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In economics we measure living standards by the amounts of goods and services people can consume. Increasing labor productivity allows us to produce more goods and services and thus also consume more goods and services, hence it improves the living standards. For example consider classic Cobb-Douglas production function: $$Y = K^{\alpha} (AL)^{1-\alpha}$$...

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Your question is ultimately one about information flow in networks under conditions of imperfect and incomplete information. I like your distinction between "easy" and "hard" to calculate - it's a good rubric for problem classification. I believe that work being done on complexity theory and information flows can help shed some light on how to think about ...

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You are most likely looking for labor or wage share defined as the ratio of labor costs to nominal GDP. It basically expresses how much share of nominal GDP gets captured by labor. You can find the data for the labor share in the US here, under that bit of text (for some reason I could not find direct link to pure dataset). The data are from the US bureau ...

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