Final answer:
The correct statement is that if the pure expectations theory holds and inflation is expected to decline, the Treasury yield curve must be downward sloping. The pure expectations theory suggests long-term rates reflect expected future short-term rates, leading to a downward-sloping yield curve if inflation is expected to decrease.
Step-by-step explanation:
The question pertains to the expectations theory and how the yield curve for interest rates might be affected if inflation is expected to decline while the real risk-free rate, r*, remains constant. Given these conditions, the correct statement is that if the pure expectations theory holds, the Treasury yield curve must be downward sloping. This is because the expectations theory suggests that long-term interest rates reflect the expected future short-term rates. If inflation is expected to decline in the future, investors would anticipate lower short-term rates, hence, the long-term rates would also decline to reflect those expectations, resulting in a downward-sloping yield curve.
Maturity risk premium is unrelated to expectations about inflation and hence statement b is incorrect. Statement c is a misinterpretation, as the expectations theory can still hold with decreasing inflation. Similarly, corporate yield curves are influenced by factors other than just inflation expectations, such as default risk, so statement d does not exclusively depend on the pure expectations theory and the expected decline in inflation.