Term and liquidity premium on the yield curve

The two problem are caused simply by the fixed demand for long term borrowing, generally from government. The yield curve runs out of X axis.

It is back to finite number lines and the fixed dimensionality of Brownian motion.  In the case of the USA we have a fixed and large requirement to roll over long term bonds, generally 2 to 10 years, and the X axis does not go beyond 30 years in our system. The XY graph runs out of terms over which it can fit a rate of change in yields for each of some finite number of terms. So at some point, terms are dropped and the curve must be steep. The rise in yields, its delta, has to be equally dense to notches on the X axis for each term. It the science of yardsticks again, using the yard stick with equal precision across all the motions.

A simple view:

Bankers and the aggregate agents are performing the same problem, mainly trying to get the yield curve to proportionally fit on an XY graph with the rate of changes matching the density of the grid equally everywhere.