SD Example 3

Oscillating Business Cycles

Capital stock drives production; production creates profits; profits drive investment; delays in capital accumulation cause oscillation.

MULTI-LOOP SYSTEM Capital Stock $K investment depreciation Prod production = K × productivity Prof profit = Prod - costs Inv investment = f(profit) reinvestment R1 B1 Capital Lag Time to build: 3 years Dynamic Behavior: Oscillating Cycles Phase 1 (Expansion): High profit → high investment → capital increases Phase 2 (Boom): Capital peaks → production peaks → but building lag ends, investment becomes excessive Phase 3 (Contraction): Excess capital → higher depreciation → profit drops → investment cuts (overcorrects) Phase 4 (Recession): Capital shrinks → production falls → profit bottoms → cycle restarts Period: Typically 3–7 years (equal to capital lag + adjustment delay) Amplitude: Determined by: investment responsiveness, capital lag, depreciation rate

STOCK

Capital Stock

Accumulation of productive assets. Increased by investment, decreased by depreciation. Time constant: 10–30 years (typical asset life).

FEEDBACK

Two Competing Loops

  • R1 (Reinforcing): Profit ↑ → Investment ↑ → Capital ↑ → Production ↑ → Profit ↑
  • B1 (Balancing): Capital ↑ → Depreciation ↑ → Profit ↓ → Investment ↓

KEY PARAMETER

Capital Lag

Time to build capital (3 years typical). Creates a delay between investment decision and capital arrival. Causes oscillations.

PATTERN

Limit Cycle

The system doesn't converge to equilibrium. Instead, it oscillates between boom and bust indefinitely. This explains business cycles.