He assumed the Euler conditions without explaining how they arrived.
Once the Euler conditions are assumed, then it is game over, the real work of economics has disappeared and we end up with a variable simulation game. We can name the exponents all we want, we can pick out and measure teddy bears vs vacuum cleaners and get the same result because once the conditions are met they are met everywhere. Labor and capital become one of many different possibilities.
Solow needed to show that the labor,capital dichotomy was the shortest path to meeting the Euler conditions. That is, folks actually went around and measured themselves against the machines and thus labor/capital is the best simulation choice.
In reality, if economics has such a thing, we meet the Euler conditions by avoiding long lines which implies meeting the Nash conditions. . From there it was simple enough to find the secret of queue management, and the game is over, sandbox wins. What people are secretly think becomes immaterial, all their economic motives can be measured by measuring line length when Nash conditions are met.
Congestion management is the basic principle of the universe.
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