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Sure. If I'm understanding your question, you want to know how these variables are included in the assumptions of fixed ratios, right?

Economic output (GDP) is a function of factors of production, or inputs, that create economic value, as well as a residual factor called "total factor productivity", which measures how effectively the other inputs are used to generate output. The level of any input employed in an economy is dictated by its productivity, which determines its contribution to output.

So to add some structure to this description, we can look at a generic model of the economy (you can use any of many forms, as applicable).

Y = A* f{K, L, N, I, etc.}, where

Y = GDP
A = Total factor productivity
F = Generic production function
K = Capital stock
L = Labour stock (Which can be a vector comprising different levels of skilled human capital, Li = [L1, L2, ... , Ln], s.t. (l1 >= l2 >= ... >= ln)
N = Natural resources
I = Institutions, etc.

The fixed ratio of Li assumes an economy in general equilibrium. K, N, and I must then exist in fixed proportions to Li, with A constant, to maintain a uniform labour productivity for all Li across sectors, regions, and time.

Not exactly. To clarify, I understand that you may disagree with the video which aeh posted. I'm trying to understand your basis for introducing the list of factors you mentioned, as a means of discrediting the author of the video (and/or discrediting the list of sources cited by the author), as "baseless". How are the factors you mentioned implied/assumed by the author and/or his cited sources?

I do not see that you've related this to ratio of post-secondary degrees.
You are discussing productivity, which is a different topic.

I refer you to Li, the elements of which were defined in fixed proportions by the speaker in the video. I left their definitions deliberately general to be defined in any way desired. You could easily say l1 = 1, l2 = 2, l3 = 7 in a unit level economy.

The point being, nobody should assume fixed labour proportions in making future decisions because productivity isn't static, particularly not as a universal constant.

Economics is the study of the allocation of scarce resources, one of which is labour. I am using a standard model from basic economic theory to disprove the author's underlying assumptions about how labour looks in equilibrium, particularly the idea that post-secondary credentialing will exist in fixed ratios across industries, regions, and time. If we are to believe he is advocating educational programming be tailored to his prescribed ratio, then students will be trained in a way that is inappropriate to the opportunities that exist for them upon completion of their studies.

I hope this answers your question. If not, I'd be happy to refer you to some resources in PM that might explain the underlying models in more detail. I'd rather not write a textbook on the thread, as that is tangential to its purpose.

Not seeing applicability to the post-secondary degrees, sorry.

What would you offer as an alternative foundation for advice in making future decisions about colleges/degrees?

Li is a vector of factor endowments of different types of human capital; a head count, if you will, of the different levels of employees with each type of credential.

My recommendation? Assume general equilibrium is unique to the region, industry, and time in which economic activity is generated. Let labour be assigned as much capital as it needs as merited by its marginal productivity (i.e. let that level fluctuate according to demand) and let enrollment levels in post-secondary programs be as market-linked as possible, with intervention only when there is a strong public policy argument.

Sorry, I get jargony quickly and forget my audience sometimes!

Yes, however there is not a scarcity of labor... this is the raison d'être for the video. Helping the new generation of students begin planning now to increase the odds that they will not be unemployed/underemployed or invest time and money in "any" degree which they may learn after-the-fact is not applicable to their strengths and/or to positions available in the job market.

Mathematical models change over time, and may not be a good "fit" for every situation. I have questioned whether it is a good "fit" here.
Not that post-secondary credentialing will exist in fixed ratios (as though the production of degrees is being limited/controlled), but that the job market calls for skills in a ratio of 1:2:7. Regions were not discussed, and the time span discussed was 80 years.

If we could see that the model was a good "fit" for the video, the model would be on-topic.
The 1:2:7 ratio (whose source he cited) may not be correct, but the model you've introduced does not seem to prove it false.

I do not believe that he has advocated for educational programming to be tailored to a ratio (ie: limit/control the number of each type of degree which can be conferred), rather he has suggested what course of action consumers in a free market may most benefit from personally. He has clearly advocated for empowering consumers with information so that their enrollment choices in post-secondary programs are as market-linked as possible. Some may say you agree, at least in part, with his recommendations.

Indigo, several of those are reasonable questions. Short of turning this thread into a second year macroeconomics lecture, which I'm sure won't earn me any friends (they don't call us dismal scientists for nothing ), I'm happy to point you in the direction of this book: it discusses the broad tools required to answer them at a high level. I highly recommend it; it's succinct and well written (I have a copy on my shelf).

http://www.amazon.ca/Macroeconomic-Theory-A-Short-Course/dp/0765611422

For an empirical validation of my first post and initial explanation to you, I'd recommend searching the Federal Reserve site for research on labour market dynamics. They'll have current numbers published across industries with forward-looking estimates and their rationale. You don't have to trust any models to see that different industries and professions have different productivities, requiring a different labour mix, counter to the opinions offered in the linked video.

The video mentioned industries, not professions. Industries are different than professions. Industries contain a large cross-section of professions, a broad array of qualifications and post-secondary education.

Some may say there is continuous scope creep with you introducing regions, professions, and other items which were not a part the video, rather than discussing what was actually said in the video.