The fixed ratio is baseless. He's implicitly assuming two things, both incorrect:
1. A fixed capital-labour ratio in all sectors and professions over time.
2. Constant total factor productivity (a proxy for technical change and the efficiency of use of factors of production-- capital, labour, natural resources, institutions, etc.) universally across industries and geographies.
As a counter example on the first, do we believe that the capital intensity of the development of biologics by doctoral biochemists requires the same capital intensity as the work of university professors of literature with doctorates, always and everywhere?
On the latter, should we believe that productivity changes in the automotive industry in New Dehli are the same as in the southern US, and eternally so?
Would you explain how capital, natural resources, institutions, etc are implied/assumed in the 1:2:7 ratio of employment by type post-secondary degree?
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.
