How does the Solow growth model work in an actual economy

Agents actually search for the indifference curve on labor.

The are looking for the point here one additional hire has little effect on company outcome. The result  is to make the labor input queue look like it came from gaussian arrivals. They issue hiring orders based on the observed output gap. Makes the dynamics look Euler.  Thus they can reconstruct the process as a Euler outcome, use exponential and simplify the process. That is the whole idea, keep linear so company accounting is accurate, the hologram effect.

But the labor queue becomes a structured queue and the real economy is producing the best linear approximation to the Euler conditions. At any given point in the process, the economic model will look like it is in equilibrated with a large error bound.  Each set of trials the agents cause the error bound to reduce. They are creating structured queues until the risk is sufficient to some necessary error of the market.

Sandbox theory. It is all about reducing round off error from a fractional approximation of low order. I have a short cut for real businesses. You want you open job designations defined well enough so you can get a labor pool about one and half three times larger then open jobs. This is a self sampled system, both labor and manager create a labor flow dynamic based on.   Management always wants one or two potential hires in the hopper, labor wants zero or one new company in the hopper. On the average this ratio minimizes volatility as it operates at the Nyquist rate.