Pure Expectations Yield Curve - CFAI SAMPLE

Can someone please explain why if investors expect stable rates of inflation in the future, the pure expectations theory suggests that the yield curve now will be flat. Surely the yield will take whatever shape the expected future short-term rates, except will be a bit less because of the inflation premium, why does it have to be flat?

Because investors are buying all segments of the curve (not talking about segmmentation theory) equally, since they don’t expect rates to take one direction or another. So, LT bonds are not bought or sold any differently than ST bonds. That’s my thinking.

Well surely in that case it would be downward sloping because of the inflation premium?

there is no unusual inflation, so there is no change in interest rates. Curve remains flat.

Aren’t interest rates pretty much determined by inflation and anticipated inflation? If inflation is expected to be high, people will consume more now and demand for borrowed funds will be higher than supply, thus pushing up rates. The opposite is true for lower expected inflation. So in summary, the way i see it, inflation expectations determine the supply and demand of financial capital which in turn determines the interest rates.