult to solve). This will give us the following set of prices:

$p = 25$ and $q=25$.

Given these prices agent will consume 2 units of bread and apes and will derive exactly $\sqrt 2$ utils from bread consumption and exactly $\sqrt 2$ utils from consumptions of NFT apes. If we would calculate GDP in this example, the GDP would be equal to $px+qy= 25\cdot 2 + 25\cdot 2 =100$ which would correctly capture that the agent derives the same value from bread and pictures of apes.

You could make the example more complex with adding layered supply chain but ultimately the reason why firms get some intermediate goods or investment goods is because they are trying to satisfy their customer's demand that is derived from marginal utility and subjective valuation of things.

Now note, nothing above should be interpreted as some sort of endorsement of NFTs. Marginal utility and hence demand for bread over long term will be almost definitely more stable than demand for NFT. The point is that you can't say that the demand for bread is somehow more objective than the demand for NFT. Both demand for bread and NFT is derived purely from subjective utility function. If utility function changes, e.g. some religion convincing people that eating bread is bad, then bread it loose any value it had previously because its value was ultimately subjective as value of everything is regardless of the fact that bread can nourish you.

> **Comments:**
> **username_0**: The utility function is not √x*√y though. It's non-linear, with y losing value in time of crisis. If crises are cyclical, it could be √x+y^sin(t), where t is time. Or something like x*y^log(x), reflecting the dependence.  
> **username_1**: @username_0 That’s inconsequential, if the value comes from utility function it’s prima facie subjective not objective. Also economic cycles are non-regular, but suppose the utility is $U=x^{0.5}y^{0.5*D}$ where D is a dummy that is 0 during economic crisis and 1 outside economic crisis (this dummy approach is better alternative to what you suggest)… it still does not make value of x any more objective than value of y they are both equally subjective, you would just discover a pattern in subjective preferences, as mentioned in my answer some preferences are more stable than other but  
> **username_1**: Whether stable or not they are subjective preferences nonetheless. In this case subjective value of NFT would drop during the crisis because the demand dropped, but that does not mean the value of NFT was somehow more subjective, the value for bread also depends on preferences and there could be shock to preferences for bread that would match the shock you hypothesize NFTs experience during economic crisis  
> **username_0**: I guess both are subjective... Hard to ask the right question. Currently, air has a value of 0, but if its supply falls to 0, other goods drop to 0 in value. So which models to look to that address this sort of value relationships?  
> **username_1**: @username_0 you can use the model above. In fact air has zero value because supply simply outpaces demand. In the utility optimization example above if I would set supply of NFT apes to 100000 their price would be essentially zero. If the supply would go to infinity price would be exactly zero. For air supply is virtually infinite but your demand is finite. This can all be modeled with (advanced) versions of model I presented in my answer. If you wanna see some more advanced versions have a look at Varian Microeconomic Analysis or MWG Microeconomic Theory, but in essence you can just extend  
> **username_1**: what I was doing above to any utility function $U(\mathbf{x})$ you find empirically plausible (where $\mathbf{x}$ is a vector of arbitrary number of inputs i.e. goods and services - you can also add leisure etc), budget constraint will always be $\mathbf{px=m}$ where $\mathbf{p}$ is price vector and $m$ income vector, and then supply can be given by whatever supply function you want, perhaps supply of cars is given by $x_{car} = 20k*p_{car}-100k$. You can also directly include firm profit max behavior where you model also firm production function etc  
> **username_1**: Although be aware that the more equations you add to the model the more difficult it is to solve, and the better computer you will need (you won't be able to solve something like this analytically on paper for diverse industries). Also if you wanna do this with realistic/empirical parameters you will have to do quite a lot of statistical analysis to estimate what parameter values are or go and try to find them in literature  

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