📈 Economics — TFT_3Pack Example Suite

Problem 1 — Market Resonance Cycles

ω = T_f / D₃

If \( D₃ \) increases, how must \( T_f \) change to keep \( ω \) constant?

Problem 2 — Utility Resonance

U = X ln(1 + τ_r)

If \( τ_r \) increases by 25%, how does utility change?

Problem 3 — Inflation Drift

I = ΛΘ D₉

If Λ decreases 10% and D₉ increases 5%, what is the net effect on inflation?

Solution 1 — Market Cycles

\( T_f' = T_f (D₃'/D₃) \). Increase T_f proportionally to D₃.

Solution 2 — Utility

Utility increases logarithmically: \( U' = X ln(1 + 1.25τ_r) \).

Solution 3 — Inflation

\( I' = 0.945I \). Inflation decreases by 5.5%.

Problem 4 — Resonant Supply-Demand Equilibrium

S(p) = D₃ τ_r p
D(p) = X / (p + ΛΘ)
        

Find equilibrium price and describe how τ_r affects it.

Problem 5 — Capital Accumulation

K(t) = K₀ e^{D₆ τ_r t}

Describe how reducing τ_r affects long-run growth.

Problem 6 — Consumption Smoothing

C_s = T_f / (1 + e^{-D₃ τ_r})

Sketch C_s(τ_r) and describe its behavior.

Problem 7 — Exchange Rate Resonance

E = X √τ_r - D₉

Describe how quadrupling τ_r affects E.

Problem 8 — Government Spending Multiplier

M = (ΛΘ + T_f) / (D₃ + τ_r)

Analyze the qualitative effect of changes in ΛΘ, T_f, and τ_r.

Diagram 1 — Market Frequency

T_f ÷ D₃ → ω
        

Diagram 2 — Utility Resonance

τ_r → ln(1 + τ_r) × X → U
        

Diagram 3 — Inflation Drift

Λ + Θ → ΛΘ × D₉ → I