The role of physical constraints on production

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Ratbek Dzhumashev discusses the physical constraints of the production process by connecting the actual amount (volume) of physical output to its mass.

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Ratbek Dzhumashev discusses the physical constraints of the production process by connecting the actual amount (volume) of physical output to its mass.

Image courtesy of interviewee. May 28, 2024

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This video discusses a debate surrounding the potential risks of long-term economic growth due to the depletion of non-renewable resources. It references early writings from 1931 that were forgotten and a revisitation in 1972 that sparked renewed interest among economists. Key figures in the debate, like Daly and Hering, critically examined existing frameworks of sustainable growth, particularly criticizing the assumptions made by the Solow model regarding the relationship between resource use and economic output.

The speaker argues that sustainable economic growth is achievable only under certain conditions, which they refer to as "in other conditions." These include acknowledging physical constraints related to resource inputs which must align with the law of conservation of mass. They propose that tangible outputs and the resources needed to produce them are fundamentally linked; thus, as production increases, so must the consumption of material inputs, contrary to the idea of dematerialization.

Through various assumptions about the properties of matter, the speaker lays out a framework suggesting that as economies grow, so will waste and pollution, unless significant efforts in pollution abatement and sustainable practices are implemented. The conclusion emphasizes the necessity for future research to account for the interplay between production, resource use, and environmental impact to foster sustainable economic growth.

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The context is based on, this debate about,

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the possibility of,

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long-term economic growth collapsing if,

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non-renewable resources will be depleted in the future.

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In early, I think in 1931, totally, wrote about this,

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but then it was forgotten.

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And later in 1972, this question was revisited

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by middles and others.

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So they wrote a book, and this book

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started kind of a debate.

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So that, debate then I think attracted the attention of,

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some economists

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and, does group hill, solo sticklet.

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They wrote a few papers, addressing this problem.

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And, they kind of showed

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that the sustainable economic growth is possible as soon as,

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for example, this democratization kind of occurs.

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And democratization, basically means

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that producing more goods while using less,

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material inputs and, to happen.

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I mean, for, for it to happen, we need

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to have something called in other conditions to hold.

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And, that's, that's, important.

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Uh, turns out, property of production.

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And in, economics, we use production functions that's

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sort of, mathematical constructs.

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And those functions, they should have this in other

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conditions, to, to be hold,

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to hold.

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I mean, and, so I can go on further. Yeah. Yeah.

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So, so the,

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and then of course, people start thinking about

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that if it is, possible or not.

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But later, there was some criticism about this.

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Uh, does group, heals all those stickless framework

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because, for example, daily in 19, 97,

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he wrote an ecological economic, journal that,

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this sounds like the evidence doesn't support this,

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solo framework assumption.

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And, later others, for example, Hering in 2006,

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Jackson 2009, they also, emphasize that,

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the, I mean the, slowdown

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of material intensity in the production is not happening.

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Uh, like if you follow this, d the, the,

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heel, solo framework,

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I think it should be happening, but it's not happening.

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And, later also, other authors, highlighted

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that, for example,

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democratization is possible only if economic growth kind of,

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is restricted.

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And, so,

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but some other people, kind of came up with this sort

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of evidence showing that if you look at the GDP data,

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then seems like, the share of, saving, I mean,

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the service are increasing

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and compared to the manufacturing part.

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But then, there also some other people like BFAs

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and Cal, they, published a few papers where they kind

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of show that using the size of GDP is not really, kind

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of correct way of showing that,

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the naturalization is happening

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because the GDP itself is not, directly, kind

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of linked to the physical aspects of production.

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And so, anyway, the, conclusion is

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that seems like dematerialization is not actually taking

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place in this world,

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and that basically means maybe that in other conditions,

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that assumed by, the does Gupta heal

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and stick solo framework may not be true.

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So, what we, what I did was that, I tried to,

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show that this condition doesn't hold,

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and what sort of implications we might have,

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if the condition doesn't hold.

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So, the in other condition itself was formulated by,

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Inad in, 1963.

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And, the intuition behind this, idea is very simple.

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Basically, it means that when,

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we reduce inputs into production, then,

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so-called marginal product of input tends to infinity.

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And if we have infinite inputs, then the marginal product of

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that input will be close to zero.

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And what is relevant in our case is

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that when inputs become small, scars,

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then can we still keep producing more, goods?

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I mean, that's the basic idea here.

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So in order to show that it's not possible, then,

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in this paper, you know, we introduced the sort

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of physical constraints, into this theory of production.

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So, I assume the same, kind

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of product function as in, this,

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heal, stickler solo framework.

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That means, usually in, economics,

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we assume production function takes on two inputs,

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capital and labor.

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But they also introduced a material resources

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as additional input.

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So I do the same, but in, in addition,

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what I do is I kind of introduce, also mass of matter.

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So in order to measure the mass.

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So yeah, I also introduce, a concept

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of, mass function.

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That's a function that kind of, if you check in the ma

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the matter, it tells you what is the mass of that matter.

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I mean, that's kind of the, abstraction.

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But, that's how I think.

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And also, I assume that,

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any tangible matter can be, measured

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and, it, it can be measured by its volume,

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because the idea is that we live, humans,

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we live in this, 3D world,

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Uh, dimension.

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So anything, we see

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or we, kind of, can, feel

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that should have volume, anything that usable

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for us should be, should have its volume.

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So, based on that, then, I make this,

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three assumptions first, that,

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and it comes from the physics of course, that, first

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of all, that, the density

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of any matter is positive.

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I mean, if you can touch and feel something,

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and it should have po positive density.

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I mean, if it has mass,

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then it should be the positive density.

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That's first thing. Second thing is

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that densities are constant.

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I mean, it doesn't really matter if you have, for example,

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10 liters of water or one liter

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of water density should be the same.

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That's the idea. I mean, also, probably,

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reasonable assumption.

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And, the other thing, the third assumption is

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that densities of the outputs, tangible outputs

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and resource used to make, to tho those outputs,

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comparable.

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I mean, you cannot really make, out

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of iron something very light

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and not really, doesn't have any mass.

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So that's, that's the big basic idea.

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They can be different, but they're still in the same order

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of kind of, values.

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So it cannot be like billion times lighter.

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Uh, I mean,

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the output cannot be billion times lighter than the,

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input used to make it.

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So that's the basic idea.

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So, given this then, so, given this, then,

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I try to use also the law of conservation

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of mass, because that's the kind of physical,

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constraint comes from there.

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So the idea is very simple. So the idea is this.

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So if we have some resources

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and we use those resources to make some tangible outputs,

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that the mass of those initial resources should be contained

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partly in output

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and partly in the waste, that we kind

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of generate while producing that, tangible output.

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So then that means, the mass of any output, I mean,

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tangible output will be proportional to the massive,

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resources used.

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I mean, that's also kind of quite simple idea,

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but, we never used it in economics,

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even though it's just like a kind of a straightforward,

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probably logic in, physics.

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So then, using this, kind of relationship

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between massive output

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and massive resources, then, I, I am able to show

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that the marginal resource product is bounded.

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And it's because it turns out the, the marginal product

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of, output will be somehow related to the ratio

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of this densities of output and resources.

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And remember that the assumption was

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that they cannot be too different.

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Yeah. So they cannot be, like, their,

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ratio cannot be, infinity.

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So that means it's bounded.

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So that means there is some, upper bound, value,

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and that kind of shows, I mean, mathematically, we can show

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that,

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we cannot really produce more tangible output

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using very little, resource.

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Basic, basic idea is that.

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So then, we, we also use this, finding

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and show that, whenever we,

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produce more tangible output, that also implies that we have

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to use more, material inputs.

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So, because they're kind of related to each other,

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so turns out we can have some long run implications from

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this sort of, conclusions.

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But to do, to make those, conclusions, we, I mean,

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need to make some, additional sort of, assumptions.

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And first one is the physical size bound.

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So what, what it, what does it mean?

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It means that, any tangible good

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that we consume should have some,

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meaningful physical size.

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Because for humans, we have some physical, sizes, right?

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So, we should have certain, houses

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of certain size clothes,

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or certain size cars of certain size, right?

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They cannot be like, mini was too small,

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then it's not meaningful for us.

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So given this, we can always, show that,

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if any good that we, consume, I mean any tangible good

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as it's minimum size, then everything

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that we produce in terms of tangible goods should be at

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least greater than that, minimum size.

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Okay? So that's one, assumption here.

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So in other words, it, it should also, if it happens

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for each, good, then it should happen

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for all goods together.

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So in aggregate, the physical size of,

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tangible goods cannot be smaller than, certain,

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kind of, minimum.

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The second, assumption is, complementarity

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because, we are talking about tangible goods only.

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Uh, but it's the same time we know

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that the GDP includes more than just tangible goods.

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We have a lot of services.

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So the here assumption is that, still

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we cannot just consume only services.

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So if we, let's say that there are two number of goods,

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there are tangible and number

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of goods that they're intangible.

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So then the ratio of this, numbers cannot be

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less than certain value.

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'cause even if we increase the number

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of different service we consume, we still need

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to consume some number of tangible goods, basically, is

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that, so in other words, we cannot just consume,

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non-tangible goods, and we'll, can go on with that.

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And, so given this cells, we can always show,

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because of this complementarity between tangible,

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non-tangible goods.

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That means whenever we produce more tangible goods,

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or let's say whenever we produce more non-tangible goods,

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then we should also produce more tangible goods.

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Because at least, there is, some sort of,

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lower bond in terms of, in terms of complementarity.

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And, so basically it means if GDP, so,

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so-called G-D-P-G-D-P measures the total output,

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which includes also tangible and intangible goods.

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Then, increase in GDP implies not only increasing,

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non-tangible part, but also tangible part.

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So anyway, in the long run, if we keep growing in terms

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of GDP, that means we should also keep increasing

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non-tangible good production.

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And also it applies

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because of this relationship between

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tangible goods and resources.

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It also implies that we should also keep using more

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resources, material resources

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to produce more tangible goods.

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So that's, that's, first kind of, conclusion I get.

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But this, the next conclusion is that,

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it comes from that, part, that waste part of that,

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generated in production.

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So, because we cannot really,

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use all resources available without any waste, so they will,

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will waste in terms, in, the process of production.

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So, but here we are assuming that,

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all waste doesn't, I mean, waste is not, I mean,

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all waste doesn't mean it's pollution.

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I mean, only part of waste, generated can be,

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or can contribute to pollution.

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And, because a part of waste might be, cleaned up,

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might be abated,

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because we, I mean,

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especially now probably we are trying to, kind

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of adopt clean, so technology so called.

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But anyway, the idea here is that,

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it's not really possible, at least, I don't see how

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how it can be done, that

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all waste will be cleaned up, so there will be some,

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part of waste that will contribute to pollution, right?

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So that's the first kind of step of, our, my logic.

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So then what happens is this.

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So if we keep growing, keep producing, more output,

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that means we keep, in, using, more

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and more material resources than part

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of resource, waste that we know.

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So the, the waste will also increasing, and

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because we generate more waste,

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and part of that waste will also contribute to pollution.

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So at the end, pollution also should increase

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unless, we kind of, very serious about, I think,

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the promoting these green technologies and

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or somehow implementing better, abatement of the,

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pollution that we generate in the process

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of, manufacturing.

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And, so,

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but again, that's the, different question in this case.

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Anyway, so I can summarize this paper by,

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I think saying this, I think,

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making the statements first, in, this by,

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I think incorporating this physical constraints into the,

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production process, I, I was able to formalize that.

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Uh, there's actually a constraint on,

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the production process

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and which implies that there is,

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so-called inad documentation doesn't really hold.

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That means we cannot really produce more output

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by using very small input material input.

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So if we want to produce more material output, that is,

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we have to, also use more, resource inputs.

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And the implication of this is that, if we keep,

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I mean growing, then that means we have to always,

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most likely, also generate pollution

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or some sort of, waste,

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and that might be damaging to the environment.

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And so the idea here is

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that future research should focus on, this sort

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of optimal growth path that,

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takes into account not only, production side,

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but also that products always takes, takes,

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resources, material sources as inputs,

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and there's always byproduct as pollution.

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So, so, by I think getting this, better,

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I guess, insights into this sort of, complicated,

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process, then maybe we can, I guess,

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I don't know, maybe understand better how

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to build sustainable growth in the future.

Debate on Sustainable Economic Growth and Resources

00:00:00 - The context is based on, this debate about, the possibility of, long-term economic growth collapsing if, non-renewable resources will be depleted in the future. In early, I think in 1931, totally, wrote about this, but then it was forgotten. And later in 1972, this question was revisited by middles and others. So they wrote a book, and this book started kind of a debate. So that, debate then I think attracted the attention of,
00:00:33 - and, does group hill, solo sticklet. They wrote a few papers, addressing this problem. And, they kind of showed that the sustainable economic growth is possible as soon as, for example, this democratization kind of occurs. And democratization, basically means that producing more goods while using less, material inputs and, to happen. I mean, for, for it to happen, we need
00:01:07 - And, that's, that's, important. turns out, property of production. And in, economics, we use production functions that's sort of, mathematical constructs. And those functions, they should have this in other conditions, to, to be hold, to hold. I mean, and, so I can go on further. Yeah. Yeah. So, so the,
00:01:36 - that if it is, possible or not. But later, there was some criticism about this. does group, heals all those stickless framework because, for example, daily in 19, 97, he wrote an ecological economic, journal that, this sounds like the evidence doesn't support this, solo framework assumption. And, later others, for example, Hering in 2006,
00:02:14 - the, I mean the, slowdown of material intensity in the production is not happening. like if you follow this, d the, the, heel, solo framework, I think it should be happening, but it's not happening. And, later also, other authors, highlighted that, for example, democratization is possible only if economic growth kind of,
00:02:44 - And, so, but some other people, kind of came up with this sort of evidence showing that if you look at the GDP data, then seems like, the share of, saving, I mean, the service are increasing and compared to the manufacturing part. But then, there also some other people like BFAs and Cal, they, published a few papers where they kind of show that using the size of GDP is not really, kind

Challenges of Dematerialization in Economic Models

00:03:13 - the naturalization is happening because the GDP itself is not, directly, kind of linked to the physical aspects of production. And so, anyway, the, conclusion is that seems like dematerialization is not actually taking place in this world, and that basically means maybe that in other conditions, that assumed by, the does Gupta heal and stick solo framework may not be true. So, what we, what I did was that, I tried to,
00:03:47 - and what sort of implications we might have, if the condition doesn't hold. So, the in other condition itself was formulated by, Inad in, 1963. And, the intuition behind this, idea is very simple. Basically, it means that when, we reduce inputs into production, then, so-called marginal product of input tends to infinity.
00:04:19 - that input will be close to zero. And what is relevant in our case is that when inputs become small, scars, then can we still keep producing more, goods? I mean, that's the basic idea here. So in order to show that it's not possible, then, in this paper, you know, we introduced the sort of physical constraints, into this theory of production.
00:04:52 - of product function as in, this, heal, stickler solo framework. That means, usually in, economics, we assume production function takes on two inputs, capital and labor. But they also introduced a material resources as additional input. So I do the same, but in, in addition, what I do is I kind of introduce, also mass of matter.
00:05:23 - So yeah, I also introduce, a concept of, mass function. That's a function that kind of, if you check in the ma the matter, it tells you what is the mass of that matter. I mean, that's kind of the, abstraction. But, that's how I think. And also, I assume that, any tangible matter can be, measured and, it, it can be measured by its volume,
00:05:54 - we live in this, 3D world, dimension. So anything, we see or we, kind of, can, feel that should have volume, anything that usable for us should be, should have its volume. So, based on that, then, I make this, three assumptions first, that, and it comes from the physics of course, that, first

Fundamental Principles of Mass and Production

00:06:25 - of any matter is positive. I mean, if you can touch and feel something, and it should have po positive density. I mean, if it has mass, then it should be the positive density. That's first thing. Second thing is that densities are constant. I mean, it doesn't really matter if you have, for example, 10 liters of water or one liter of water density should be the same. That's the idea. I mean, also, probably, reasonable assumption. And, the other thing, the third assumption is
00:06:58 - and resource used to make, to tho those outputs, comparable. I mean, you cannot really make, out of iron something very light and not really, doesn't have any mass. So that's, that's the big basic idea. They can be different, but they're still in the same order of kind of, values. So it cannot be like billion times lighter. I mean, the output cannot be billion times lighter than the,
00:07:26 - So that's the basic idea. So, given this then, so, given this, then, I try to use also the law of conservation of mass, because that's the kind of physical, constraint comes from there. So the idea is very simple. So the idea is this. So if we have some resources and we use those resources to make some tangible outputs, that the mass of those initial resources should be contained
00:07:58 - and partly in the waste, that we kind of generate while producing that, tangible output. So then that means, the mass of any output, I mean, tangible output will be proportional to the massive, resources used. I mean, that's also kind of quite simple idea, but, we never used it in economics, even though it's just like a kind of a straightforward, probably logic in, physics. So then, using this, kind of relationship
00:08:32 - and massive resources, then, I, I am able to show that the marginal resource product is bounded. And it's because it turns out the, the marginal product of, output will be somehow related to the ratio of this densities of output and resources. And remember that the assumption was that they cannot be too different. Yeah. So they cannot be, like, their, ratio cannot be, infinity. So that means it's bounded. So that means there is some, upper bound, value,
00:09:06 - that, we cannot really produce more tangible output using very little, resource. Basic, basic idea is that. So then, we, we also use this, finding and show that, whenever we, produce more tangible output, that also implies that we have to use more, material inputs. So, because they're kind of related to each other, so turns out we can have some long run implications from

Assumptions on Tangible Goods and Economic Growth

00:09:40 - But to do, to make those, conclusions, we, I mean, need to make some, additional sort of, assumptions. And first one is the physical size bound. So what, what it, what does it mean? It means that, any tangible good that we consume should have some, meaningful physical size. Because for humans, we have some physical, sizes, right? So, we should have certain, houses of certain size clothes,
00:10:10 - They cannot be like, mini was too small, then it's not meaningful for us. So given this, we can always, show that, if any good that we, consume, I mean any tangible good as it's minimum size, then everything that we produce in terms of tangible goods should be at least greater than that, minimum size. Okay? So that's one, assumption here.
00:10:41 - for each, good, then it should happen for all goods together. So in aggregate, the physical size of, tangible goods cannot be smaller than, certain, kind of, minimum. The second, assumption is, complementarity because, we are talking about tangible goods only. but it's the same time we know that the GDP includes more than just tangible goods. We have a lot of services. So the here assumption is that, still
00:11:14 - So if we, let's say that there are two number of goods, there are tangible and number of goods that they're intangible. So then the ratio of this, numbers cannot be less than certain value. 'cause even if we increase the number of different service we consume, we still need to consume some number of tangible goods, basically, is that, so in other words, we cannot just consume, non-tangible goods, and we'll, can go on with that.
00:11:46 - because of this complementarity between tangible, non-tangible goods. That means whenever we produce more tangible goods, or let's say whenever we produce more non-tangible goods, then we should also produce more tangible goods. Because at least, there is, some sort of, lower bond in terms of, in terms of complementarity. And, so basically it means if GDP, so, so-called G-D-P-G-D-P measures the total output,
00:12:17 - Then, increase in GDP implies not only increasing, non-tangible part, but also tangible part. So anyway, in the long run, if we keep growing in terms of GDP, that means we should also keep increasing non-tangible good production. And also it applies because of this relationship between tangible goods and resources. It also implies that we should also keep using more resources, material resources to produce more tangible goods.

Production Waste and Environmental Impacts

00:12:50 - But this, the next conclusion is that, it comes from that, part, that waste part of that, generated in production. So, because we cannot really, use all resources available without any waste, so they will, will waste in terms, in, the process of production. So, but here we are assuming that, all waste doesn't, I mean, waste is not, I mean,
00:13:19 - I mean, only part of waste, generated can be, or can contribute to pollution. And, because a part of waste might be, cleaned up, might be abated, because we, I mean, especially now probably we are trying to, kind of adopt clean, so technology so called. But anyway, the idea here is that, it's not really possible, at least, I don't see how
00:13:51 - all waste will be cleaned up, so there will be some, part of waste that will contribute to pollution, right? So that's the first kind of step of, our, my logic. So then what happens is this. So if we keep growing, keep producing, more output, that means we keep, in, using, more and more material resources than part of resource, waste that we know. So the, the waste will also increasing, and
00:14:21 - and part of that waste will also contribute to pollution. So at the end, pollution also should increase unless, we kind of, very serious about, I think, the promoting these green technologies and or somehow implementing better, abatement of the, pollution that we generate in the process of, manufacturing. And, so, but again, that's the, different question in this case.
00:14:54 - I think saying this, I think, making the statements first, in, this by, I think incorporating this physical constraints into the, production process, I, I was able to formalize that. there's actually a constraint on, the production process and which implies that there is, so-called inad documentation doesn't really hold.
00:15:24 - by using very small input material input. So if we want to produce more material output, that is, we have to, also use more, resource inputs. And the implication of this is that, if we keep, I mean growing, then that means we have to always, most likely, also generate pollution or some sort of, waste, and that might be damaging to the environment.

Towards Sustainable Growth Path Research

00:15:56 - that future research should focus on, this sort of optimal growth path that, takes into account not only, production side, but also that products always takes, takes, resources, material sources as inputs, and there's always byproduct as pollution. So, so, by I think getting this, better, I guess, insights into this sort of, complicated, process, then maybe we can, I guess,
00:16:26 - to build sustainable growth in the future.

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