Economics core problems

Problem 1 – Market resonance cycles#

A market oscillates with triadic frequency

$$ ω = \frac{T_f}{D_3}. $$

If $$D_3$$ increases due to regulatory friction, how must $$T_f$$ change to keep $$ω$$ constant?

Problem 2 – Utility resonance#

Utility under a resonance-based model is

$$ U = X \ln(1 + τ_r), $$

where $$X = F_3 T_f$$.

If $$τ_r$$ increases by 25%, how does $$U$$ change?

Problem 3 – Inflation drift#

Inflation drift is modeled as

$$ I = ΛΘ D_9. $$

If $$Λ$$ decreases by 10% but $$D_9$$ increases by 5%, what is the net effect on $$I$$?