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https://en.wikipedia.org/wiki/Exchange_value mentions 4 notions of value: economic value, exchange value, use value, price. But this article also mentions that these are Marxian concepts and the contemporary economy do not make distinction among those values and the notion of the market price is sufficient to explain the value of the good of service.

Actually I would like to follow the path of contemporary orthodox economic theory, not heterodox theory. But I feel that there can be cases, where goods can have value that is different from the market price and it would be worth to capture and determine those other values:

  • value of energy unit produced by different technologies (oil or green). One can argue that the same unit of energy that is sold by the same market price have different societal value because of some environment harm
  • culture goods: they are not usually appropriately priced by the society, e.g. many countries have subsidies for the concerts of contemporary classical music or for the culture periodicals
  • scientific discovery service: scientific discovery usually is not priced accordingly - wages for the scientists are small but the impact of their discoveries can be enormous.

So - some valuation always happen in government subsidies etc. Are there valuation theories (orthodox, conventional, non-Marxian) that try to capture this valuation process (e.g. for green economy, for cultural goods, for science investments) in some common terms? Are there game theories that try to determine the multiple types of value for some item?

My question is very important - computer science and artificial intelligence consider reinforcement learning as the most promising approach for the emergence of intelligence. Such learning process requires reward function. One can argue that the simple market price is the best reward function. But - if governments have some subsidy process, some support process for some parts of economy then the value theory and valuation games are very important for the determination of the reward function that is used for the training artificial general intelligence?

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    $\begingroup$ "they are not usually appropriately priced by the society, e.g. many countries have subsidies for the concerts of contemporary classical music or for the culture periodicals" Are you sure you mean "society"? It is society who decides on subsidy. Perhaps this is an example of market failure. $\endgroup$ – Giskard Nov 25 '19 at 23:05
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    $\begingroup$ "scientific discovery usually is not priced accordingly - wages for the scientists are small but the impact of their discoveries can be enormous" Emphasis on the word "can". In expected value, do scientists earn less than they could? $\endgroup$ – Giskard Nov 25 '19 at 23:06
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    $\begingroup$ "capture this valuation process [...] in some common terms" What do you mean by "common terms"? Is marginal societal benefit a "common term"? $\endgroup$ – Giskard Nov 25 '19 at 23:07
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    $\begingroup$ "Are there game theories that try to determine the multiple types of value for some item?" Sorry, but I simply do not understand this sentence. $\endgroup$ – Giskard Nov 25 '19 at 23:07
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    $\begingroup$ Okay, so what is your exact question? What is the "best" value function? $\endgroup$ – Giskard Nov 25 '19 at 23:08
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The current mainstream theory of value is the subjective theory of value: goods or services have value that people subjectively believe that they have. Rembrandt paintings cost millions because someone subjectively thinks they are worth that much.

If there are no market failures the market price captures the subjective value through supply demand interactions.

However, in case of environment there are market failures. For example, due to lack of property rights to clean air firms use it for free and hence the subjective value of clean air is not reflected in market price. This would be example of negative externality. Externalities can be also positive, for example basic research can’t be patented so it’s value is more than scientist can get out of it by supplying their ideas on market.

If there is a negative or positive externality the subjective value is still there but it’s incredibly hard to find out. An example of how economists try to find this would be to use some econometric techniques like for example hedonic pricing which tries to estimate the value not captured in market price by observing how other market values change when availability of the good suffering the externality changes (for example by looking how pollution affect housing prices). Other techniques exists I would recommend starting with the hedonic pricing as it’s the most simple ones and you will see that many articles discussing it will point out to more complex techniques.

Also note that in many cases government might already correct for these externalities by taxes and subsidies or by issuing property rights over clean air by tradable polluting permits (cap and trade). Assuming, the government where you live already corrects for externalities and does it properly the market price would reflect also the subjective valuation of environmental goods etc.

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