Adam Smith

But what if the deer is more nutritious than the beever?

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No one said anything about nutrition. Read the last sentence of what you posted again

Is it really the idle that affect the growth of an economy or is it unprofitable investments and other factors?

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He's saying that the quantity of labor is a good measure of worth, but what about the properties of the product/service? They don't have to be proportional to the degree of labor

The cost for the hunter is not necessarily what he will be paid, but if the cost is greater then what he can sell the ware for then less hunters will collect this ware until the price has risen to that level in which the cost is no higher than the selling price. Guided by the invisible hand.

>Guided by the invisible hand.
Guided by supply and demand rather... But I think I get your explanation cause it assumes a balance has been reached among rational participants

The invisible hand is what allows supply and demand to reach an equilibrium, the term was coined by Adam Smith.

In this example if this was the case they would only hunt deer(you get more for less) until it became harder to hunt than a beaver. But the problem with this is people want variety. So even in your example it may be worth giving 2 deer for a beaver.

>what if the deer is more nutritious than the beever?
The deer would be more nutritious than the beever. The costs of production would still be different. When tastes were more fixed and economies weren't as dynamic things were more static. Smith is thinking very statically.

I don't think you "get" what he's getting at:
en.wikipedia.org/wiki/Productive_and_unproductive_labour

You're introducing new assumptions. What if tastes are fixed?

Yeah but my understanding of the invisible hand is that it's just a metaphor for conveying the idea that self-interest can result in group interest in a free market. The free market allows reaching a supply/demand equilibrium